Chapter 12- Lesson 1:

Chapter 12- Lesson 2:

Chapter 12- Lesson 3:

Guided Practice – The Pythagorean Theorem – Page No. 378

Question 1.
Find the length of the missing side of the triangle

a2 + b2 = c2 → 242 + ? = c2 → ? = c2
The length of the hypotenuse is _____ feet.
_____ feet

Answer: The length of the hypotenuse is 26 feet.

Explanation: According to Pythagorean Theorem, we shall consider values of a = 24ft, b = 10ft.
Therefore c = √(a2 +b2)
c = √(242 + 102)
= √(576 + 100)
= √676 = 26ft

Question 2.
Mr. Woo wants to ship a fishing rod that is 42 inches long to his son. He has a box with the dimensions shown.

a. Find the square of the length of the diagonal across the bottom of the box.
________ inches

Explanation: Here we consider the length of the diagonal across the bottom of the box as d.
Therefore, according to Pythagorean Theorem
W2 + l2 = d2
402 + 102 = d2
1600 + 100 = d2
1700 = d2

Question 2.
b. Find the length from a bottom corner to the opposite top corner to the nearest tenth. Will the fishing rod fit?
________ inches

Explanation: We denote by r, the length from the bottom corner to the opposite top corner. We use our Pythagorean formula to find r.
h2 + s2 = r2
102 + 1700 = r2
100 + 1700 = r2
1800 = r2,    r = √1800 => 42.42 inches

ESSENTIAL QUESTION CHECK-IN

12.1 Independent Practice – The Pythagorean Theorem – Page No. 379

Find the length of the missing side of each triangle. Round your answers to the nearest tenth.

Question 4.

________ cm

Explanation: According to Pythagorean theorem we consider values of a = 4cm, b = 8cm.
c2 = a2 + b2
= 42 + 82
= 16 + 64
c2= 80, c= √80 => 8.944
After rounding to nearest tenth value c= 8.9cm

Question 5.

________ in.

Explanation: According to Pythagorean theorem we consider values of b = 8in, c= 14in
c2 = a2 + b2
142 = a2 + 82
196 = a2 + 64
a2 = 196 – 64
a  = √132 => 11.4891
a = 11.5 in

Question 6.
The diagonal of a rectangular big-screen TV screen measures 152 cm. The length measures 132 cm. What is the height of the screen?
________ cm

Explanation: Let’s consider the diagonal of the TV screen as C = 152cm, length as A = 132 cm, and height of the screen as B.

As C2 = A2 + B2
1522 = 1322 + B2
23,104 = 17,424 + B2
B2 = 23,104 – 17,424
B = √5680 => 75.365
So the height of the screen B = 75.4cm

Question 7.
Dylan has a square piece of metal that measures 10 inches on each side. He cuts the metal along the diagonal, forming two right triangles. What is the length of the hypotenuse of each right triangle to the nearest tenth of an inch?
________ in.

Explanation:

Using the Pythagorean Theorem, we have:
a2 + b2 = c2
102 + 102 = c2
100 + 100 = c2
200 = c2
We are told to round the length of the hypotenuse of each right triangle to the nearest tenth of an inch, therefore: c = 14.1in

Question 8.
Represent Real-World Problems A painter has a 24-foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. To the nearest tenth of a foot, how high can the ladder safely reach?
________ ft

Explanation: Consider the below diagram. Length of the ladder C = 24ft, placed at a distance from the base B = 8ft, let the safest height be A.

By using Pythagorean Theorem:
C2 = A2 + B2
242 = A2 + 82
576 = A2 + 64
A2 = 576 – 64 => 512
A = √512 => 22.627
After rounding to nearest tenth, value of A = 22.6ft

Question 9.
What is the longest flagpole (in whole feet) that could be shipped in a box that measures 2 ft by 2 ft by 12 ft?

________ ft

Answer: The longest flagpole (in whole feet) that could be shipped in this box is 12 feet.

Explanation: From the above diagram we have to find the value of r, which gives us the length longest flagpole that could be shipped in the box. Where width w = 2ft, height h = 2ft and length l = 12ft.

First find s, the length of the diagonal across the bottom of the box.
w2 + l2 = s2
22 + 122 = s2
4 + 144 = s2
148 = s2
We use our expression for s to find r, since triangle with sides s, r, and h also form a right-angle triangle.
h2 + s2 = r2
22 + 148 = r2
4 + 148 = r2
152 = r2
r = 12.33ft.

Question 10.
Sports American football fields measure 100 yards long between the end zones, and are 53 $$\frac{1}{3}$$ yards wide. Is the length of the diagonal across this field more or less than 120 yards? Explain.
____________

Answer: The diagonal across this field is less than 120 yards.

Explanation: From the above details we will get a diagram as shown below.

We are given l = 100 and w = 53  =  . If we denote with d the diagonal of the field, using the Pythagorean Theorem, we have:
l2 + w2 = d2
1002 + (160/3)2 = d2
10000 + (25600/9) = d2
9*10000 + 9*(25600/9) = 9* d2
90000 + 25600 = 9 d2
(115600/9) = d2
(340/9) = d2
d = 113.3
Hence the diagonal across this field is less than 120 yards.

Question 11.
Justify Reasoning A tree struck by lightning broke at a point 12 ft above the ground as shown. What was the height of the tree to the nearest tenth of a foot? Explain your reasoning.

________ ft

Answer: The total height of the tree was 52.8ft

Explanation:

By using the Pythagorean Theorem
a2 + b= c2
122 + 392 = c2
144 + 1521 = c2
1665 = c2
We are told to round the length of the hypotenuse to the nearest tenth of a foot, therefore: c = 40.8ft.
Therefore, the total height of the tree was:
height = a+c
height = 12 +40.8
height = 52.8 feet

FOCUS ON HIGHER ORDER THINKING – The Pythagorean Theorem – Page No. 380

Question 12.
Multistep Main Street and Washington Avenue meet at a right angle. A large park begins at this corner. Joe’s school lies at the opposite corner of the park. Usually, Joe walks 1.2 miles along Main Street and then 0.9 miles up Washington Avenue to get to school. Today he walked in a straight path across the park and returned home along the same path. What is the difference in distance between the two round trips? Explain.
________ mi

Answer: Joe walks 1.2 miles less if he follows the straight path across the park.

Explanation: Using the Pythagorean Theorem, we find the distance from his home to school following the straight path across the park:
a2 + b= c2
1.22 + 0.92 = c2
1.44 + 0.81 = c2
2.25 = c2
1.5 = c
Therefore, the distance of Joe’s round trip following the path across the park is 3 miles (dhome-school + dschool-home = 1.5 + 1.5). Usually, when he walks along Main Street and Washington Avenue, the distance of his round trip is 4.2 miles (dhome-school + dschool-home = (1.2 + 0.9) + (0.9+1.2)). As we can see, Joe walks 1.2 miles less if he follows the straight path across the park.

Question 14.
Persevere in Problem-Solving A square hamburger is centered on a circular bun. Both the bun and the burger have an area of 16 square inches.

a. How far, to the nearest hundredth of an inch, does each corner of the burger stick out from the bun? Explain.
________ in

Answer: Each corner of the burger sticks out 0.57 inches from the bun.

Explanation: Frist, we need to find the radius r of the circular bun. We know that its area A is 16 square inches, therefore:

A = πr2
16 = 3.14*r2
r2 = (16/3.14)
r = 2.26

Then, we need to find the sides of the square hamburger. We know that its area A is 16 square inches, therefore:
A = s2
16 = s2
s = 4
Using the Pythagorean Theorem, we have to find the diagonal d of the square hamburger:
s2 + s2 = d2
42 + 42 = d2
16 + 16 = d2
32 = d2
d = 5.66
To find how far each corner of the burger sticks out from the bun, we denote this length by a and we get:
a = (d/2) – r => (5.66/2) – 2.26
a = 0.57.
Therefore, Each corner of the burger sticks out 0.57 inches from the bun.

Question 14.
b. How far does each bun stick out from the center of each side of the burger?
________ in

Answer: Each bun sticks out 0.26 inches from the center of each side of the burger.

Explanation:

We found that r = 2.26 and s = 4. To find how far does each bun stick out from the center of each side of the burger, we denote this length by b and we get:
b = r – (s/2) = 2.26 – (4/2)
b = 0.26 inches.

Question 14.
c. Are the distances in part a and part b equal? If not, which sticks out more, the burger or the bun? Explain.

Answer: The distances a and b are not equal. From the calculations, we found that the burger sticks out more than the bun.

Guided Practice – Converse of the Pythagorean Theorem – Page No. 384

Question 1.
Lashandra used grid paper to construct the triangle shown.

a. What are the lengths of the sides of Lashandra’s triangle?
_______ units, _______ units, _______ units,

Answer: The length of Lashandra’s triangle is 8 units, 6 units, 10 units.

Question 1.
b. Use the converse of the Pythagorean Theorem to determine whether the triangle is a right triangle.

The triangle that Lashandra constructed is/is not a right triangle.
_______ a right triangle

Answer: Lashandra’s triangle is right angled triangle as it satisfied the Pythagorean theorem

Explanation:
Verifying with Pythagorean formula a2 + b= c2
82 + 62 = 102
64 + 36 =100
100 = 100.

Question 2.
A triangle has side lengths 9 cm, 12 cm, and 16 cm. Tell whether the triangle is a right triangle.
Let a = _____, b = _____, and c = ______.

By the converse of the Pythagorean Theorem, the triangle is/is not a right triangle.
_______ a right triangle

Answer: The given triangle is not a right-angled triangle

Explanation: Verifying with Pythagorean formula a2 + b= c2
92 + 122 = 162
81 + 144 = 256
225 ≠ 256.
Hence given dimensions are not from the right-angled triangle.

ESSENTIAL QUESTION CHECK-IN

Question 4.
How can you use the converse of the Pythagorean Theorem to tell if a triangle is a right triangle?
Knowing the side lengths, we substitute them in the formula a2 + b= c2, where c contains the biggest value.
If the equation holds true, then the given triangle is a right triangle. Otherwise, it is not a right triangle.

12.2 Independent Practice – Converse of the Pythagorean Theorem – Page No. 385

Tell whether each triangle with the given side lengths is a right triangle.

Question 5.
11 cm, 60 cm, 61 cm
______________

Answer: Since 112 + 602 = 612, the triangle is a right-angled triangle.

Explanation: Let a = 11, b = 60 and c= 61
Using the converse of the Pythagorean Theorem a2 + b= c2
112 + 602 = 612
121 + 3600 = 3721
3721 = 3721.
Since 112 + 602 = 612, the triangle is a right-angled triangle.

Question 8.
15 m, 36 m, 39 m
______________

Answer: Since 152 + 362 = 392, the triangle is a right-angled triangle.

Explanation: Let a = 15, b = 36 and c= 39
Using the converse of the Pythagorean Theorem a2 + b= c2
152 + 362 = 392
225 + 1296 = 1521
1521 = 1521.
Since 152 + 362 = 392, the triangle is a right-angled triangle.

Question 9.
20 mm, 30 mm, 40 mm
______________

Answer: Since 202 + 302 ≠ 402, the triangle is not a right-angled triangle.

Explanation: Let a = 20, b = 30 and c= 40
Using the converse of the Pythagorean Theorem a2 + b= c2
202 + 302 = 402
400 + 900 = 1600
1300 ≠ 1600.
Since 202 + 302 ≠ 402, the triangle is not a right-angled triangle.

Question 10.
20 cm, 48 cm, 52 cm
______________

Answer: Since 202 + 482 = 522, the triangle is a right-angled triangle.

Explanation: Let a = 20, b = 48 and c= 52
Using the converse of the Pythagorean Theorem a2 + b= c2
202 + 482 = 522
400 + 2304 = 2704
2704 = 2704.
Since 202 + 482 = 522, the triangle is a right-angled triangle.

Question 13.
35 in., 45 in., 55 in.
______________

Answer: Since 352 + 452 ≠ 552, the triangle is not a right-angled triangle.

Explanation: Let a = 35, b = 45 and c= 55
Using the converse of the Pythagorean Theorem a2 + b= c2
352 + 452 = 552
1225 + 2025 = 3025
3250 ≠ 3025.
Since 352 + 452 ≠ 552, the triangle is not a right-angled triangle.

Question 14.
25 cm, 14 cm, 23 cm
______________

Answer: Since  142 + 232 ≠ 252, the triangle is not a right-angled triangle.

Explanation: Let a = 14, b = 23 and c= 25 (longest side)
Using the converse of the Pythagorean Theorem a2 + b= c2
142 + 232 = 252
196 + 529 = 625
725 ≠ 625.
Since  142 + 232 ≠252, the triangle is not a right-angled triangle.

Question 15.
The emblem on a college banner consists of the face of a tiger inside a triangle. The lengths of the sides of the triangle are 13 cm, 14 cm, and 15 cm. Is the triangle a right triangle? Explain.
________

Answer: Since  132 + 142 ≠ 152, the triangle is not a right-angled triangle.

Explanation: Let a = 13, b = 14 and c= 15
Using the converse of the Pythagorean Theorem a2 + b= c2
132 + 142 = 152
169 + 196 = 225
365 ≠ 225.
Since  132 + 142 ≠ 152, the triangle is not a right-angled triangle.

Question 18.
History In ancient Egypt, surveyors made right angles by stretching a rope with evenly spaced knots as shown. Explain why the rope forms a right angle.

Answer: The rope has formed a right-angled triangle because the length of its sides follows Pythagorean Theorem.

Explanation: The knots are evenly placed at equal distances
The lengths in terms of knots are a=4 knots, b = 3knots, c = 5 knots
Therefore a2 + b= c2
42 + 3= 52
16+9 = 25
25 = 25.
Hence rope has formed a right-angled triangle because the length of its sides follows Pythagorean Theorem.

Converse of the Pythagorean Theorem – Page No. 386

Question 19.
Justify Reasoning Yoshi has two identical triangular boards as shown. Can he use these two boards to form a rectangle? Explain.

Answer: Since it was proved that both can form a right-angled triangle, we can form a rectangle by joining them.

Explanation: Given both triangles are identical, if both are right-angled triangles then we can surely join to form a rectangle.
Let’s consider a = 0.75, b= 1 and c=1.25.
By using converse Pythagorean Theorem a2 + b= c2
0.752 + 12 = 1.252
0.5625 + 1 = 1.5625
1.5625 = 1.5625.
Since it was proved that both can form a right-angled triangles, we can form a rectangle by joining them.

FOCUS ON HIGHER ORDER THINKING

Question 21.
Make a Conjecture Diondre says that he can take any right triangle and make a new right triangle just by doubling the side lengths. Is Diondre’s conjecture true? Test his conjecture using three different right triangles.
_______

Answer: Yes, Diondre’s conjecture is true. By doubling the sides of a right triangle would create a new right triangle.

Explanation: Given a right triangle, the Pythagorean Theorem holds. Therefore, a2 + b= c2
If we double the side lengths of that triangle, we get:
(2a)2 + (2b)= (2c)2
4a2 + 4b2 = 4c2
4(a2 + b2) = 4c2
a2 + b= c2
As we can see doubling the sides of a right triangle would create a new right triangle.We can test that by using three different right triangles.

The triangle with sides a = 6, b = 8 and c = 10 is a right triangle. We double its sides and check if the new triangle is a right triangle. After doubling value of a = 12, b = 16 and c = 20.
122 + 162 = 202
144 + 256 = 400
400 = 400
Hence proved!
Since 122 + 162 = 202, the new triangle is a right triangle by the converse of the Pythagorean Theorem.

The triangle with sides a = 3, b = 4 and c = 5 is a right triangle. We double its sides and check if the new triangle is a right triangle. After doubling value of a = 6, b = 8 and c = 10.
62 + 82 = 102
36 + 64 = 100
100 = 100
Hence proved!
Since 62 + 82 = 102, the new triangle is a right triangle by the converse of the Pythagorean Theorem.

The triangle with sides a = 12, b = 16 and c = 20 is a right triangle. We double its sides and check if the new triangle is a right triangle. After doubling value of a = 24, b = 32 and c = 40.
242 + 322 = 402
576 + 1024 = 1600
1600 = 1600
Hence proved!
Since 242 + 322 = 402, the new triangle is a right triangle by the converse of the Pythagorean Theorem.

Question 22.
Draw Conclusions A diagonal of a parallelogram measures 37 inches. The sides measure 35 inches and 1 foot. Is the parallelogram a rectangle? Explain your reasoning.
_______

Answer: Since 122 + 352 = 372, the triangle is right triangle. Therefore, the given parallelogram is a rectangle.

Explanation: A rectangle is a parallelogram where the interior angles are right angles. To prove if the given parallelogram is a rectangle, we need to prove that the triangle formed by the diagonal of the parallelogram and two sides of it, is a right triangle. Converting all the values into inches, we have a = 12, b = 35 and c = 37. Using the converse of the Pythagorean Theorem, we have:
a2 + b= c2
122 + 352 = 372
144 + 1225 = 1369
1369 = 1369.
Since 122 + 352 = 372, the triangle is right triangle. Therefore, the given parallelogram is a rectangle.

Question 23.
Represent Real-World Problems A soccer coach is marking the lines for a soccer field on a large recreation field. The dimensions of the field are to be 90 yards by 48 yards. Describe a procedure she could use to confirm that the sides of the field meet at right angles.

Answer: To confirm that the sides of the field meet at right angles, she could measure the diagonal of the field and use the converse of the Pythagorean Theorem. If a2 + b= c2 (where a = 90, b = 48, and c is the length of the diagonal), then the triangle is a right triangle. This method can be used for every corner to decide if they form right angles or not.

Guided Practice – Distance Between Two Points – Page No. 390

Question 1.
Approximate the length of the hypotenuse of the right triangle to the nearest tenth using a calculator.

_______ units

Answer: The length of the hypotenuse of the right triangle to the nearest tenth is 5.8 units.

Explanation: From the above figure let’s take
Length of the vertical leg = 3 units
Length of the horizontal leg = 5 units
let length of the hypotenuse = c
By using Pythagorean Theorem a2 + b= c2
c2 = 32 + 52
c2 = 9 +25
c = √34 => 5.830.
Therefore Length of the hypotenuse of the right triangle to the nearest tenth is 5.8 units.

Question 3.
A plane leaves an airport and flies due north. Two minutes later, a second plane leaves the same airport flying due east. The flight plan shows the coordinates of the two planes 10 minutes later. The distances in the graph are measured in miles. Use the Pythagorean Theorem to find the distance shown between the two planes.

_______ miles

Answer: The distance between the two planes is 103.6 miles.

Explanation:
Length of the vertical dv = √(80 -1)2 + √(1-1)2
= √792 => 79.
Length of the horizontal dh = √(68 -1)2 + √(1-1)2
= √672 => 67.
Distance between the two planes D = √(792 + 672)
= √(6241+4489) => √10730
= 103.5857 => 103.6 miles.

ESSENTIAL QUESTION CHECK-IN

Question 4.
Describe two ways to find the distance between two points on a coordinate plane.

Explanation: We can draw a right triangle whose hypotenuse is the segment connecting the two points and then use the Pythagorean Theorem to find the length of that segment. We can also the Distance formula to find the length of that segment.

For example, plot three points; (1,2), (20,2), and (20,12)

Using the Pythagorean Theorem:

The length of the horizontal leg is the absolute value of the difference between the x-coordinates of points (1,2) and (20,2).
|1 – 20| = 19
The length of the horizontal leg is 19.

The length of the vertical leg is the absolute value of the difference between the y-coordinates of the points (20,2) and (20,12).
|2 – 12| = 10
The length of the vertical leg is 10.

Let a = 19, b = 10 and let c represent the hypotenuse. Find c.
a2 + b= c2
192 + 10= c2
361 + 100 = c2
461 = c2
distance is 21.5 = c

Using the Distance formula:
d= √( x2 – x1)2 + √( y2 – y1)2
The length of the horizontal leg is between (1,2) and (20,2).
d= √( x2 – x1)2 + √( y2 – y1)2
=  √(20 -1)2 + √(2-2)2
= √(19)2 + √(0)2
= √361 => 19
The length of the vertical leg is between (20,2) and (20,12).
d= √( x2 – x1)2 + √( y2 – y1)2
=  √(20 -20)2 + √(12-2)2
= √(0)2 +√(10)2
= √100 => 10
The length of the diagonal leg is between (1,2) and (20,12).
d= √( x2 – x1)2 + √( y2 – y1)2
=  √(20 -1)2 + √(12-2)2
= √(19)2 + √(10)2
= √(361+100) => √461 = 21.5

12.3 Independent Practice – Distance Between Two Points – Page No. 391

Question 5.
A metal worker traced a triangular piece of sheet metal on a coordinate plane, as shown. The units represent inches. What is the length of the longest side of the metal triangle? Approximate the length to the nearest tenth of an inch using a calculator. Check that your answer is reasonable.

_______ in.

Answer: The length of the longest side of the metal triangle to the nearest tenth is 7.8 units.

Explanation: From the above figure let’s take
Length of the vertical leg = 6 units
Length of the horizontal leg = 5 units
let length of the hypotenuse = c
By using Pythagorean Theorem a2 + b= c2
c2 = 62 + 52
c2 = 36 +25
c = √61 => 7.8
Therefore Length of the longest side of the metal triangle to the nearest tenth is 7.8 units.

Question 7.
The coordinates of the vertices of a rectangle are given by R(- 3, – 4), E(- 3, 4), C (4, 4), and T (4, – 4). Plot these points on the coordinate plane at the right and connect them to draw the rectangle. Then connect points E and T to form diagonal $$\overline { ET }$$.
a. Use the Pythagorean Theorem to find the exact length of $$\overline { ET }$$.

Explanation:
Taking into consideration the triangle TRE, the length of the vertical leg (ER) is 8 units. The length of the horizontal leg (RT) is 7 units. Let a = 8 and b =7. Let c represent the length of the hypotenuse, the diagonal ET. We use the Pythagorean Theorem to find c.
a2 + b= c2
c2 = 82 + 72
c2 = 64 +49
c = √113 => 10,63.
The diagonal ET is about 10.63 units long.

Question 7.
b. How can you use the Distance Formula to find the length of $$\overline { ET }$$ ? Show that the Distance Formula gives the same answer.

Answer: The diagonal ET is about 10.63 units long. As we can see the answer is the same as the one we found using the Pythagorean Theorem.

Explanation: Using the distance formula, in a coordinate plane, the distance d between the points E(-3,4) and T(4, -4) is:
d= √( x2 – x1)2 + √( y2 – y1)2
=  √(4 – (-3))2 + √(- 4 – 4)2
= √(7)2 + √(-8)2
= √(49+64) => √113 = 10.63.
The diagonal ET is about 10.63 units long. As we can see the answer is the same as the one we found using the Pythagorean Theorem.

Question 8.
Multistep The locations of three ships are represented on a coordinate grid by the following points: P(- 2, 5), Q(- 7, – 5), and R(2, – 3). Which ships are farthest apart?

Answer: Ships P and Q are farthest apart

Explanation: Distance Formula: In a coordinate plane, the distance d between two points (x1,y1) and (x2,y2) is:

d= √( x2 – x1)2 + √( y2 – y1)2
The distance d1 between the two points P(-2,5) and Q(-7,-5) is:
d1 = √( xQ – xP)2 + √( yQ – yP)2
= √(-7 – (-2))2 + √(- 5 – 5)2
= √(-5)2 + √(-10)2
= √(25+100) => √125 = 11.18

The distance d2 between the two points Q(-7,-5) and R(2,-3) is:
d3 = √( xR – xQ)2 + √( yR – yQ)2
= √(2 – (-7))2 + √(- 3 – 5)2
= √(9)2 + √(2)2
= √(81+4) => √85 = 9.22

The distance d3 between the two points P(-2,5) and R(2,-3) is:
d3 = √( xR – xP)2 + √( yR – yP)2
= √(2 – (-2))2 + √(- 3 – 5)2
= √(4)2 + √(-8)2
= √(16+64) => √80 = 8.94.
As we can see, the greatest distance is d1 11.8, which means that ships P and Q are farthest apart.

Distance Between Two Points – Page No. 392

Question 9.
Make a Conjecture Find as many points as you can that are 5 units from the origin. Make a conjecture about the shape formed if all the points 5 units from the origin were connected.

Explanation: Some of the points that are 5 units away from the origin are: (0,5), (3,4), (4,3),(5,0),(4,-3),(3,-4),(0,-5),(-3,-4),(-4,-3),(-5,0),(-4,3),(-3,4) etc, If all the points 5 units away from the origin are connected, a circle would be formed.

Question 10.
Justify Reasoning The graph shows the location of a motion detector that has a maximum range of 34 feet. A peacock at point P displays its tail feathers. Will the motion detector sense this motion? Explain.

Answer: Considering each unit represents 1 foot, the motion detector, and peacock are 33.5 feet apart. Since the motion detector has a maximum range of 34 feet, it means that it will sense the motion of the peacock’s feathers.

Explanation: The coordinates of the motion detector are said to be (0,25), whereas the coordinates of the peacock are (30,10). In a coordinate plane, the distance d between the points (0,25) and (30,10) is:
d = √( x2 – x1)2 + √( y2 – y1)2
= √(30 – 0)2 + √(10 – 25)2
= √(30)2 + √(-15)2
= √(900+225) => √1125.
Rounding answer to the nearest tenth:
d = 33.5 feet.
Considering each unit represents 1 foot, the motion detector and peacock are 33.5 feet apart. Since the motion detector has a maximum range of 34 feet, it means that it will sense the motion of the peacock’s feathers.

FOCUS ON HIGHER ORDER THINKING

Question 11.
Persevere in Problem Solving One leg of an isosceles right triangle has endpoints (1, 1) and (6, 1). The other leg passes through the point (6, 2). Draw the triangle on the coordinate plane. Then show how you can use the Distance Formula to find the length of the hypotenuse. Round your answer to the nearest tenth.

Explanation:

One leg of an isosceles right triangle has endpoints (1,1) and (6,1), which means that the leg is 5 units long. Since the triangle is isosceles, the other leg should be 5 units long too, therefore the endpoints of the second leg that passes through the point (6,2) are (6,1) and (6,6).
In the coordinate plane, the length of the hypotenuse is the distance d between points (1,1) and (6,6).
d = √( x2 – x1)2 + √( y2 – y1)2
= √(6 – 1)2 + √(6 – 1)2
= √(5)2 + √(5)2
= √(25+25) => √50.
d = 7.1.
The hypotenuse is around 7.1 units long.

Question 12.
Represent Real-World Problems The figure shows a representation of a football field. The units represent yards. A sports analyst marks the locations of the football from where it was thrown (point A) and where it was caught (point B). Explain how you can use the Pythagorean Theorem to find the distance the ball was thrown. Then find the distance.

_______ yards

Answer: The distance between point A and B is 37 yards

Explanation:

To find the distance between points A and B, we draw segment AB and label its length d. Then we draw the vertical segment AC and Horizontal segment CB. We label the lengths of these segments a and b. triangle ACB is a right triangle with hypotenuse AB.
Since AC is a vertical segment, its length, a, is the difference between its y-coordinates. Therefore, a = 26 – 14 = 12 units.
Since CB is a horizontal segment, its length b is the difference between its x-coordinates. Therefore, b = 75 – 40 = 35units.
We use the Pythagorean Theorem to find d, the length of segment AB.
d2 = a2 + b2
d2 = 122 + 352
d2 = 144 + 1225
d2 = 1369 => d = √1369 => 37
The distance between points A and B is 37 yards

Ready to Go On? – Model Quiz – Page No. 393

12.1 The Pythagorean Theorem

Find the length of the missing side.

Question 1.

________ meters

Answer: Length of the missing side is 28m

Explanation: Lets consider value of a = 21 and c = 35.
Using Pythagorean Theorem a2 + b= c2
212 + b2 = 352
441 + b2 = 1225
b2= 784 => b = √784 = 28.
Therefore length of missing side is 28m.

Question 2.

________ ft

Answer: Length of missing side is 34ft

Explanation: Let’s consider value of a = 16 and b = 30.
Using Pythagorean Theorem a2 + b= c2
162 + 302 = c2
256 + 900 = c2
c2= 1156 => c = √1156 = 34.
Therefore length of missing side is 34ft.

12.2 Converse of the Pythagorean Theorem

Tell whether each triangle with the given side lengths is a right triangle.

Question 3.
11, 60, 61
____________

Answer: Since 112 + 602 = 612, by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.

Explanation: Let a = 11, b = 60 and c= 61
Using the converse of the Pythagorean Theorem a2 + b= c2
112 + 602 = 612
121 + 3600 = 3721
3721 = 3721
Since 112 + 602 = 612, by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.

Question 4.
9, 37, 40
____________

Answer: Since  92 + 372 ≠ 402, by the converse of the Pythagorean Theorem, we say that the given sides are not in the shape of a right-angled triangle.

Explanation: Let a = 9, b = 37 and c= 40
Using the converse of the Pythagorean Theorem a2 + b= c2
92 + 372 = 402
81 + 1369 = 1600
1450 ≠ 3721.
Since  92 + 372 ≠ 402, by the converse of the Pythagorean Theorem, we say that the given sides are not in the shape of a right-angled triangle.

Question 7.
Keelie has a triangular-shaped card. The lengths of its sides are 4.5 cm, 6 cm, and 7.5 cm. Is the card a right triangle?
____________

Answer: Since 4.52 + 62 = 7.52, by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of a right-angled triangle.

Explanation: Let a = 4.5, b = 6 and c= 7.5
Using the converse of the Pythagorean Theorem a2 + b= c2
4.52 + 62 = 7.52
20.25 + 36 = 56.25
56.25= 56.25
Since 4.52 + 62 = 7.52, by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of a right-angled triangle.

12.3 Distance Between Two Points

Find the distance between the given points. Round to the nearest tenth.

Question 8.
A and B
________ units

Answer: The distance between A and B is 6.7 units

Explanation: A= (-2,3) and B= (4,6)

Distance between A and B is d = √( x2 – x1)2 + √( y2 – y1)2
= √(4 – (-2)2 + √(6 – 3)2
= √(6)2 + √(3)2
= √(36+9) => √45 = 6.7 units

ESSENTIAL QUESTION

Question 11.
How can you use the Pythagorean Theorem to solve real-world problems?
We can use the Pythagorean Theorem to find the length of a side of a right triangle when we know the lengths of the other two sides. This application is usually used in architecture or other physical construction projects. For example, it can be used to find the length of a ladder, if we know the height of the wall and the distance on the ground from the wall of the ladder.

Selected Response – Mixed Review – Page No. 394

Question 1.
What is the missing length of the side?

A. 9 ft
B. 30 ft
C. 39 ft
D. 120 ft

Question 2.
Which relation does not represent a function?
Options:
A. (0, 8), (3, 8), (1, 6)
B. (4, 2), (6, 1), (8, 9)
C. (1, 20), (2, 23), (9, 26)
D. (0, 3), (2, 3), (2, 0)

Explanation: The value of X is the same for 2 points and 2 values of Y [(2, 3), (2, 0)]. The value of X is repeated for a function to exist, no two points can have the same X coordinates.

Question 3.
Two sides of a right triangle have lengths of 72 cm and 97 cm. The third side is not the hypotenuse. How long is the third side?
Options:
A. 25 cm
B. 45 cm
C. 65 cm
D. 121 cm

Explanation:
Given a= 72 cm
b= ?
c= 97 cm
As a2+b2=c 2
722+b2= 972
5,184+b2= 9,409
b2= 9,409-5,184
b= √4,225
b= 65 cm.

Question 4.
To the nearest tenth, what is the distance between point F and point G?

Options:
A. 4.5 units
B. 5.0 units
C. 7.3 units
D. 20 units

Explanation:
Given F= (-1,6) =(x1,y1).
G= (3,4) = (x2,y2).
The difference between F&G points is
d= √(x2-x1)2 + (y2-y1)2
=  √(3 – (-1))2 + (4 – 6)2
= √(4)2 + (-2)2
= √16+4
= √20
= 4.471
= 4.5 units.

Question 5.
A flagpole is 53 feet tall. A rope is tied to the top of the flagpole and secured to the ground 28 feet from the base of the flagpole. What is the length of the rope?
Options:
A. 25 feet
B. 45 feet
C. 53 feet
D. 60 feet

Explanation:

By Pythagorean theorem
a2+b2=c 2
532+282= C2
2,809+784= C2
C2 = 9,409-5,184
C2 = 3,593
C= √3,593
C= 59.94 feet
=60 feet.

Question 6.
Which set of lengths is not the side lengths of a right triangle?
Options:
A. 36, 77, 85
B. 20, 99, 101
C. 27, 120, 123
D. 24, 33, 42

Explanation:
Check if side lengths in option A form a right triangle.
Let a= 36, b= 77, c= 85
By Pythagorean theorem
a2+b2=c 2
362+772= 852
1,296+ 5,929= 7,225
7,225= 7,225
As 362+772= 852 the triangle is a right triangle.

Check if side lengths in option B form a right triangle.
Let a= 20, b= 99, c= 101
By Pythagorean theorem
a2+b2=c 2
202+992= 1012
400+ 9,801= 10,201
10,201= 10,201
As 202+992= 1012 the triangle is a right triangle.

Check if side lengths in option B form a right triangle.
Let a= 27, b= 120, c= 123
By Pythagorean theorem
a2+b2=c 2
272+1202= 1232
729+ 14,400= 15,129
15,129= 15,129
As 272+1202= 1232 the triangle is a right triangle.

Check if side lengths in option B form a right triangle.
Let a= 27, b= 120, c= 123
By Pythagorean theorem
a2+b2=c 2
242+332= 422
576+ 1,089= 1,764.
1,665= 1,764
As 242+332 is not equal to 422 the triangle is a right triangle.

Question 7.
A triangle has one right angle. What could the measures of the other two angles be?
Options:
A. 25° and 65°
B. 30° and 15°
C 55° and 125°
D 90° and 100°

A. 25° and 65°

Question 8.
A fallen tree is shown on the coordinate grid below. Each unit represents 1 meter.

a. What is the distance from A to B?
_______ meters

Explanation:
A= (-5,3)
B= (8,0)
Distance between A & B is
D= √{8-(-5)2 + (0-3)2
= √(13)2 + (-3)2
= √169+9
= √178
= 13.34  m.

Question 8.
b. What was the height of the tree before it fell?
_______ meters

Explanation:
Length of the broken part= 13.3 m
Length of vertical part= 3 m
Total Length = 13.3 m + 3 m
= 16.3 m.

Final Words

In addition to the exercise problems, we have provided the solutions for the review questions. So all the students are requested to test their knowledge and solve the problems provided at the end of this chapter. Refer to HMH Go Math Grade 8 Answer Key and try to score the highest marks in the exams. Hope you liked the explanations provided in this chapter. Stay tuned to get the solutions according to the list of the chapters of all the grades.

Refer:

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Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables

Download Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables pdf for free of cost. It is very important for the students to learn the fundamentals at the secondary level. In order to help you guys, we are providing the answers to all the questions in HMH Go Math Grade 6 Chapter 9 Solution Key Independent and Dependent Variables.

Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables

The Independent and Dependent Variables chapter consists of the topics like equations and tables, analyze relationships, graphs etc. It is essential for students to know the relationship between the graphs and tables in this chapter. You can know different methods of solving the problems by using Go Math Grade 6 Solution Key Chapter 9 Independent and Dependent Variables. All you have to do is to tap the below-given links.

Lesson 1: Independent and Dependent Variables

Lesson 2: Equations and Tables

Lesson 3: Problem Solving • Analyze Relationships

Mid-Chapter Checkpoint

Lesson 4: Graph Relationships

Lesson 5: Equations and Graphs

Chapter 9 Review/Test

Share and Show – Page No. 493

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 1.
An online store lets customers have their name printed on any item they buy. The total cost c in dollars is the price of the item p in dollars plus $3.99 for the name. Type below: ________________ Answer: c = p +$3.99

Explanation:
The independent variable is c, the price of the item because it is not going to depend on anything else.
The dependent variable is p because the total cost depends on how many items there are, whether your name is marked on it, etc.
The equation would be:
c = p + $3.99 Question 2. A raft travels downriver at a rate of 6 miles per hour. The total distance d in miles that the raft travels is equal to the rate times the number of hours h. Type below: ________________ Answer: d = 6 × h Explanation: Speed of the raft= 6 miles per hour Total distance (d) of the raft = rate × number of hours h The dependent variable is the number of hours h The independent variable is distance d. The equation would be: d = 6 × h Question 3. Apples are on sale for$1.99 a pound. Sheila buys p pounds of apples for a total cost of c dollars.
Type below:
________________

Answer: c = p × $1.99 Explanation: Apples are on sale for$1.99 a pound
p = pounds of apples
c = total cost of dollars
The equation would be:
c = p × $1.99 c is the independent variable. p is the dependent variable. On Your Own Identify the independent and dependent variables. Then write an equation to represent the relationship between them. Question 5. Billy has$25. His father is going to give him more money. The total amount t Billy will have is equal to the amount m his father gives him plus the $25 Billy already has. Type below: ________________ Answer: t = m +$25

Explanation:
Billy has $25. His father is going to give him more money. The total amount t Billy will have is equal to the amount m his father gives him plus the$25 Billy already has.
The equation would be:
t = m + $25 t is the independent variable m is the dependent variable. Question 6. Connect Symbols and Words Describe a situation that can be represented by the equation c = 12b. Type below: ________________ Answer: Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the cost of the necklace c. The equation is c = 12n Question 7. Belinda pays$4.25 for each glass she buys. The total cost c is equal to the price per glass times the number of glasses n plus $9.95 for shipping and handling. Write an equation and use it to find how much it will cost Belinda to buy 12 glasses. Type below: ________________ Answer: Belinda pays$4.25 for each glass she buys. The total cost c is equal to the price per glass times the number of glasses n plus $9.95 for shipping and handling. The equation is: c = 4.25n + 9.95 Now we have to find the cost of 12 glasses. c = 4.25(12) + 9.95 c = 60.95 It takes$60.95 to buy 12 glasses.

Unlock the Problem – Page No. 494

Question 8.
Benji decides to save $15 per week to buy a computer program. Write an equation that models the total amount t in dollars Benji will have saved in w weeks. a. What does the variable t represent? Type below: ________________ Answer: t represents the total amount in dollars Banji saved. Question 8. b. Which is the dependent variable? Which is the independent variable? How do you know? Type below: ________________ Answer: w is the dependent variable. t is the independent variable. w is dependent because it represents the number of weeks. So, we have to multiply 15 by w. t is an independent variable because t determines the value of a dependent variable. Question 8. c. How can you find the total amount saved in w weeks? Type below: ________________ Answer: We can find the total amount saved in w weeks by multiplying 15 with w. Question 8. d. Write an equation for the total amount that Benji will have saved. Type below: ________________ Answer: t = 15w Question 9. Coach Diaz is buying hats for the baseball team. The total cost c is equal to the number of hats n that he buys times the sum of the price per hat h and a$2 charge per hat to have the team name printed on it. Write an equation that can be used to find the cost of the hats.
Type below:
________________

Answer: c = n + 2h

Explanation:
Coach Diaz is buying hats for the baseball team.
The total cost c is equal to the number of hats n that he buys times the sum of the price per hat h and a $2 charge per hat to have the team name printed on it. c represents the total cost. n is the number of hats h is the price per hat. The equation is c is equal to the number of hats plus price per hat and$2.
c = n + 2h

Question 10.
A steel cable that is $$\frac{1}{2}$$ inch in diameter weighs 0.42 pound per foot. The total weight in pounds w is equal to 0.42 times of the number of feet f of steel cable. Choose the letter or equation that makes each sentence true.
The independent variable is ______________ .
The dependent variable is ______________ .
The equation that represents the relationship between the variables is ______________ .

A steel cable that is $$\frac{1}{2}$$ inch in diameter weighs 0.42 pound per foot.
The total weight in pounds w is equal to 0.42 times of the number of feet f of steel cable.
The equation would be:
w = 0.2f
f is the dependent variable
w is the dependent variable.

Independent and Dependent Variables – Page No. 495

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 2.
An online clothing store charges $6 for shipping, no matter the price of the items. The total cost c in dollars is the price of the items ordered p plus$6 for shipping.
Type below:
________________

Answer: c = p + 6

Explanation:
Given,
An online clothing store charges $6 for shipping, no matter the price of the items. The total cost c in dollars is the price of the items ordered p plus$6 for shipping.
The equation would be:
c = p + $6 where c = cost in dollars p is the price of items The independent variable is c. The dependent variable is p Question 3. Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the number of necklaces n. Type below: ________________ Answer: b = 12n Explanation: Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the number of necklaces n. b = total number of beads n = number of necklaces The equation would be: b = 12n b is the independent variable n is the dependent variable. Problem Solving Question 4. Maria earns$45 for every lawn that she mows. Her earnings e in dollars depend on the number of lawns n that she mows. Write an equation that represents this situation.
Type below:
________________

Explanation:
Maria earns $45 for every lawn that she mows. Her earnings e in dollars depend on the number of lawns n that she mows. e = earnings in dollars n = number of lawns The equation would be: e = 45n e is the independent variable. n is the dependent variable. Question 6. Write a situation in which one unknown is dependent on another unknown. Write an equation for your situation and identify the dependent and independent variables. Type below: ________________ Answer: Byron is playing a game. He earns 10 points for each question he answers correctly. His total score s equals the number of correct answers a time a. Answer: Dependent variable: s Independent variable: a Equation: s = 10a Lesson Check – Page No. 496 Question 1. There are 12 boys in a math class. The total number of students s depends on the number of girls in the class g. Write an equation that represents this situation. Type below: ________________ Answer: s = 12 + g Explanation: There are 12 boys in a math class. The total number of students s depends on the number of girls in class g. The equation would be: s = 12 + g s is the independent variable. g is the dependent variable. Spiral Review Question 3. The formula F = $$\frac{9}{5}$$C + 32 gives the Fahrenheit temperature for a Celsius temperature of C degrees. Gwen measured a Celsius temperature of 35 degrees. What is this temperature in degrees Fahrenheit? ______ °F Answer: 95 degrees Explanation: The formula F = $$\frac{9}{5}$$C + 32 gives the Fahrenheit temperature for a Celsius temperature of C degrees. C = 35 F = 9C ÷ 5 + 32 F = 9(35) ÷ 5 + 32 F = 315 ÷ 5 + 32 F = 63 + 32 F = 95 degrees Question 4. Write an equation to represent this sentence. The difference of a number n and 1.8 is 2. Type below: ________________ Answer: n – 1.8 = 2 Explanation: The difference of a number n and 1.8 is 2. The phrase difference is nothing but subtraction. The equation would be: n – 1.8 = 2 Question 6. Graph x ≤ 4.5 on a number line. Type below: ________________ Answer: Share and Show – Page No. 499 Use the equation to complete the table. Question 1. y = x + 3 Type below: ________________ Answer: Substitute the value of x in the above equation. The equation is x + 3. Question 2. y = 2x + 1 Type below: ________________ Answer: Substitute the value of x in the above equation. The equation is y = 2x + 1 On Your Own Write an equation for the relationship shown in the table. Then find the unknown value in the table. Question 3. Type below: ________________ Answer: The equation is y = 2x The output is multiple of 2 and x For x = 10 The output is y = 2x y = 2 × 10 = 20 Question 4. Type below: ________________ Answer: y = x ÷ 2 The output is the quotient of x and 2. The output for x = 40 is y = 40 ÷ 2 y = 20 Question 5. The table shows the current cost of buying apps for a cell phone. Next month, the price of each app will double. Write an equation you can use to find the total cost y of buying x apps next month. Type below: ________________ Answer: y = 3x Explanation: The equation is multiple of 3 and x. The equation is y = 3x Question 6. A beach resort charges$1.50 per hour plus $4.50 to rent a bicycle. The equation c = 1.50x + 4.50 gives the total cost c of renting a bicycle for x hours. Use numbers and words to explain how to find the cost c of renting a bicycle for 6 hours. Type below: ________________ Answer: A beach resort charges$1.50 per hour plus $4.50 to rent a bicycle. The equation c = 1.50x + 4.50 gives the total cost c of renting a bicycle for x hours. For x = 1 c = 1.50(1) + 4.50 c = 1.50 + 4.50 c =$6.00
For x = 2
c = 1.50(2) + 4.50
c = 3.00 + 4.50
c = $7.50 For x = 3 c = 1.50(3) + 4.50 c = 4.50 + 4.50 c =$9.00
For x = 4
c = 1.50(4) + 4.50
c = 6.00 + 4.50
c = $10.50 </aCause and Effect – Page No. 500 The reading skill cause and effect can help you understand how a change in one variable may cause a change in another variable. In karate, a person’s skill level is often shown by the color of his or her belt. At Sara’s karate school, students must pass a test to move from one belt level to the next. Each test costs$23. Sara hopes to move up 3 belt levels this year. How will this affect her karate expenses?

Question 7.
Write an equation to show the relationship between cause and effect. Then use the equation to solve the problem.
Type below:
________________

Explanation:
Let x represent the number of belt levels Sara moves up and let y represent the increase in dollars in her karate expenses.
Write the equation:
y = 23x
Sara plans to move up 3 levels, so replace x with 3
y = 23 × 3
y = 69
So, if Sara moves up 3 belt levels this year, her karate expenses will increase by $69. Write an equation to show the relationship between cause and effect. Then use the equation to solve the problem. Question 8. Classes at Tony’s karate school cost$29.50 per month. This year he plans to take 2 more months of classes than he did last year. How will this affect Tony’s karate expenses?
Type below:
________________

The equation is y = 29.50x
where x is the number of additional classes
y is the increase in dollars in expenses.
She has a coupon for $6 off her total cost. b represents the total cost in dollars for b books. So, the equation to represent the total cost is 10b – 6. Question 5. Which of the following are solutions to the inequality n > 7? n = 7 n = 6.9 n = 7.2 n = 6$$\frac{1}{2}$$ Type below: ________________ Answer: n = -7 Explanation: Substitute the value of n in the inequality. n > 7 n = -7 -7 > -7 Thus -7 is the solution. n = 6.9 -6.9 > -7 -6.9 is not the solution. n = 7.2 -7.2 > -7 -7.2 is less than – 7 Thus -7.2 is not the solution. n = 6$$\frac{1}{2}$$ 6$$\frac{1}{2}$$ > -7 6$$\frac{1}{2}$$ is not the solution. Question 6. Marcus sold brownies at a bake sale. He sold d dollars worth of brownies. He spent$5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings. Write an equation that represents this situation. Type below: ________________ Answer: p = d – 5.50 Explanation: Marcus sold brownies at a bake sale. He sold d dollars worth of brownies. He spent$5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings. p represents the total profit in dollars. d is the dollars worth of brownies. The equation is p = d – 5.50 Share and Show – Page No. 505 Question 1. A soccer coach is ordering shirts for the players. The table shows the total cost based on the number of shirts ordered. How much will it cost the coach to order 18 shirts?$ _______

Explanation:
First, find a pattern and write an equation.
The cost is $15 multiplied by the number of shirts. c =$15 × n
Next, use the equation to find the cost of 18 shirts.
c = $15 × n c =$15 × 18
c = $270 So, the cost of 18 shirts is$270.

Question 2.
What if the coach spent $375 to purchase a number of shirts? Could you use the same equation to find how many shirts the coach bought? Explain. Type below: ________________ Answer: Yes, I could use the same equation. I could substitute 375 for the variable c and solve for n. Question 3. The table shows the number of miles the Carter family drove over time. If the pattern continues, will the Carter family have driven more than 400 miles in 8 hours? Explain. Type below: ________________ Answer: 376 miles Explanation: First, find a pattern and write an equation. The distance is 47 miles multiplied by the number of hours. y = 47 × x Next, use the equations to find the distance for 8 hours. y = 47x y = 47 × 8 y = 376 So, the family will have driven 376 miles in 8 hours, which is less than 400 miles. On Your Own – Page No. 506 Question 5. A group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June. If the pattern continues, how many hours will they practice in November? _______ hours Answer: 36 hours Explanation: Given that, a group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June. The equation would be h = 4m m = 9 h = 4 × 9 = 36 Thus the group practiced 36 hours in the month of November. Question 6. The table shows the number of hours Jacob worked and the amount he earned each day. At the end of the week, he used his earnings to buy a new pair of skis. He had$218 left over. How much did the skis cost?
$_______ Answer: 142 Explanation: First, add the total amount he earned. 60 + 84 + 72 + 96 + 48 = 360 Jacob earned$360 for the week.
If he has $218 leftover, this means that the cost of the skis is 360 – 218 = 14 Therefore the cost of the skis is$142.

Question 7.
Pose a Problem Look back at Problem 6. Use the data in the table to write a new problem in which you could use the strategy to find a pattern. Then solve the problem.
Type below:
________________

How much money would Jacob earn if he worked for 10 hours?
From the table, we can see that the pattern is that Jacob earns $12 per hour. The equation is s = 12h Where s is the total pay and h is the number of hours worked. s = 12h s = 12 × 10 s = 120 Thus Jacob earned$120 for 10 hours.

Question 8.
Draw Conclusions Marlon rode his bicycle 9 miles the first week, 18 miles the second week, and 27 miles the third week. If the pattern continues, will Marlon ride exactly 100 miles in a week at some point? Explain how you determined your answer.
Type below:
________________

Answer: No, Marlon will not ride exactly 100 miles in a week at some point.
Each number in the pattern is a multiple of 9 and 100 is not a multiple of 9.

Question 9.
A diving instructor ordered snorkels. The table shows the cost based on the number of snorkels ordered.

If the diving instructor spent $1,024, how many snorkels did he order? Use numbers and words to explain your answer. _______ snorkels Answer: 32 Explanation: Use the table to find the equation. c represents the cost based on the number of snorkels. s represents the number of snorkels The equation would be: c = 32s The diving instructor spent$1,024
c = 1024
1024 = 32s
s = 1024/32
s = 32
Thus the diving instructor gets 32 snorkels for $1024. Problem Solving Analyze Relationships – Page No. 507 The table shows the number of cups of yogurt needed to make different amounts of a fruit smoothie. Use the table for 1–3. Question 1. Write an equation to represent the relationship. Type below: ________________ Answer: c = 3b Explanation: c represents number of cups of yogurt b represents the batches From the table, we can observe that b is multiplied with 3 to get cups of yogurt. So, the equation to find the number of cups of yogurt is c = 3b Question 2. How much yogurt is needed for 9 batches of smoothie? _______ cups Answer: 27 Explanation: Given that there are 9 batches of smoothie. By using the above equation we can find the number of cups. c = 3b c = 3 × 9 = 27 cups Thus 27 cups of yogurt is need to make 9 batches of smoothie. Question 3. Jerry used 33 cups of yogurt to make smoothies. How many batches did he make? _______ batches Answer: 11 batches Explanation: Jerry used 33 cups of yogurt to make smoothies. Use the equation to find the batches. c = 3b 33 = 3b b = 33/3 b = 11 Therefore jerry made 11 batches of smoothie. The table shows the relationship between Winn’s age and his sister’s age. Use the table for 4–5. Question 4. Write an equation to represent the relationship. Type below: ________________ Answer: s = w + 4 Explanation: By using the table we can find the relationship between wine’s age and wine’s sister’s age. Winn’s sister’s age will be the sum of Winn’s age and 4. So, the equation is s = w + 4 Question 5. When Winn is 14 years old, how old will his sister be? _______ years old Answer: 18 Explanation: Use the equation s = w + 4 W = 14 years s = 14 + 4 s = 18 years Thus winn’s sister’s age is 18 years. Question 6. Write a problem for the table. Use a pattern and an equation to solve your problem. Type below: ________________ Answer: m = 16h Explanation: Jerry runs 16 miles per hour. How many miles he can run in 5 hours? The equation is m = 16h m = 16 × 5 = 80 miles Therefore jerry runs 80 miles in 5 hours. Lesson Check – Page No. 508 Question 1. The table shows the total cost c in dollars of n gift baskets. What will be the cost of 9 gift baskets? Answer:$108

Explanation:
By seeing the above we can say that the equation is
c = 12n
n = 9
c = 12 × 9
c = $108 Thus the cost of 9 gift baskets is$108.

Question 2.
The table shows the number of minutes m that Tara has practiced after d days. If Tara has practiced for 70 minutes, how many days has she practiced?

_______ days

Explanation:
The table shows the number of minutes m that Tara has practiced after d days.
The equation would be
m = 35d
If Tara has practiced for 70 minutes
m = 70
Use the equation to find the number of days she practiced.
70 = 35d
d = 70/35
d = 2 days
Thus Tara has practiced 2 days.

Spiral Review

Question 3.
Soccer shirts cost $15 each, and soccer shorts cost$18 each. The expression 15n + 18n represents the total cost in dollars of n uniforms. Simplify the expression by combining like terms.
Type below:
________________

Explanation:
Soccer shirts cost $15 each, and soccer shorts cost$18 each.
The expression 15n + 18n represents the total cost in dollars of n uniforms.
Now combine the like terms.
15n + 18n = 33n

Question 4.
What is an equation that represents the relationship in the table?

Type below:
________________

Answer: y = x ÷ 2

Explanation:
By seeing the above table we can find the relationship between x and y.
y is the quotient of x and 2.
We get the value of y when you divide x by 2.
The equation is y = x ÷ 2

Question 6.
Marisol plans to make 9 mini-sandwiches for every 2 people attending her party. Write a ratio that is equivalent to Marisol’s ratio.
Type below:
________________

Explanation:
Given that, Marisol plans to make 9 mini-sandwiches for every 2 people attending her party.
The ratio will be 9:2
Now we need to write the equivalent ratio for the 9 sandwiches for every 2 people i.e, 9:2
We know that the equivalent ratio can be written as
9/2 × 3/3 = 27/6
9/2 × 5/5 = 45/6
Thus the equivalent fractions are 27/6 and 45/6.

Mid-Chapter Checkpoint – Vocabulary – Page No. 509

Choose the best term from the box to complete the sentence.

Question 1.
A(n) _____ has a value that determines the value of another quantity.
Type below:
________________

An Independent variable has a value that determines the value of another quantity.

Question 2.
A variable whose value is determined by the value of another quantity is called a(n) _____.
Type below:
________________

A variable whose value is determined by the value of another quantity is called a Dependent variable.

Concepts and Skills

Identify the independent and dependent variables.

Write an equation for the relationship shown in the table. Then find the unknown value in the table.

Question 5.

Type below:
________________

Explanation:
The equation is y = 7x
x = 7
y = 7 × 7 = 49
Thus the unknown value y is 49.

Question 6.

Type below:
________________

Explanation:
The equation for the above table is
y = x ÷ 5
Use the equation to find the value of y where x = 60
y = 60 ÷ 5
y = 12
Thus the unknown value is 12.

Write an equation that describes the pattern shown in the table.

Question 7.
The table shows how the number of pepperoni slices used depends on the number of pizzas made.

Type below:
_______________

Explanation:
The table shows how the number of pepperoni slices used depends on the number of pizzas made.
y is 17 times of x.
The equation for the above table is y = 17x

Question 8.
Brayden is training for a marathon. The table shows how the number of miles he runs depends on which week of training he is in.

Type below:
________________

Answer: m = w + 5

Explanation:
Brayden is training for a marathon. The table shows how the number of miles he runs depends on which week of training he is in.
m is equal to the sum of w and 5.
Thus the equation is m = w + 5.

Page No. 510

Question 9.
The band has a total of 152 members. Some of the members are in the marching band, and the rest are in the concert band. Write an equation that models how many marching band members m there are if there are c concert band members.
Type below:
________________

Answer: m = 152 – c

Explanation:
Given,
The band has a total of 152 members. Some of the members are in the marching band, and the rest are in the concert band.
m is equal to the difference of 152 and c.
The equation is m = 152 – c

Question 11.
Amy volunteers at an animal shelter. She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June. If the pattern continues, how many hours will she work in December?
_______ hours

Explanation:
Amy volunteers at an animal shelter.
She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June.
As she started working from the march. December will be the 10th month.
Keep on adding 2 hours for each month you get 28 hours for December.
Thus she worked 28 hours in December.

Question 12.
Aaron wants to buy a new snowboard. The table shows the amount that he has saved. If the pattern in the table continues, how much will he have saved after 1 year?

$_______ Answer:$540

Explanation:
Aaron wants to buy a new snowboard. The table shows the amount that he has saved.
The equation will be s = 45m
s is the money saved
m is the number of months
1 year = 12 months
s = 45 × 12
s = 540

The above graph shows that the cost of 5 DVDs is $75. Question 7. Both tables and graphs can be used to represent relationships between two variables. Explain how tables and graphs are similar and how they are different. Type below: ________________ Answer: Tables and graphs can be useful tools for helping people make decisions. However, they only provide part of a story. Inferences often have to be made from the data shown. As well as being able to identify clearly what the graph or table is telling us, it is important to identify what parts of the story are missing. Lesson Check – Page No. 516 Question 1. Mei wants to graph the relationship represented by the table. Write an ordered pair that is a point on the graph of the relationship. Type below: ________________ Answer: y = 8x Question 2. An online bookstore charges$2 to ship any book. Cole graphs the relationship that gives the total cost y in dollars to buy and ship a book that costs x dollars. Name an ordered pair that is a point on the graph of the relationship.
Type below:
________________

An online bookstore charges $2 to ship any book. Cole graphs the relationship that gives the total cost y in dollars to buy and ship a book that costs x dollars. y = x + 2 x = 4 y = 4 + 2 y = 6 The ordered pair is (4,6) Spiral Review Question 3. Write an expression that is equivalent to 6(g + 4). Type below: ________________ Answer: 6(g + 4) 6 × g + 6 × 4 6g + 24 Question 5. Graph n > 2 on a number line. Type below: ________________ Answer: Question 6. Sam is ordering lunch for the people in his office. The table shows the cost of lunch based on the number of people. How much will lunch cost for 35 people?$ _____

Explanation:
Sam is ordering lunch for the people in his office.
The table shows the cost of lunch based on the number of people.
The equation is c = 8n
c = 8 × 35
c = 280
Thus the lunch cost for 35 people is $280. Share and Show – Page No. 519 Graph the linear equation. Question 1. y = x + 2 Type below: ________________ Answer: Question 2. y = 3x Type below: ________________ Answer: Write the linear equation for the relationship shown by the graph. Question 3. Type below: ________________ Answer: y = x – 1 Question 4. Type below: ________________ On Your Own Graph the linear equation. Question 5. y = x + 1 Type below: ________________ Answer: Question 6. y = 2x − 1 Type below: ________________ Answer: Question 7. Identify Relationships The graph shows the number of loaves of bread y that Kareem bakes in x hours. Write the linear equation for the relationship shown by the graph. Type below: ________________ Answer: The ordered pairs are (1,1), (2,2), (4,4), (5,5) Look for a pattern among the pairs: each y value is the same as the corresponding x-value. The equation is y = x y = x Problem Solving + Applications – Page No. 520 The graph shows the growth of a bamboo plant. Use the graph for 8–9. Question 8. Write a linear equation for the relationship shown by the graph. Use your equation to predict the height of the bamboo plant after 7 days. Type below: ________________ Answer: Write the ordered pairs from the graph: (1,50), (2,100), (3,150), (4,200), (5,250). Look for a pattern among the pairs: each y value is 50 times the corresponding x value. The equation is y = 50x For x = 7, the solution is y = 50 × 7 = 350. So, the height of the bamboo plant after 7 days will be 350 centimeters. Question 10. Maria graphed the linear equation y = x + 3. Then she used her ruler to draw a vertical line through the point (4, 0). At what point do the two lines intersect? Type below: ________________ Answer: y = x + 3 y = 4 + 0 = 4 y = 4 + 3 = 7 The coordinate is (4, 7) Question 11. Antonio claims the linear equation for the relationship shown by the graph is y = $$\frac{1}{2}$$x + 2. Use numbers and words to support Antonio’s claim. Type below: ________________ Answer: The ordered pairs (2,3) and (6,5) on the line make the equation. y = $$\frac{1}{2}$$x + 2 y = 1/2 × 2 + 2 y = 1 + 2 = 3 y = 1/2 × 6 + 2 y = 3 + 2 = 5 Equations and Graphs – Page No. 521 Graph the linear equation. Question 1. y = x − 3 Type below: ________________ Answer: Question 2. y = x ÷ 3 Type below: ________________ Answer: Write a linear equation for the relationship shown by the graph. Question 3. Type below: ________________ Answer: By seeing the above graph we can say that the equation is y = x + 1 Question 4. Type below: ________________ Answer: The ordered pairs are (1,4), (1.5,6), (2,8) By seeing the above pairs we can say that the equation is y = 4x Problem Solving Question 5. Dee is driving at an average speed of 50 miles per hour. Write a linear equation for the relationship that gives the distance y in miles that Dee drives in x hours. Type below: ________________ Answer: y = 50x Explanation: Dee is driving at an average speed of 50 miles per hour. y represents the distance in miles x is the number of hours. y is equal to the product of 50 and x. y = 50x Question 6. Graph the relationship from Exercise 5. Type below: ________________ Answer: Question 7. Explain how to write a linear equation for a line on a graph. Type below: ________________ Answer: To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. Lesson Check – Page No. 522 Question 1. A balloon rises at a rate of 10 feet per second. What is the linear equation for the relationship that gives the height y in feet of the balloon after x seconds? Type below: ________________ Answer: The linear equation for the relationship is y = 10x Question 2. Write the linear equation that is shown by the graph. Type below: ________________ Answer: Write the ordered pairs from the graph: (3,3), (5,5), (8,8) Look for a pattern among the pairs: each y value is the same as the corresponding x-value. The equation is y = x Spiral Review Question 4. Which of the following are solutions of j ≥ 0.6? j = 1 j = 0.6 j = $$\frac{3}{5}$$ j = 0.12 j = 0.08 Type below: ________________ Answer: j = $$\frac{3}{5}$$ Explanation: Substitute the values of j in the inequality. j = 1 1 ≥ 0.6 1 is greater than 0.6 but not equal. Thus 1 is not the solution of j ≥ 0.6. j = 0.6 -0.6 ≥ 0.6 -0.6 is less than 0.6 Thus -0.6 is not the solution of j ≥ 0.6. j = $$\frac{3}{5}$$ $$\frac{3}{5}$$ ≥ 0.6 $$\frac{3}{5}$$ = 0.6 0.6 ≥ 0.6 Thus $$\frac{3}{5}$$ is the solution. j = 0.12 0.12 ≥ 0.6 0.12 is less than 0.6. Thus 0.12 is not the solution of j ≥ 0.6. j = 0.08 0.08 ≥ 0.6 0.08 is less than 0.6. Thus 0.08 is not the solution of j ≥ 0.6. Question 5. Red grapes cost$2.49 per pound. Write an equation that shows the relationship between the cost c in dollars and the number of pounds of grapes p.
Type below:
________________

Explanation:
Given,
Red grapes cost $2.49 per pound. c is the cost in dollars. p is the number of pounds of grapes. The equation c is equal to the product of the number of pounds of grapes and$2.49
c = 2.49p

Chapter 9 Review/Test – Page No. 523

Question 1.
A box of peanut butter crackers contains 12 individual snacks. The total number of individual snacks s is equal to 12 times the number of boxes of crackers b.
The independent variable is _____.
The dependent variable is _____.
The equation that represents the relationship between the variables is _____.

The independent variable is b.
The dependent variable is s.
The equation that represents the relationship between the variables is s = 12b.

Question 2.
A stationery store charges $8 to print logos on paper purchases. The total cost c is the price of the paper p plus$8 for printing the logo.
For numbers 2a–2d, select True or False for each statement.
2a. The total cost c depends on the price of the paper.
2b. c is the dependent variable.
2c. p is the independent variable.
2d. The equation that represents the relationship between the variables is c = 8p.
2a. ____________
2b. ____________
2c. ____________
2d. ____________

2a. True
2b. True
2c. True
2d. False

Explanation:
2a. c represents the relationship between the two quantities.
So, the statement “The total cost c depends on the price of the paper” is true.
2b. c is the total cost so the statement “c is the dependent variable” is true.
2c. p represents the price to print logos
So, the statement “p is the independent variable” is true.
2d. The total cost c is the price of the paper p plus $8 for printing the logo. The equation would be: c = 8 + p Thus the statement “The equation that represents the relationship between the variables is c = 8p” is false. Question 3. An electrician charges$75 an hour for labor and an initial fee of $65. The total cost c equals 75 times the number of hours x plus 65. Write an equation for the relationship and use the equation to complete the table. Type below: ________________ Answer: c = 75x + 65 Substitute the value of x in the equation. Page No. 524 Question 4. The community center offers classes in arts and crafts. There is a registration fee of$125 and each class costs $79. The total cost c in dollars equals 79 times the number of classes n plus 125. For numbers 4a–4d, select True or False for each statement. 4a. The registration fee is$120.
4b. n is the independent variable.
4c. c is the dependent variable.
4d. The cost for 7 classes is $678. 4a. ____________ 4b. ____________ 4c. ____________ 4d. ____________ Answer: 4a. False 4b. True 4c. True 4d. True Explanation: 4a. The registration fee is$120.
The registration fee is $125, not$120.
So, the statement is false.
4b. n is the independent variable.
n represents the number of classes.
The statement is true.
4c. c is the dependent variable.
c depends on the registration fee.
Thus the statement is true.
4d. The cost for 7 classes is $678 79 × 7 + 125 =$678
Thus the statement is true.

Question 5.
Ms. Walsh is buying calculators for her class. The table shows the total cost based on the number of calculators purchased.

If Ms. Walsh spent a total of $525, how many calculators did she buy? Use numbers and words to explain your answer. Type below: ________________ Answer: She bought 35 calculators. I found a pattern and wrote the equation c = 15n. Since I know that Mrs.Walsh spent a total of$525, I can substitute 525 for c and solve for n
525 = 15n
n = 35

Chapter 9 Review/Test – Page No. 525

Question 6.
The table shows the number of cups of lemonade that can be made from cups of lemon juice.

Mary Beth says the number of cups of lemon juice j depends on the number of cups of lemonade l. She says the equation j = 7l represents the relationship between the cups of lemon juice j and the cups of lemonade l. Is Mary Beth correct? Use words and numbers to explain why or why not.
Type below:
________________

Mary Beth is not correct. The number of cups of lemonade l depends on the number of cups of lemon juice j.
So l is the dependent variable and j is the independent variable.
The equation showing the relationship is l = 7j

Question 7.
For numbers 7a–7d, choose Yes or No to indicate whether the points, when graphed, would lie on the same line.
7a. (1, 6), (2, 4), (3, 2), (4, 0)
7b. (1, 1), (2, 4), (3, 9), (4, 16)
7c. (1, 3), (2, 5), (3, 7), (4, 9)
7d. (1, 8), (2, 10), (3, 12), (4, 14)
7a. ____________
7b. ____________
7c. ____________
7d. ____________

7a. Yes

7b. No

7c. Yes

7d. Yes

Question 8.
Graph the relationship represented by the table to find the unknown value.

Type below:
________________

Chapter 9 Review/Test – Page No. 526

Question 9.
Graph the relationship represented by the table.

Type below:
________________

Question 10.
Miranda’s wages are $15 per hour. Write a linear equation that gives the wages w in dollars that Miranda earns in h hours. Type below: ________________ Answer: w = 15h Question 11. The table shows the number of miles m that Lucinda could walk in h hours. Graph the relationship between hours h and miles m. Then write the equation that shows the relationship. Type below: ________________ Answer: m = 4h Chapter 9 Review/Test – Page No. 527 Question 13. Lacy is staying at a hotel that costs$85 per night. The total cost c in dollars of Lacy’s stay is 85 times the number of nights n she stays.
For numbers, 13a–13d, select True or False for each statement.
13a. The number of nights n is dependent on the cost c.
13b. n is the independent variable.
13c. c is the dependent variable.
13d. The equation that represents the total cost is c = 85n.
13a. ____________
13b. ____________
13c. ____________
13d. ____________

13a. False
13b. True
13c. True
13d. True

Explanation:
13a. The number of nights n is dependent on the cost c.
n is independent on the cost c.
So, the statement is false.
13b. n is the independent variable.
The statement is true.
13c. c is the dependent variable.
c is dependent because it depends on the cost c.
So, the statement is true.
13d. The equation that represents the total cost is c = 85n.
The equation is true.

Question 14.
A taxi cab company charges an initial fee of $5 and then$4 per mile for a ride. Use the equation c = 4x + 5 to complete the table.

Type below:
________________

Substitute the value of x in the equation.
We get,

Chapter 9 Review/Test – Page No. 528

Question 15.
A grocery display of cans is arranged in the form of a pyramid with 1 can in the top row, 3 in the second row from the top, 5 in the third row, and 7 in the fourth row. The total number of cans c equals 2 times the row r minus 1. Use the equation c = 2r − 1 to complete the table.

Type below:
________________

A grocery display of cans is arranged in the form of a pyramid with 1 can in the top row, 3 in the second row from the top, 5 in the third row, and 7 in the fourth row.
c = 2r − 1
Substitute r in the equation.

Question 16.
The graph shows the number of words Mason read in a given amount of minutes. If Mason continues to read at the same rate, how many words will he have read in 5 minutes?

______ words

By seeing the above graph we can say that Mason can read 1000 words in 5 minutes.

Question 17.
Casey claims the linear equation for the relationship shown by the graph is c = 25j. Use numbers and words to support Casey’s claim.

Type below:
________________

Answer: The ordered pairs (1,25), (3,75), (5,125) and (7,175) each make the equation c = 25j

Conclusion:

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Lesson 1: Lines, Rays, and Angles

Lesson 2: Classify Triangles by Angles

Lesson 3: Parallel Lines and Perpendicular Lines

Mid-Chapter Checkpoint

Lesson 5: Line Symmetry

Lesson 6: Find and Draw Lines of Symmetry

Lesson 7: Problem Solving • Shape Patterns

Review/Test

Common Core – New – Page No. 553

Lines, Rays, and Angles

Draw and label an example of the figure.

Question 1.
obtuse ∠ABC

Think: An obtuse angle is greater than a right angle. The middle letter, B, names the vertex of the angle.
_________

Explanation:
An obtuse angle is greater than a right angle. The middle letter, B, names the vertex of the angle.

Question 2.
$$\overrightarrow{G H}$$
_________

Explanation:
GH is a ray that has one endpoint and continues without an end in one direction.

Question 3.
acute ∠JKL
_________

Explanation:
Angle JKL is an acute angle that is less than a right angle.

Question 4.
$$\overline{B C}$$

Explanation:
BC is a line that continues without an end in both directions.

Use the figure for 5–8.

Question 5.
Name a line segment.

line segment EF

Explanation:

EF line is a straight path of points that continues without an end in both directions.

Question 6.
Name a right angle.
∠ _____

∠EJF

Explanation:
EJF is a right angle that forms a square corner.

Question 7.
Name an obtuse angle.
obtuse ∠ _____

∠CEJ

Explanation:
CEJ is an obtuse angle that is greater than a right angle.

Question 8.
Name a ray.

Ray JD

Explanation:
JD is a ray that has one endpoint and continues without an end in one direction.

Problem Solving

Use the figure at the right for 9–11.

Question 9.
Classify ∠AFD
_________

Obtuse Angle

Explanation:
AFD is an obtuse angle that is greater than a right angle.

Question 10.
Classify ∠CFE.
_________

Right Angle

Explanation:
∠CFE is a right angle that forms a square corner.

Question 11.
Name two acute angles.
acute ∠ _____ acute ∠ _____

∠AFB and ∠DFE

Explanation:
∠AFB and ∠DFE are two acute angles with less than a right angle.

Common Core – New – Page No. 554

Lesson Check

Question 1.
The hands of a clock show the time 12:25.

Which best describes the angle between the hands of the clock?
Options:
a. acute
b. right
c. obtuse
d. straight

c. obtuse

Explanation:
The hands of the time 12:25 are forming at greater than a right angle. So, the answer is the Obtuse angle.

Spiral Review

Question 3.
Jan’s pencil is 8.5 cm long. Ted’s pencil is longer. Which could be the length of Ted’s pencil?
Options:
a. 0.09 cm
b. 0.8 cm
c. 8.4 cm
d. 9.0 cm

d. 9.0 cm

Explanation:
9 ones is greater than 8 ones. So, 9.0 cm > 8.5 cm

Question 4.
Kayla buys a shirt for $8.19. She pays with a$10 bill. How much change should she receive?
Options:
a. $1.81 b.$1.89
c. $2.19 d.$2.81

a. $1.81 Explanation: Kayla buys a shirt for$8.19. She pays with a $10 bill. To find the change she received,$10 – $8.19 = 1.81 Question 6. Jose jumped 8 $$\frac{1}{3}$$ feet. This was 2 $$\frac{2}{3}$$ feet farther than Lila jumped. How far did Lila jump? Options: a. 5 $$\frac{1}{3}$$ b. 5 $$\frac{2}{3}$$ c. 6 $$\frac{1}{3}$$ d. 11 Answer: b. 5 $$\frac{2}{3}$$ Explanation: Jose jumped 8 $$\frac{1}{3}$$ feet. This was 2 $$\frac{2}{3}$$ feet farther than Lila jumped. 8 $$\frac{1}{3}$$ – 2 $$\frac{2}{3}$$ = $$\frac{25}{3}$$ – $$\frac{8}{3}$$ = $$\frac{7}{3}$$ = 5 $$\frac{2}{3}$$ Page No. 557 Classify each triangle. Write acute, right, or obtuse. Question 2. _____ Answer: Obtuse triangle; Angle B and Angle C are both acute. Angle A is obtuse. Explanation: From triangle ABC, Angle B, and Angle C are both acute with less than a right angle. Angle A is obtuse angle that is greater than a right angle. Question 3. _____ Answer: Obtuse triangle; Angle A and Angle C are both acute. Angle B is obtuse. Explanation: From triangle ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle. A triangle with an obtuse angle is called an obtuse triangle. Question 4. _____ Answer: Acute triangle; Angle A, Angle B, and Angle C are acute angles. Explanation: From triangle ABC, Angle A, Angle B, and Angle C are acute angles with less than a right angle. A triangle with three acute angles called an acute triangle. So, the given triangle is an acute triangle. Question 6. _____ Answer: Acute triangle; Angle A, Angle B, and Angle C are acute angles. Explanation: From triangle ABC, Angle A, Angle B, and Angle C are acute angles with less than a right angle. A triangle with three acute angles called an acute triangle. So, the given triangle is an acute triangle. Question 7. _____ Answer: Right Triangle; ∠A and ∠C are acute angles. ∠B is Right angle Explanation: ∠A and ∠C are acute angles with less than a right angle. ∠B is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle. Question 8. Cross out the figure that does not belong. Explain. Type below: _________ Answer: Explanation: From the given image, 1, 3, and 4 have two acute angles, and one obtuse angle. 2 have three acute angles. Page No. 558 Use the Venn diagram for 9–10. Question 9. Which triangles do NOT have an obtuse angle? Explain. _______ triangles Answer: 4 triangles; Triangle DEF, Triangle SPN, Triangle ABC, and Triangle GHP are don’t have an obtuse angle. Triangle DEF, Triangle SPN are acute angles. An acute triangle is a triangle with three acute angles. Triangle ABC, and Triangle GHP are right angles. A right triangle is a triangle with one right angle. The sum of the triangle is 180 degrees. A right triangle has 90 degrees. So, the remaining angles must be acute angles. Question 10. How many triangles have at least two acute angles? Explain. _______ triangles Answer: 4 triangles; Triangle DEF, Triangle SPN, Triangle ABC, and Triangle GHP at least two acute angles. Triangle DEF, Triangle SPN are acute angles. An acute triangle is a triangle with three acute angles. Triangle ABC, and Triangle GHP are right angles. A right triangle is a triangle with one right angle and two acute angles. Question 11. Use the square shown at the right. Draw a line segment from point M to point P. Name and classify the triangles formed by the line segment. Type below: _________ Answer: Angle MNP and Angle MQP Explanation: The line segment from M to P forms Angle MNP and Angle MQP. Question 12. Write the letter of the triangle under its correct classification. Type below: _________ Answer: Explanation: Triangle A and triangle B have three acute angles. So, they are acute triangles. Triangle D and triangle F have one obtuse angle. So, they are obtuse triangles. Triangle C and triangle E have one right angle. So, they are right triangles. Common Core – New – Page No. 559 Classify Triangles Classify each triangle. Write acute, right, or obtuse. Question 1. Think: Angles A and C are both acute. Angle B is obtuse. Answer: Obtuse triangle; Angle A and Angle C are both acute. Angle B is obtuse. Explanation: From triangle ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle. Question 4. _________ Answer: Obtuse triangle; Angle L and Angle N are both acute. Angle M is obtuse. Explanation: From triangle LMN, Angle L and Angle N are both acute with less than a right angle. Angle M is an obtuse angle that is greater than a right angle. A triangle with an obtuse angle is called an obtuse triangle. Problem Solving Question 5. Use figure ABCD below. Draw a line segment from point B to point D. Name and classify the triangles formed. Two _________ triangles △ _________ △ _________ Answer: Two Acute triangles. △ ABD △ BCD Explanation: If we draw a line segment from point B to point D, then there are two traingles formed with less than right angles. They are △ ABD and △ BCD. Question 6. Use figure ABCD below. Draw a line segment from point A to point C. Name and classify the triangles formed. Two _________ triangles △ _________ △ _________ Answer: Two Acute triangles. △ ABC △ ADC Explanation: If we draw a line segment from point A to point C, then there are two traingles formed with less than right angles. They are △ ABC and △ ADC. Common Core – New – Page No. 560 Lesson Check Question 1. Stephen drew this triangle. How many obtuse angles does the triangle have? Options: a. 0 b. 1 c. 2 d. 3 Answer: a. 0 Explanation: The given image has three acute angles. So, there are 0 obtuse angles. Spiral Review Question 3. Oliver drew the figure below to show light traveling from the sun to Earth. Name the figure he drew. Options: a. segment SE b. ray SE c. line SE d. ray ES Answer: b. ray SE Explanation: SE is a ray that has one endpoint and continues without an end in one direction. Question 6. A basketball team averaged 105 points per game. How many points did the team score in 6 games? Options: a. 605 points b. 630 points c. 900 points d. 6,030 points Answer: b. 630 points Explanation: A basketball team averaged 105 points per game. They score in 6 games = 6 x 105 = 630 points. Page No. 563 Question 1. Draw and label $$\overline{Q R} \| \overline{S T}$$. Think: Parallel lines never intersect. Parallel line segments are parts of parallel lines. Type below: _________ Answer: $$\overline{Q R} \| \overline{S T}$$ Explanation: Parallel lines never intersect. Parallel line segments are parts of parallel lines. Use the figure for 2 and 3. Question 2. Name two line segments that appear to be parallel. Type below: _________ Answer: Line Segment CB and Line Segment DF. Explanation: Line Segment CB and Line Segment DF are parallel lines. The both lines never intersect and are always the same distance apart. Question 3. Name two line segments that appear to be perpendicular. Type below: _________ Answer: Line Segment CB and Line Segment BF are perpendicular lines. Explanation: Line Segment CB and Line Segment DF are perpendicular lines. Both lines intersect to form four right angles. Use the figure for 4–5. Question 4. Name a pair of lines that are perpendicular. Type below: _________ Answer: FJ and HG are perpendicular lines. Explanation: FJ and HG lines intersect each other and form four right angles. Question 5. Name a pair of lines that appear to be parallel. Type below: _________ Answer: DC and FJ are parallel lines. Explanation: DC and FJ are never intersected and are always the same distance apart. Question 6. $$\overline{R S} \| \overline{T U}$$ Type below: _________ Answer: $$\overline{R S} \| \overline{T U}$$ Explanation: Parallel lines never intersect. Parallel line segments are parts of parallel lines. Question 9. $$\overset { \longleftrightarrow }{ JK }$$ ⊥ $$\overset { \longleftrightarrow }{ LM }$$ Type below: _________ Answer: $$\overset { \longleftrightarrow }{ JK }$$ ⊥ $$\overset { \longleftrightarrow }{ LM }$$ Explanation: JK and LM are two lines that intersected each other to form right angles. Question 10. $$\overset { \longleftrightarrow }{ ST }$$ intersecting $$\overset { \longleftrightarrow }{ UV }$$ at point X Type below: _________ Answer: Explanation: ST and UV are two lines intersecting at point X. Question 11. $$\overset { \longleftrightarrow }{ AB }$$ || $$\overset { \longleftrightarrow }{ FG }$$ Type below: _________ Answer: $$\overset { \longleftrightarrow }{ AB }$$ || $$\overset { \longleftrightarrow }{ FG }$$ Explanation: Parallel lines never intersect. Parallel line segments are parts of parallel lines. Use the figure for 12–13. Question 12. Dan says that $$\overset { \longleftrightarrow }{ HL }$$ is parallel to $$\overset { \longleftrightarrow }{ IM }$$. Is Dan correct? Explain. _____ Answer: No; HL and IM are not parallel lines. Parallel lines are always the same distance apart. But from the given image, the H and I may intersect if the line is extended. Question 13. Name two intersecting line segments that are not perpendicular. Type below: _________ Answer: JM and KG are two intersecting line segments and are also not perpendicular. Page No. 564 Use the house plan at the right for 14–16. Question 14. What geometric term describes a corner of the living room? _________ Answer: The corner of the living room is a vertex. Corners of any shape are vertexes. Question 15. Name three parts of the plan that show line segments. _________ Answer: Kitchen, Living Room, and Master Bedroom. Question 16. Name a pair of line segments that appear to be parallel _________ Answer: Two sidelines of Living Room are parallel. Two sidelines of Master Bedroom are parallel. Use the map at the right for 17–19. Question 17. Name a street that appears to be parallel to S 17th Street. _________ Answer: S 18th Street Explanation: S 18th Street is parallel to S 17th Street. They never meet each other and are always the same distance apart. Question 18. Use Diagrams Name a street that appears to be parallel to Vernon Street. _________ Answer: Perry Street Explanation: Perry Street is parallel to Vernon Street. They never meet each other and are always the same distance apart. Question 19. Name a street that appears to be perpendicular to S 19th Street. _________ Answer: Austin Street Explanation: Austin Street is perpendicular to S 19th Street. They are intersect with each other and form four right angles. Question 20. Choose the labels to make a true statement. Type below: _________ Answer: Line AB is perpendicular to Line EF. Common Core – New – Page No. 565 Parallel Lines and Perpendicular Lines Use the figure for 1–3. Question 1. Name a pair of lines that appear to be perpendicular. Think: Perpendicular lines form right angles. $$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ EF }$$ appear to form right angles. $$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ EF }$$ Answer: $$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ EF }$$ Explanation: Perpendicular lines form right angles. $$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ EF }$$ appear to form right angles. $$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ EF }$$ Question 2. Name a pair of lines that appear to be parallel. _____ and _____ Answer: $$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ CD}$$ Explanation: Parallel lines never interest each other. $$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ CD}$$ are parallel lines. Question 3. Name another pair of lines that appear to be perpendicular. _____ and _____ Answer: $$\overset { \longleftrightarrow }{ CD }$$ and $$\overset { \longleftrightarrow }{ EF }$$ Explanation: Perpendicular lines form right angles. $$\overset { \longleftrightarrow }{ CD }$$ and $$\overset { \longleftrightarrow }{ EF }$$ appear to form right angles. $$\overset { \longleftrightarrow }{ CD }$$ and $$\overset { \longleftrightarrow }{ EF }$$ Draw and label the figure described. Question 6. $$\overset { \longleftrightarrow }{ FH }$$ ⊥ $$\overset { \longleftrightarrow }{ JK }$$ Answer: Explanation: FH and JK are two lines that intersect each other to form four right angles. Problem Solving Use the street map for 7–8. Question 7. Name two streets that intersect but do not appear to be perpendicular. Type below: _________ Answer: Maple and Oak or Oak and Birch Explanation: Maple and Oak or Oak and Birch; They are intersecting with each other and not perpendicular. Question 8. Name two streets that appear to be parallel to each other. Type below: _________ Answer: Maple and Birch Explanation: Maple and Birch are streets and do not intersect with each other. They appear to be parallel to each other. Common Core – New – Page No. 566 Lesson Check Question 1. Which capital letter appears to have perpendicular line segments? Options: a. N b. O c. T d. V Answer: c. T Explanation: T has two lines and is interesting to form four right angles. Question 2. In the figure, which pair of line segments appear to be parallel? Options: a. $$\overline{F G} \text { and } \overline{G H}$$ b. $$\overline{F J} \text { and } \overline{G H}$$ c. $$\overline{F G} \text { and } \overline{J H}$$ d. $$\overline{J H} \text { and } \overline{F J}$$ Answer: c. $$\overline{F G} \text { and } \overline{J H}$$ Explanation: $$\overline{F G} \text { and } \overline{J H}$$ are parallel lines that never intersect Spiral Review Question 3. Nolan drew a right triangle. How many acute angles did he draw? Options: a. 0 b. 1 c. 2 d. 3 Answer: c. 2 Explanation: A triangle with one right angle will have two acute angles. Question 4. Mike drank more than half the juice in his glass. What fraction of the juice could Mike have drunk? Options: a. $$\frac{1}{3}$$ b. $$\frac{2}{5}$$ c. $$\frac{3}{6}$$ d. $$\frac{5}{8}$$ Answer: d. $$\frac{5}{8}$$ Explanation: Mike drank more than half the juice in his glass. He drunk $$\frac{5}{8}$$ of the juice. Question 5. A school principal ordered 1,000 pencils. He gave an equal number to each of 7 teachers until he had given out as many as possible. How many pencils were left? Options: a. 2 b. 4 c. 6 d. 142 Answer: c. 6 Explanation: A school principal ordered 1,000 pencils. He gave an equal number to each of 7 teachers until he had given out as many as possible. He shared 142 pencils for each of 7 teachers. So, 142 X 7 = 994. The remaining pencils are 6. Question 6. A carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. How many ounces of juice did she buy? Options: a. 364 ounces b. 370 ounces c. 384 ounces d. 402 ounces Answer: c. 384 ounces Explanation: A carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. 64 X 6 = 384 ounces of juice she can buy. Page No. 569 Question 1. Tell whether the quadrilateral is also a trapezoid, parallelogram, rhombus, rectangle, or square. Think: ____ pairs of parallel sides ____ sides of equal length ____ right angles Quadrilateral ABCD is also a __________ __________ Answer: 2 pairs of parallel sides 4 sides of equal length 0 right angles. Quadrilateral ABCD is also a Rhombus Explanation: A Rhombus is a quadrilateral that has 2 pairs of parallel sides and 4 sides of equal lengths. Classify each figure as many ways as possible. Write quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square. Question 4. _________ _________ _________ Answer: Quadrilateral, Parallelogram, and Rhombus Explanation: 2 pairs of parallel sides 4 sides of equal length 0 right angles. Given quadrilateral is Rhombus and Parallelogram. A Rhombus is a quadrilateral that has 2 pairs of parallel sides and 4 sides of equal lengths, and 0 right angles. Question 5. _________ _________ Answer: Quadrilateral and Parallelogram Explanation: 2 pairs of parallel sides 2 pairs of sides of equal length 0 right angles. Given quadrilateral is Parallelogram. A Parallelogram is a quadrilateral that has 2 pairs of parallel sides and 2 pairs of sides of equal lengths, and 0 right angles. Question 6. _________ _________ _________ Answer: Quadrilateral and Square Explanation: 2 pairs of parallel sides 4 sides of equal length 4 right angles. Given quadrilateral is Square. A Square is a quadrilateral that has 2 pairs of parallel sides and 4 sides of equal lengths, and 4 right angles. Question 7. _________ _________ Answer: Quadrilateral and Trapezoid Explanation: 1 pair of parallel sides 0 sides of equal length 0 right angles. Given quadrilateral is Trapezoid. A Square is a quadrilateral that has 1 pair of parallel sides and 0 sides of equal lengths, and 0 right angles. Page No. 570 Question 9. Classify the figure. Select all that apply. Options: a. quadrilateral b. trapezoid c. parallelogram d. rectangle e. rhombus f. square Answer: a. quadrilateral b. trapezoid c. parallelogram Explanation: A Parallelogram is a quadrilateral that has 2 pairs of parallel sides and 2 pairs of sides of equal lengths, and 0 right angles. The Louvre Museum is located in Paris, France. Architect I. M. Pei designed the glass and metal structure at the main entrance of the museum. This structure is called the Louvre Pyramid. Below is a diagram of part of the entrance to the Louvre Pyramid. Question 10. Describe the quadrilaterals you see in the diagram. _________ _________ Answer: Trapezoid and Rhombus Explanation: There are 2 quadrilaterals available in the given image. One is a Trapezoid with 1 pair of parallel sides. Another one is Rhombus is with 2 pairs of parallel sides and 4 sides of equal lengths, and 0 right angles. Question 11. How many triangles do you see in the diagram? Explain. ______ triangles Answer: 11 triangles Explanation: The given image has 11 triangles Common Core – New – Page No. 571 Classify Quadrilaterals Classify each figure as many ways as possible. Write quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square. Question 1. Think: 2 pairs of parallel sides 4 sides of equal length 0 right angles quadrilateral, parallelogram, rhombus Answer: Quadrilateral, Parallelogram, and rhombus. Explanation: 2 pairs of parallel sides 4 sides of equal length 0 right angles Quadrilateral, Parallelogram, and rhombus. Question 2. Type below: _________ Answer: Quadrilateral, Parallelogram, Rectangle Explanation: 2 pairs of parallel sides 2 pairs of sides of equal length 4 right angles Quadrilateral, Parallelogram, Rectangle Question 3. Type below: _________ Answer: Explanation: 1 pair of parallel sides 2 sides of equal length 0 right angles Quadrilateral, Trapezoid Question 4. Type below: _________ Answer: Quadrilateral Explanation: 0 pair of parallel sides 0 sides of equal length 0 right angles Quadrilateral Question 5. Type below: _________ Answer: Quadrilateral, Parallelogram, and rhombus Explanation: 2 pairs of parallel sides 4 sides of equal length 0 right angles Quadrilateral, Parallelogram, and rhombus Question 6. Type below: _________ Answer: Explanation: 1 pair of parallel sides 0 sides of equal length 2 right angles Quadrilateral, Trapezoid Question 7. Type below: _________ Answer: Explanation: 2 pairs of parallel sides 2 pairs of sides of equal length 0 right angles Quadrilateral, Parallelogram Problem Solving Common Core – New – Page No. 572 Lesson Check Question 1. Joey is asked to name a quadrilateral that is also a rhombus. What should be his answer? Options: a. square b. rectangle c. parallelogram d. trapezoid Answer: a. square Explanation: The quadrilateral square is also called a rhombus. Both square and rhombus have 2 pairs of parallel sides and 4 sides of equal length. Question 2. Which quadrilateral has exactly one pair of parallel sides? Options: a. square b. rhombus c. parallelogram d. trapezoid Answer: d. trapezoid Explanation: A trapezoid has exactly one pair of parallel sides. Spiral Review Question 3. Terrence has 24 eggs to divide into equal groups. What are all the possible numbers of eggs that Terence could put in each group? Options: a. 1, 2, 3, 4 b. 2, 4, 6, 8, 12 c. 1, 2, 3, 4, 6, 8, 12, 24 d. 24, 48, 72, 96 Answer: c. 1, 2, 3, 4, 6, 8, 12, 24 Explanation: Terrence has 24 eggs to divide into equal groups. Terence could put in each group in 1, 2, 3, 4, 6, 8, 12, 24 ways. Question 4. In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7. What number should Jenna say? Options: a. 31 b. 35 c. 39 d. 43 Answer: b. 35 Explanation: In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7. 7 + 4 = 11 11 + 4 = 15 15 + 4 = 19 19 + 4 = 23 23 + 4 = 27 27 + 4 = 31 31 + 4 = 35. Jenna says 35. Question 5. Lou eats $$\frac{6}{8}$$ of a pizza. What fraction of the pizza is left over? Options: a. $$\frac{1}{8}$$ b. $$\frac{1}{4}$$ c. $$\frac{1}{2}$$ d. $$\frac{3}{4}$$ Answer: b. $$\frac{1}{4}$$ Explanation: Lou eats $$\frac{6}{8}$$ of a pizza. So, 6 parts of pizza is finished and remaining 2 parts of pizza is remained. So, the left over pizza is $$\frac{2}{8}$$ = $$\frac{1}{4}$$. Question 6. Which capital letter appears to have parallel lines? Options: a. D b. L c. N d. T Answer: c. N Explanation: N has two parallel lines that never intersect each other. Page No. 573 Choose the best term from the box to complete the sentence. Question 1. A _______ is part of a line between two endpoints. _________ Answer: line segment Question 2. A _______ forms a square corner. _________ Answer: Right angle Question 3. An _______ is greater than a right angle and less than a straight angle. _________ Answer: Obtuse angle Question 4. The two-dimensional figure that has one endpoint is a ________. _________ Answer: ray Question 5. An angle that forms a line is called a _______. _________ Answer: straight line Question 6. On the grid below, draw a polygon that has 2 pairs of parallel sides, 2 pairs of sides equal in length, and 2 acute and 2 obtuse angles. Tell all the possible names for the figure. Type below: _________ Answer: Parallelogram Explanation: The possible polygon that has 2 pairs of parallel sides, 2 pairs of sides equal in length, and 2 acute and 2 obtuse angles is Parallelogram. Draw the figure. Question 7. parallel lines Type below: _________ Answer: Explanation: QR and ST are two parallel lines. they never intersect each other. Question 8. obtuse ∠ABC Type below: _________ Answer: Explanation: From triangle, ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle. Question 9. intersecting lines that are not perpendicular Type below: _________ Answer: Explanation: ST and UV are two lines intersecting at point X. Question 10. acute ∠RST Type below: _________ Answer: Page No. 574 Question 14. What is the correct name of the figure shown? _________ Answer: Ray Explanation: EF is a ray that has one endpoint and continues without an end in one direction. Question 15. Describe the angles of an obtuse triangle. Type below: _________ Answer: An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles. Page No. 577 Tell whether the parts on each side of the line match. Is the line a line of symmetry? Write yes or no. Question 1. ____ Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Question 2. ____ Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Question 3. ____ Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Question 4. ____ Answer: No; Explanation: The line of symmetry divides a shape into two parts that are not with the same size and shape. Tell if the blue line appears to be a line of symmetry. Write yes or no. Question 5. ____ Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Question 6. ____ Answer: No; Explanation: The line of symmetry divides a shape into two parts that are not the same size and shape. Question 7. ____ Answer: No; Explanation: The line of symmetry divides a shape into two parts that are not the same size and shape. Question 8. ____ Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Tell if the blue line appears to be a line of symmetry. Write yes or no. Question 9. ____ Answer: No; Explanation: The line of symmetry divides a shape into two parts that are not the same size and shape. Question 10. ____ Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Question 11. ____ Answer: No; Explanation: The line of symmetry divides a shape into two parts that are not with the same size and shape. Question 12. ____ Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Question 13. Which best describes the symmetry in the letter I? Type below: ________ Answer: The two parts of the folded I match exactly. The fold line is a line of symmetry. Explanation: Take the Horizontal line in the middle of the Letter I. Cut out the tracing. Fold the tracing over a horizontal line. The two parts of the folded I match exactly. The fold line is a line of symmetry. Page No. 578 Question 14. Which shape has a correctly drawn line of symmetry? a. What do you need to find? Type below: ________ Answer: Find the shape that has an exact line of symmetry. Question 14. b. How can you tell if the line of symmetry is correct? Type below: ________ Answer: If the two parts of the folded match exactly, then the line is a line of symmetry. Question 14. c. Tell how you solved the problem. Type below: ________ Answer: From fig 1 to 4, the fig 2 is has a line of symmetry that can exactly separate the two parts equally. Question 14. d. Circle the correct shape above. Type below: ________ Answer: Question 15. Reason Abstractly Draw a line of symmetry in the figure shown. Answer: Question 16. Evie’s birthday is on the 18th of May. Since May is the 5th month, Evie wrote the date as shown. Evie says all the numbers she wrote have line symmetry. Is she correct? Explain. Answer: No; The number 5 doesn’t have a line of symmetry. So, Evie explanation is wrong. Common Core – New – Page No. 579 Line Symmetry Tell if the dashed line appears to be a line of symmetry. Write yes or no. Question 1. yes Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Question 2. ____ Answer: No; Explanation: The line of symmetry divides a shape into two parts that are not with the same size and shape. Question 3. ____ Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Question 4. ____ Answer: No; Explanation: The line of symmetry divides a shape into two parts that are not with the same size and shape. Question 5. ____ Answer: No; Explanation: The line of symmetry divides a shape into two parts that are not with the same size and shape. Question 6. ____ Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Question 7. ____ Answer: No; Explanation: The line of symmetry divides a shape into two parts that are not with the same size and shape. Question 8. ____ Answer: Yes; Explanation: The line of symmetry divides a shape into two parts that are the same size and shape. Complete the design by reflecting over the line of symmetry. Question 9. Answer: Question 10. Answer: Problem Solving Question 11. Kara uses the pattern below to make paper dolls. The dashed line represents a line of symmetry. A complete doll includes the reflection of the pattern over the line of symmetry. Complete the design to show what one of Kara’s paper dolls looks like. Answer: Common Core – New – Page No. 580 Lesson Check Question 1. Which best describes the line of symmetry in the letter D? Options: a. horizontal b. vertical c. diagonal d. half turn Answer: a. horizontal Explanation: The horizontal line of symmetry in the letter D can exactly separate two parts equally. Question 2. Which shape has a correctly drawn line of symmetry? Options: a. b. c. d. Answer: b. Explanation: Image b has a line of symmetry that separates two parts equally. Spiral Review Question 3. The class has 360 unit cubes in a bag. Johnnie divides the unit cubes equally among 8 groups. How many unit cubes will each group get? Options: a. 40 b. 44 c. 45 d. 48 Answer: c. 45 Explanation: The class has 360 unit cubes in a bag. Johnnie divides the unit cubes equally among 8 groups. 360/8= 45. Question 4. There are 5,280 feet in one mile. How many feet are there in 6 miles? Options: a. 30,680 b. 31,260 c. 31,608 d. 31,680 Answer: d. 31,680 Explanation: There are 5,280 feet in one mile. So, for 6 miles = 6 x 5, 280 = 31,680. Page No. 583 Question 1. The shape at the right has line symmetry. Draw the 2 lines of symmetry. Type below: _________ Answer: Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1. Question 2. _________ Answer: more than 1 Explanation: There is more than 1 line of symmetries that separates two parts equally. Question 3. _________ Answer: more than 1 Explanation: There is more than 1 lines of symmetries that separates two parts equally. Question 4. _________ Answer: 1 line Explanation: There is 1 line of symmetry that separates two parts equally. Question 5. _________ Answer: zero lines Explanation: There is no line of symmetries that separates two parts equally. Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1. Question 6. _________ Answer: more than 1 Explanation: There is more than 1 lines of symmetries that separate two parts equally. Question 7. _________ Answer: zero lines Explanation: There is no line of symmetries that separates two parts equally. Question 8. _________ Answer: zero lines Explanation: There is no line of symmetries that separates two parts equally. Question 9. _________ Answer: 1 line Explanation: There is 1 line of symmetry that separates two parts equally. Practice: Copy and Solve Does the design have line symmetry? Write yes or no. If your answer is yes, draw all lines of symmetry. Question 10. ____ Answer: Yes; Question 11. _____ Answer: No; Question 12. _____ Answer: Yes; Question 13. _____ Answer: No; Question 14. Draw a figure that has 5 sides and exactly 1 line of symmetry. Type below: _________ Answer: Explanation: the above 5 sides shape has only 1 line symmetry Page No. 584 Use the chart for 15–17. Question 15. Which letters appear to have only 1 line of symmetry? Type below: _________ Answer: A, B, C, D, E, T, U, V, W Explanation: The letters A, B, C, D, E, T, U, V, W have only 1 line of symmetry. Question 16. Which letters appear to have zero lines of symmetry? Type below: _________ Answer: J, N, S Explanation: The letters J, N, S have only zero lines of symmetry. Question 17. The letter C has horizontal symmetry. The letter A has vertical symmetry. Which letters appear to have both horizontal and vertical symmetry? Type below: _________ Answer: H and I Explanation: The letters H and I have both horizontal and vertical symmetry. Question 18. Verify the Reasoning of Others Jeff says that the shape has only 2 lines of symmetry. Does his statement make sense? Explain. Type below: _________ Answer: No; Jeff’s explanation is wrong. Because the given shape has only 2 lines of symmetry. Question 19. Match each figure with the correct number of lines of symmetry it has. Type below: _________ Answer: Common Core – New – Page No. 585 Find and Draw Lines of Symmetry Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1. Question 1. 1 Answer: more than 1 Explanation: There is more than 1 line of symmetry that separates two parts equally. Question 2. ________ Answer: more than 1 Explanation: There is more than 1 line of symmetry that separates two parts equally. Question 3. ________ Answer: Zero Explanation: There are 0 lines of symmetries. Question 4. ________ Answer: more than 1 Explanation: There is more than 1 line of symmetry that separates two parts equally. Does the design have line symmetry? Write yes or no. If your answer is yes, draw all lines of symmetry. Question 5. _____ Answer: Yes; Question 6. _____ Answer: Yes; _____ Answer: No; Question 8. ______ Answer: Yes; Draw a shape for the statement. Draw the line or lines of symmetry. Question 9. zero lines of symmetry Answer: Question 10. 1 line of symmetry Answer: Question 11. 2 lines of symmetry Answer: Problem Solving Use the chart for 12–13. Question 12. Which number or numbers appear to have only 1 line of symmetry? _____ Answer: 3 Explanation: The number 3 has only 1 line of symmetry. Question 13. Which number or numbers appear to have 2 lines of symmetry? _____ Answer: 0 and 8 Explanation: The numbers 0 and 8 appear to have 2 lines of symmetry. Common Core – New – Page No. 586 Lesson Check Question 1. How many lines of symmetry does this shape appear to have? Options: a. 0 b. 2 c. 6 d. 12 Answer: c. 6 Explanation: The given shape has 6 lines of symmetries. Question 2. Which of the following shapes appears to have exactly 1 line of symmetry? Options: a. b. c. d. Answer: d. Explanation: The trapezoid has exactly 1 line of symmetry. Spiral Review Question 3. Richard practiced each of 3 piano solos for $$\frac{5}{12}$$ hour. How long did he practice in all? Options: a. $$\frac{2}{3}$$ hours b. 1 $$\frac{1}{4}$$ hours c. 1 $$\frac{1}{3}$$ hours d. 1 $$\frac{5}{12}$$ hours Answer: b. 1 $$\frac{1}{4}$$ hours Explanation: Richard practiced each of 3 piano solos for $$\frac{5}{12}$$ hour. $$\frac{5}{12}$$ hour = 1 $$\frac{1}{4}$$ hours hours. Question 6. Kevin draws a figure that has four sides. All sides have the same length. His figure has no right angles. What figure does Kevin draw? Options: a. square b. trapezoid c. rhombus d. rectangle Answer: c. rhombus Explanation: Page No. 589 Question 1. Marisol is making a pattern with blocks. What might the missing shape be? First, look at the blocks. Next, describe the pattern. Type below: _________ Answer: The first image 1 has three line segments. The next shape will have four line segments. Question 1. Finally, draw the missing shape. Type below: _________ Answer: Question 2. Use the shapes to write a number pattern. Then describe the pattern in the numbers. Answer: Shape 1: Triangle Shape 2: Square Shape 3: Pentagon Shape 4: Hexagon Shape 5: Heptagon Question 3. What if the pattern continued? Write an expression to describe the number of sides the sixth shape has in Marisol’s pattern. Type below: _________ Answer: If the pattern continued, then the next shape will have one more extra line segment to it. The sixth shape will become the octagon. Shape 6: Octagon Question 4. Sahil made a pattern using circles. The first nine circles are shown. Describe the pattern. If Sahil continues the pattern, what might the next three circles be? Type below: _________ Answer: The pattern is repeated for every three circles. One big circle followed by two small circles. Page No. 590 Use the toy quilt designs for 5–6. Question 5. Lu is making a quilt that is 20 squares wide and has 24 rows. The border of the quilt is made by using each toy design equally as often. Each square can hold one design. How many of each design does she use for the border? ______ times Answer: The border will have 20 squares two times, and 24 squares two times as well, that is the perimeter or the border, because a quilt has 4 sides: 20 X 2 + 24 X 2 = 40 + 48 = 88 So, the border will have 88 squares in total. So if the border can have only one design, Lu can use any toy design 88 times if she wants the border to have the same toy design in it. Question 6. Communicate Starting in the first square of her quilt, Lu lined up her toy designs in this order: plane, car, fire truck, helicopter, crane, and wagon. Using this pattern unit, which design will Lu place in the fifteenth square? Explain how you found your answer. _________ Answer: The answer is fire truck. As the pattern repeats, the fifteenth square will fire the truck. Question 8. Norris drew the pattern shown. Label the circles to show the colors in the fourth figure of the pattern. Type below: _________ Answer: Common Core – New – Page No. 591 Problem Solving Shape Patterns Solve each Problem. Question 1. Marta is using this pattern to decorate a picture frame. Describe the pattern. Draw what might be the next three figures in the pattern. Possible answer: the pattern repeats: one trangle followed by two squares. Answer: The pattern repeats one triangle followed by two squares. Question 2. Describe the pattern. Draw what might be the next three figures in the pattern. How many circles are in the sixth figure in the pattern? _____ circles Answer: Add one more column with 1 more circle than in the previous column; 21. Question 3. Larry stencils this pattern to make a border at the top of his bedroom walls. Describe the pattern. Draw what might be the missing figure in the pattern. Answer: 2 triangles placed side to side followed by 2 sets of 2 triangles placed vertex to vertex Common Core – New – Page No. 592 Lesson Check Question 1. What might be the next three figures in this pattern? Options: a. b. c. d. Answer: a. Explanation: the pattern has odd numbers of up arrows then even number of down arrows. So, the next three figures are . Question 2. Which might be the missing figure in the following pattern? Options: a. b. c. d. Answer: a. Explanation: From the pattern, the missing image will have a vertical rectangle with the circle and X mark in it. Spiral Review Question 4. Olivia finished a race in 40.64 seconds. Patty finished the race in 40.39 seconds. Miguel finished the race in 41.44 seconds. Chad finished the race in 40.46 seconds. Who finished the race in the least time? Options: a. Olivia b. Patty c. Miguel d. Chad Answer: b. Patty Explanation: Patty finished the race in 40.39 seconds which is the least time compared to others. Question 5. Justin bought 6 ribbons for an art project. Each ribbon is $$\frac{1}{4}$$ yard long. How many yards of ribbon did Justin buy? Options: a. $$\frac{2}{3}$$ yard b. 1 $$\frac{1}{4}$$ yards c. 1 $$\frac{1}{2}$$ yards d. 1 $$\frac{3}{4}$$ yards Answer: c. 1 $$\frac{1}{2}$$ yards Explanation: Justin bought 6 ribbons for an art project. Each ribbon is $$\frac{1}{4}$$ yard long. So, 6 X $$\frac{1}{4}$$ = $$\frac{3}{2}$$ = 1 $$\frac{1}{2}$$ yards. Question 6. Kyle and Andrea were asked to make a list of prime numbers. Kyle: 1, 3, 7, 19, 23 Andrea: 2, 3, 5, 7, 11 Whose list is correct? Options: a. Only Kyle’s list b. Only Andrea’s list c. Both lists are correct. d. Neither list is correct. Answer: b. Only Andrea’s list Explanation: 1 is not a prime number. So, the answer is Only Andrea’s list is correct. Page No. 593 Question 1. Gavin is designing a kite. He sketched a picture of the kite. How many right angles does the kite appear to have? _____ right angles Answer: 0 right angles Explanation: There is no right angles in the given shape. Question 2. Write the letter of the triangle under its correct classification. Answer: Explanation: C and F are Acute angles with less than right angles. B and D are Obtuse Angles with more than right angles. A and E are Right Angles. Question 3. Select the angles that identify an obtuse triangle. Mark all that apply. Options: a. acute, acute, acute b. acute, acute, obtuse c. right, acute, acute d. obtuse, right, acute Answer: b. acute, acute, obtuse Explanation: An obtuse triangle will have one obtuse angle and two acute angles. Page No. 594 Question 4. Write the word that describes the part of Figure A written below. $$\overline{E B}$$ _________ $$\overset { \longleftrightarrow }{ AB }$$ _________ $$\overrightarrow{G A}$$ _________ ∠EBG _________ ∠CGB _________ Answer: $$\overline{E B}$$ line segment. $$\overset { \longleftrightarrow }{ AB }$$ Line. $$\overrightarrow{G A}$$ Ray. ∠EBG right angle. ∠CGB acute angle. Explanation: $$\overline{E B}$$ is a line segment that has two endpoints connected to form a line. $$\overset { \longleftrightarrow }{ AB }$$ is a Line that continues without an end in both directions. $$\overrightarrow{G A}$$ is a Ray that has one endpoint and continues without an end in one direction. ∠EBG right angle. ∠CGB is an acute angle with less than the right angle. Question 5. What term best describes the figure shown below? Answer: perpendicular lines Explanation: The lines are forming four right angles they form squares. So, both lines are perpendicular lines. Question 6. Naomi leaves for her trip to Los Angeles on the 12th day of August. Since August is the 8th month, Naomi wrote the date as shown. Naomi says all the numbers she wrote have line symmetry. Is she correct? Explain your thinking. _______ Answer: Naomi is incorrect. The number 2 does not have a line of symmetry because if it were cut out, there would be no way to fold it in half so that the two parts matched exactly. Page No. 595 Question 7. Max made a pennant that looks like a triangle. How can you classify the triangle based on its angles? The triangle is a(n) ____________ triangle. Answer: The triangle is an acute triangle. Explanation: The triangle is an acute triangle. because it has angles with less than right angles. Question 8. Choose the labels to make a true statement. _____ is parallel to ______ Answer: Line AB is parallel to line CD. Explanation: From the given image, Line AB is parallel to line CD. Question 9. Classify the figure. Select all that apply. Options: a. quadrilateral b. trapezoid c. parallelogram d. rectangle e. rhombus f. square Answer: a. quadrilateral b. trapezoid c. parallelogram d. rectangle Explanation: The given image has 2 parallel sides, 2 pairs of sides of length, and four right angles. So, the possible answers are quadrilateral, trapezoid, parallelogram, and rectangle. Page No. 596 Question 11. Match each figure with the correct number of lines of symmetry it has. Answer: Explanation: Image 1: 1 line of symmetry Image 2: 2 lines of symmetry Image 3: 0 lines of symmetry Image 4: More than 2 lines of symmetry. Question 12. Barb drew the pattern shown. Use the square shown to draw the missing pattern. □ Answer: Explanation: The fourth shape must consist of one extra square box in the top line and bottom line. Question 13. Claudia drew the figure below. Draw a line of symmetry on Claudia’s figure. Answer: Explanation: The image can have one line symmetry. Question 14. Write the word or words that best describe this figure. _________ Answer: Ray Explanation: The ray has one endpoint and continues without an end in one direction. Page No. 597 Question 16. Mike drew a figure with opposite sides parallel. Write the pairs of parallel sides. What figure is it? Answer: Line DG is parallel to Line FE and Line DE is parallel to Line GF; the figure is a parallelogram. Question 17. Circle the letter that does not have line symmetry. Answer: Explanation: The S does not have line symmetry. Question 18. Joseph made a pattern using ovals and rectangles. The first four figures of his pattern are shown. Draw the next figure in the pattern. Answer: Question 19. Jeremy drew Figure 1 and Louisa drew Figure 2. Part A Jeremy says both figures are rectangles. Do you agree with Jeremy? Support your answer. _____ Answer: Yes; both figures have 2 pairs of parallel sides, opposite sides that are equal in length, and 4 right angles. Question 19. Part B Louisa says both figures are rhombuses. Do you agree with Louisa? Support your answer. _____ Answer: No; figure 2 is a rhombus since it has 2 pairs of parallel sides and 4 sides of equal length. Figure 1 does not have 4 sides of equal length so it cannot be a rhombus. Page No. 598 Question 20. Veronica found the number of lines of symmetry for the figure below. How many lines of symmetry does it have? ______ lines of symmetry Answer: 2 lines of symmetry Explanation: the given shape can have 2 lines of symmetry. Question 21. Jordan drew the pattern below. Part A Describe the pattern. Answer: Each figure has 2 more squares than the preceding figure. Question 21. Part B Write a rule using numbers to find the number of squares in any figure in the pattern. Answer: multiply the figure number by 2. Question 21. Part C Draw Figure 5. Answer: Page No. 603 Tell what fraction of the circle the shaded angle represents. Question 1. $$\frac{□}{□}$$ Answer: $$\frac{1}{2}$$ Explanation: Half of the part is shaded out of the circle. So, the answer is 1/2. Question 2. $$\frac{□}{□}$$ Answer: $$\frac{1}{4}$$ Explanation: $$\frac{1}{4}$$ part of the circle is shaded out of the circle. Question 3. $$\frac{□}{□}$$ Answer: $$\frac{3}{4}$$ Explanation: 3 parts of the circle is shaded out of the circle Question 4. $$\frac{□}{□}$$ Answer: $$\frac{1}{1}$$ = 1 Explanation: The complete circle is shaded. So, the answer is 1. Question 5. $$\frac{□}{□}$$ Answer: $$\frac{1}{2}$$ Explanation: Half of the part is shaded out of the circle. So, the answer is 1/2. Question 6. $$\frac{□}{□}$$ Answer: $$\frac{1}{12}$$ Tell whether the angle on the circle shows a $$\frac{1}{4}, \frac{1}{2}, \frac{3}{4}$$, or 1 full turn clockwise or counterclockwise. Question 7. Type below: ________ Answer: $$\frac{3}{4}$$; counterclockwise Explanation: The image shows the counterclockwise and formed fraction of $$\frac{3}{4}$$. Question 8. Type below: ________ Answer: $$\frac{1}{2}$$; clockwise Explanation: The image shows the clockwise and formed fraction of $$\frac{1}{2}$$. Question 9. Type below: ________ Answer: $$\frac{1}{4}$$; clockwise Explanation: The image shows the clockwise and formed fraction of $$\frac{1}{4}$$. Question 10. Susan watched the game from 1 p.m. to 1:30 p.m. Describe the turn the minute hand made. Type below: ________ Answer: The minute hand made a $$\frac{1}{2}$$ turn clockwise. Page No. 604 Question 12. Malcolm drew this angle on the circle. Which of the following describes the angle? Mark all that apply. Options: a. $$\frac{3}{4}$$ turn b. $$\frac{1}{4}$$ turn c. clockwise d. counterclockwise Answer: a. $$\frac{3}{4}$$ turn d. counterclockwise Explanation: The image show the $$\frac{3}{4}$$ turn and also the counterclockwise. Sense or Nonsense? Question 13. Whose statement makes sense? Whose statement is nonsense? Explain your reasoning. Type below: __________ Answer: The girl’s statement makes sense. The boy’s statement makes non-sense. Because from the figure it is clearly shown that the shaded part is $$\frac{1}{4}$$ of the circle. There is no particular direction given to measure the shaded part. Conclusion: Finally, you will find detailed solutions to all questions that you’re looking for. So, you can attempt the exam with utmost confidence and secure good grades in the exams. The topics covered in Ch 10 Two-dimensional figures are such Lines, Rays, Angles, Classify Triangles by Angles, Parallel Lines and Perpendicular Lines, etc. Understand how to solve the problems of two-dimensional figures by accessing our Go Math Grade 4 Solution Key Chapter 10 Two-dimensional figures Homework Practice FL. Go Math Grade 2 Answer Key Chapter 2 Numbers to 1,000 Go Math Grade 2 Chapter 2 Answer Key Numbers to 1,000 Numbers to 1,000 Show What you know Identify Numbers to 30 Write how many. Question 1. Answer: Leaves = 17. Explanation: In the above-given figure, Given that, there are 17 leaves. so leaves = 17. Question 2. Answer: bug = 24. Explanation: In the above-given figure, Given that, there are 24 bugs. so bug = 24. Place Value: 2-Digit Numbers Circle the value of the red digit. Question 3. Answer: The value of the red digit = 4. Explanation: In the above-given figure, Given that, the place value of 2 digits. the number is 47. so the value of the red digit = 4. Question 4. Answer: The value of the red digit = 4. Explanation: In the above-given figure, Given that, the place value of 2 digits. the number is 84. so the value of the red digit = 4. Question 5. Answer: The value of the red digit = 6. Explanation: In the above-given figure, Given that, the place value of 2 digits. the number is 65. so the value of the red digit = 6 Compare 2-Digit Numbers Using Symbols Compare. Write >, <, or =. Question 6. Answer: 42 is greater than 37. Explanation: In the above-given question, given that, The numbers are 37, 42. 42 is greater than 37. Question 7. Answer: 40 is less than 33. Explanation: In the above-given question, given that, The numbers are 33, 40. 40 is less than 33. Numbers to 1,000 Vocabulary Builder Visualize It Fill in the boxes of the graphic organizer. Write sentences using fewer and more. Answer: Fewer. 9 pens are fewer than 11 pens. 3 pens are fewer than 6 pens. More: 11 pens are more than 9 pens. 6 pens are more than 3 pens. Explanation: In the above-given figure, given that the words more and fewer. Fewer. 9 pens are fewer than 11 pens. 3 pens are fewer than 6 pens. More: 11 pens are more than 9 pens. 6 pens are more than 3 pens. Understand Vocabulary Use the review words. Complete the sentences. Question 1. 3 and 9 are digits in the number 39. Answer: 3 and 9 are digits in the number 39. Explanation: In the above-given question, given that, 3 and 9 are digits in the number 39. Question 2. 7 is in the _ones__ place in the number 87. Answer: 7 is in the ones place in the number 87. Explanation: In the above-given figure, given that the place values. 7 is in the ones place in the number 87. Question 3. 8 is in the ___ place in the number 87. Answer: 8 is in the tens place in the number 87. Explanation: In the above-given figure, given that the place values. 8 is in the tens place in the number 87. Numbers to 1,000 Game: Fish for Digits Materials Play with a partner. 1. Name a place for a digit. You can say tens place or ones place. Toss the 2. Match the number on the and the place that you named with a fish. 3. Put a on that fish. Take turns. 4. Match all the fish. The player with more on the board wins. Answer: 1.The dice is in the tens place. 2. The dice named with the fish is 53. 3. The red on the fish is 53. Explanation: 1.The dice is in the tens place. 2. The dice named with the fish is 53. 3. The red on the fish is 53. Numbers to 1,000 Vocabulary Game Going Places with GOMATH! Words Guess the Word For 3 to 4 players Materials • timer How to Play 1. Take turns to play. 2. Choose a math word, but do not say it aloud. 3. Set the timer for 1 minute. 4. Give a one-word clue about your word. Give each player one chance to guess your word. 5. If nobody guesses correctly, repeat Step 4 with a different clue. Repeat until a player guesses the word or time runs out. 6. The first player to guess the word gets 1 point. If the player can use the word in a sentence, he or she gets 1 more point. Then that player gets a turn. 7. The first player to score 5 points wins. The Write Way Reflect Choose one idea. Write about it in the space below. • Draw and write about all the different ways you can show the number 482. Use a separate piece of paper for your drawing. • Explain how to compare two numbers. • Write sentences that include at least two of these terms. Answer: a. 400 + 80 + 2. 400 + 0 + 82. 300 + 180 + 2 200 + 280 + 2 100 + 380 + 2 b. 9 is greater than 3. 6 is less than 10. c. 2 is in the tens place is the digit 27. 400 + 80 + 2 is equal to the 482. Explanation: In the above-given question, Given words are placed value, is equal to, hundreds, and thousands. a. 400 + 80 + 2. 400 + 0 + 82. 300 + 180 + 2 200 + 280 + 2 100 + 380 + 2 b. 9 is greater than 3. 6 is less than 10. c. 2 is in the tens place is the digit 27. 400 + 80 + 2 is equal to the 482. Lesson 2.1 Group Tens as Hundreds Essential Question How do you group tens as hundreds? Answer: Ten groups of 10’s are 100. Explanation: In the above-given question, give that, group 10’s as 100. so 10 groups of 10’s are 100. Listen and Draw Circle groups of ten. Count the groups of ten. Answer: Ten groups of 10’s are 100. Explanation: In the above-given question, give that, group 10’s as 100. so 10 groups of 10’s are 100. Math Talk MATHEMATICAL PRACTICES Describe How many ones are in 3 tens? How many ones are in 7 tens? Explain. Answer: 30 ones are in 3 tens. 7 ones are in 7 tens. Explanation: In the above-given question, given that 30 ones are in 3 tens. 7 ones are in 7 tens. Share and Show MATH BOARD Write how many tens. Circle groups of 10 tens. Write how many hundreds. Write the number. Question 1. Answer: 20 tens. 2 hundred. The number is 200. Explanation: In the above-given figure, given that there are 20 tens. 2 hundred. The number is 200. Question 2. Answer: 30 tens. 3 hundred. The number is 300. Explanation: In the above-given figure, given that there are 30 tens. 3 hundred. The number is 300. Question 3. Answer: 40 tens. 4 hundred. The number is 400. Explanation: In the above-given figure, given that there are 40 tens. 4 hundred. The number is 400. Question 4. Answer: 50 tens. 5 hundred. The number is 500. Explanation: In the above-given figure, given that there are 50 tens. 5 hundred. The number is 500. On Your Own Write how many tens. Circle groups of 10 tens. Write how many hundreds. Write the number. Question 5. Answer: 70 tens. 7 hundred. The number is 700. Explanation: In the above-given figure, given that there are 70 tens. 7 hundred. The number is 700. Question 6. Answer: 60 tens. 6 hundred. The number is 600. Explanation: In the above-given figure, given that there are 60 tens. 6 hundred. The number is 600. Question 7. Answer: 90 tens. 9 hundred. The number is 900. Explanation: In the above-given figure, given that there are 90 tens. 9 hundred. The number is 900. Question 8. THINK SMARTER Wally has 400 cards. How many stacks of 10 cards can he make? Answer: Wally can make 4 stacks of 10 cards. Explanation: In the above-given figure, given that Wally has 400 cards. wally can make 4 stacks of 10 cards. Problem Solving • Applications Solve. Write or draw to explain. Question 9. Mrs. Martin has 80 boxes of paper clips. There are 10 paper clips in each box. How many paper clips does she have? 800__ paper clips Answer: The paper clips Mrs. Martin has 800. Explanation: In the above-given question, given that Mrs. Martin has 80 boxes of paper clips. There are 10 paper clips in each box. The paper clips do she have = 800. Question 10. THINK SMARTER Pencils are sold in boxes of 10 pencils. Mr. Lee needs 100 pencils. He has 40 pencils. How many boxes of 10 pencils should he buy? __ boxes of 10 pencils Draw a picture to explain your answer. Answer: 6 boxes of 10 pencils should he buy. Explanation: In the above-given figure, given that, Pencils are sold in boxes of 10 pencils. Mr. Lee needs 100 pencils. He has 40 pencils. 6 boxes of 10 pencils should he buy. TAKE HOME ACTIVITY • Ask your child to draw a quick picture of 20 tens and then tell you how many hundreds there are. Group Tens as Hundreds Homework & Practice 2.1 Write how many tens. Circle groups of 10 tens. Write how many hundreds. Write the number. Question 1. Answer: 40 tens. 4 hundred. The number is 400. Explanation: In the above-given figure, given that there are 40 tens. 4 hundred. The number is 400. Question 2. Answer: 60 tens. 6 hundred. The number is 600. Explanation: In the above-given figure, given that there are 60 tens. 6 hundred. The number is 600. Problem Solving Solve. Write or draw to explain. Question 3. Farmer Gray has 30 flowerpots. He plants 10 seeds in each pot. How many seeds does he plant? _300__ seeds Answer: The seeds do he plant = 300. Explanation: In the above-given figure, given that farmer, gray has 30 flower pots. He plants 10 seeds in each pot. He plants 300 seeds. Question 4. WRITE Math Ella has 50 stacks of ten pennies in each stack. Describe how to find how many pennies Ella has in all. ________50 ten_____________________________ _________5 hundreds____________________________ __________500___________________________ _____________________________________ Answer: Ella has in all = 500. Explanation: In the above-given figure, given that Ella has 50 stacks of 10 pennies in each stack. Ella has in all = 500. Lesson Check Question 1. Mai has 40 tens. Write how many hundreds. Write the number. Answer: The number is 4. Explanation: Given that, Mari has 40 tens, Mari has 4 hundred. Question 2. There are 80 tens. Write how many hundreds. Write the number. Answer: The number is 8. Explanation: Given that, Mari has 80 tens, Mari has 8 hundred. Question 3. Write the number equal to 5 tens and 13 ones. Answer: The number is 63. Explanation: In the above-given figure, Given that, The number equal to 5 tens and 13 ones. The number is 63. Question 4. Count by fives. 5, 10, 15 _20_, _25_, _30_, _35__ Answer: 20, 25, 30, 35. Explanation: In the above-given question, given that count by fives. The numbers are 5, 10, and 15. 20, 25, 30, and 35. Question 5. Carlos has 58 pencils. What is the value of the digit 5 in this number? __________tens_____place______________________ Answer: The value of the digit 5 in this number is tens place. Explanation: In the above-given figure, Given that, Carlos has 58 pencils. The value of the digit 5 in the number is tens place. Question 6. Circle the sum that is an even number. 2 + 3 = 5 4 + 4 = 8 5 + 6 = 11 8 + 7 = 15 Answer: The sum that is an even number is 4 + 4 = 8. Explanation: In the above-given question, Given that the numbers are 2 + 3 = 5 4 + 4 = 16 5 + 6 = 11 8 + 7 = 15. 4 + 4 = 8 is even number. Lesson 2.3 Model 3-Digit Numbers Essential Question How do you show a 3-digit number using blocks? Answer: 3 packs of blocks are 300. Explanation: In the above-given question, given that we show a 3-digit number by using blocks. we use 3 packs of blocks. 300. Listen and Draw Use Draw to show what you did. Math Talk MATHEMATICAL PRACTICES If Jack had 14 tens, how many hundreds and tens would he have? Explain Model and Draw In the number 348, the 3 is in the hundreds place, the 4 is in the tens place, and the 8 is in the ones place. Answer: The number is 348. Explanation: In the above-given figure, given that, number 348 in many ways. 300 + 40 + 8 = 348. Share and Show MATH Board Write how many hundreds, tens, and ones. Show with . Then draw a quick picture. Answer: The number is 111. Explanation: In the above-given figure, given that, number 111 with 1 hundred, 1 ten, 1 one. 100 + 10 + 1 = 111. Question 1. 234 _2_ hundreds + _3_ tens + _4_ ones Answer: The number is 234. Explanation: In the above-given figure, given that, number 234 with 2 hundred, 3 ten, 4 one. 200 + 30 + 4 = 234. Question 2. 156 _1_ hundreds + _5_ tens + _6_ ones Answer: The number is 156. Explanation: In the above-given figure, given that, number 156 with 1 hundred, 5 ten, 6 one. 100 + 50 + 6 = 234. On Your Own Write how many hundreds, tens, and ones. Show with . Then draw a quick picture. Answer: The number is 111. Explanation: In the above-given figure, given that, number 111 with 1 hundred, 1 ten, 1 one. 100 + 10 + 1 = 111. Question 3. 125 _1_ hundreds + _2_ tens + _5_ ones Answer: The number is 125. Explanation: In the above-given figure, given that, number 125 with 1 hundred, 2 ten, 5 one. 100 + 20 + 5 = 125. Question 4. 312 _3_ hundreds + _1_ tens + _2_ ones Answer: The number is 312. Explanation: In the above-given figure, given that, number 312 with 3 hundred, 1 ten, 2 one. 300 + 10 + 2 = 312. Question 5. _6_ hundreds + _2_ tens + _3_ ones Answer: The number is 623. Explanation: In the above-given figure, given that, number 623 with 6 hundred, 2 ten, 3 one. 600 + 20 + 3 = 623. Question 6. _5_ hundreds + _1_ tens + _2_ ones Answer: The number is 512. Explanation: In the above-given figure, given that, number 512 with 5 hundred, 1 ten, 2 one. 500 + 10 + 2 = 512. Question 7. THINK SMARTER Lexi needs 144 beads. A large box holds 100 beads. A medium box holds 10 beads. A small box holds 1 bead. Lexi already had 1 large box and 4 small boxes. How many medium boxes of beads does she need? _4_ medium boxes. Answer: Lexi needs 4 medium boxes of beads. Explanation: In the above-given question, Given that, Lexi needs 144 beads. A large box holds 100 beads. a medium box holds 10 beads. small box holds 1 bead. so Lexi needs 4 medium boxes of beads. 100 + 10 + 10 + 10 + 10 + 4. Problem Solving • Applications WRITE Math Question 8. THINK SMARTER How are the numbers 342 and 324 alike? How are they different? ________________________ ________________________ ________________________ Answer: The numbers 342 and 324 are different. Explanation: In the above-given question, given that, 342 and 324 are alike. but they are different. in hundreds place 3 is common, but tens and ones place is different. MATHEMATICAL PRACTICES Model with Mathematics write the number for the clue. Question 9. A model for my number has 2 hundred blocks, no tens blocks, and 3 one blocks. My number is _203_ Answer: My number is 203. Explanation: In the above-given figure, given that, A model for my number has 2 hundred blocks, no tens blocks, and 3 one blocks. my number is 203. Question 10. A model for my number has 3 hundred blocks, 5 tens blocks, and no one’s blocks. My number is _350_ Answer: My number is 350. Explanation: In the above-given figure, given that, A model for my number has 3 hundred blocks, 5 tens blocks, and no one blocks. my number is 350. Question 11. THINK SMARTER There are 2 boxes of 100 pencils and some single pencils on the table. Choose all the numbers that show how many pencils could be on the table. Answer: The pencils are 203, 207. Explanation: In the above-given figure, given that, There are 2 boxes of 100 pencils and some single pencils on the table. single pencils are 3 and 7. The pencils are 203, 207. TAKE HOME ACTIVITY • Write the number 438. Have your child tell you the values of the digits in the number 438. Model 3-Digit Numbers Homework & Practice 2.3 Write how many hundreds, tens, and ones. Show with . Then draw a quick picture. Question 1. 118 Answer: The number is 118. Explanation: In the above-given figure, given that, number 118 with 1 hundred, 1 ten, 8 one. 100 + 10 + 8 = 118. Question 2. 246 Answer: The number is 246. Explanation: In the above-given figure, given that, number 246 with 2 hundred, 4 ten, 6 one. 200 + 40 + 6 = 246. Problem Solving Question 3. Write the number that matches the clues. • My number has 2 hundred. • The tens digit is 9 more than the ones digit. My number is _293__ Answer: The number is 293. Explanation: In the above-given figure, given that, number 293 with 2 hundred, 9 ten, 3 one. 200 + 90 + 3 = 293. Question 4. WRITE Math Write a 3-digit number using digits 2, 9, 4. Draw a quick picture to show the value of your number. Answer: The number is 249. Explanation: In the above-given figure, given that, number 249 with 2 hundred, 4 ten, 9 one. 200 + 40 + 9 = 249. Lesson Check Question 1. What number is shown with these blocks? Answer: The number is 246. Explanation: In the above-given figure, given that, number 246 with 2 hundred, 4 ten, 6 one. 200 + 40 + 6 = 246. Spiral Review Question 2. Write the number with the same value as 28 tens. ______0__+ ____28____+______0_______________ Answer: The number is 28. Explanation: In the above-given figure, given that, number 28 with 0 hundred, 28 ten, 0 one. 0 + 28+ 0 = 28. Question 3. Describe 59 in two other ways. _5_ tens _9_ ones _5_ + _9_ Answer: The number is 59. Explanation: In the above-given figure, given that, number 59 with 0 hundred, 5 ten, 9 one. 0 + 5+ 9= 59. Question 4. Circle the odd number. Answer: The odd number is 11. Explanation: In the above-given question: given that, circle the odd number. the numbers are 11, 12, 18, 20. an odd number is 11. Question 5. Write the number equal to 7 tens and 3 ones. ____73__________ The number is 73. Explanation: In the above-given figure, given that, number 73 with 0 hundred, 7 ten, 3 one. 0 + 7 + 3= 73. Lesson 2.4 Hundreds, Tens, and Ones Essential Question How do you write the 3-digit number that is shown by a set of blocks? Listen and Draw Write the number of hundreds, tens, and ones. Then draw a quick picture. Answer: The number is 246. Explanation: In the above-given figure, given that, number 246 with 2 hundred, 4 ten, 6 one. 200 + 40 + 6 = 246. Answer: The number is 264. Explanation: In the above-given figure, given that, number 264 with 2 hundred, 6 ten, 4 one. 200 + 60 + 4 = 264. Math Talk MATHEMATICAL PRACTICES Describe how the two numbers are alike. Describe how they are different. Share and Show MATH BOARD Write how many hundreds, tens, and ones are in the model. Write the number in two ways. Question 1. Answer: The number is 160. Explanation: In the above-given figure, given that, number 160 with 1 hundred, 6 ten, 0 one. 100 + 60 + 0 = 160. Question 2. Answer: The number is 225. Explanation: In the above-given figure, given that, number 225 with 2 hundred, 2 ten, 5 one. 200 + 20 + 5 = 225. Question 3. Answer: The number is 239. Explanation: In the above-given figure, given that, number 239 with 2 hundred, 3 ten, 9 one. 200 + 30 + 9 = 239. On Your Own Write how many hundreds, tens, and ones are in the model. Write the number in two ways. Question 4. Answer: The number is 304. Explanation: In the above-given figure, given that, number 304 with 3 hundred, 0 ten, 4 one. 300 + 0 + 4 = 304. Question 5. Answer: The number is 378. Explanation: In the above-given figure, given that, number 378 with 3 hundred, 7 ten, 8 one. 300 + 7 + 8 = 378. Question 6. Answer: The number is 426. Explanation: In the above-given figure, given that, number 426 with 4 hundred, 2 ten, 6 one. 400 + 2 + 6 = 426. Solve. Write or draw to explain. Question 7. THINK SMARTER A model for my number has 4 ones blocks, 5 tens blocks, and 7 hundreds blocks. What number am I? Answer: The number is 754. Explanation: In the above-given figure, given that, number 754 with 7 hundred, 5 ten, 4 one. 700 + 5 + 4 = 754. Problem Solving • Applications Question 8. GO DEEPER The hundreds digit of my number is greater than the tens digit. The ones digit is less than the tens digit. What could my number be? Write it in two ways. __3__ + _2___ + __1__ _321___ Answer: The number is 321. Explanation: In the above-given figure, given that, number 321 with 3 hundred, 2 ten, 1 one. 300 + 2 + 1 = 321. Question 9. THINK SMARTER Karen has these bags of marbles. How many marbles does Karen have? ___ marbles Explain how you used the picture to find the number of marbles Karen has. ________200___+___30____+_____0______________ __________230___________________________ _____________________________________ Answer: 230 marbles. Explanation: In the above-given question, Given that, Karen has 2 bags with 100 marbles. 3 bags of 10 marbles. Karen has 230 marbles. TAKE HOME ACTIVITY • Say a 3-digit number, such as 546. Have your child draw a quick picture for that number. Answer: The number is 546. Explanation: In the above-given figure, given that, number 546 with 5 hundred, 4 ten, 3 one. 500 + 4 + 6 = 546. Hundreds, Tens, and Ones homework & Practice 2.4 Write how many hundreds, tens, and ones are in the model. Write the number in two ways. Question 1. Answer: The number is 143. Explanation: In the above-given figure, given that, number 143 with 1 hundred, 4 ten, 3 one. 100 + 4 + 3 = 143. Question 2. Answer: The number is 245. Explanation: In the above-given figure, given that, number 245 with 2 hundred, 4 ten, 5 one. 200 + 4 + 5 = 245. Problem Solving Question 3. Write the number that answers the riddle. Use the chart. A model for my number has 6 ones blocks, 2 hundreds blocks, and 3 tens blocks. What number am I? Answer: The number is 236. Explanation: In the above-given figure, given that, number 236 with 2 hundred, 3 ten, 6 one. 200 + 3 + 6 = 236. Question 4. WRITE Math Write a number that has a zero in the tens place. Draw a quick picture for your number. Answer: The number is 206. Explanation: In the above-given figure, given that, number 206 with 2 hundred, 0 ten, 6 one. 200 + 0 + 6 = 206. Lesson Check Question 1. Write the number 254 as a sum of hundreds, tens, and ones. Answer: The number is 254. Explanation: In the above-given figure, given that, number 254 with 2 hundred, 5 ten, 4 one. 200 + 5 + 4 = 254. Question 2. Write the number 307 as a sum of hundreds, tens, and ones. Answer: The number is 307. Explanation: In the above-given figure, given that, number 307 with 3 hundred, 0 ten, 7 one. 300 + 0 + 7 = 307. Spiral Review Question 3. Describe 83 in two other ways. _8__ tens _3_ ones __80_ + _3__ Answer: The number is 83. Explanation: In the above-given figure, given that, number 83 with 8 ten, 3 one. 80+ 3 = 83. Question 4. Write 86 in words. __Eightysix________ Answer: The number is 86. Explanation: In the above-given figure, given that, number 86 with 8 ten, 6 one. 80+ 6 = 86. Question 5. Write the number with the same value as 32 tens. _________________ Answer: The number is 32. Explanation: In the above-given figure, given that, number 32 with 32 ten, 0 one. 32+ 0 = 32. Question 6. Circle the odd number. Answer: An odd number is 17. Explanation: In the above-given question, given numbers are: 2, 6, 10, and 17. 17 is an odd number. Lesson 2.5 Place Value to 1,000 Essential Question How do you know the values of the digits in numbers? Listen and Draw Write the numbers. Then draw quick pictures. __ sheets of color paper Answer: Sheets of color paper = 203. Explanation: In the above-given question, given that, draw a quick picture. so, I am assuming 203. __ sheets of plain paper Answer: Sheets of plain paper = 543. Explanation: In the above-given question, given that, draw a plain picture. so, I am assuming 543. Math Talk MATHEMATICAL PRACTICES Describe how 5 tens is different from 5 hundred. Model and Draw The place of a digit in a number tells its value. The 3 in 327 has a value of 3 hundred, or 300. The 2 in 327 has a value of 2 tens, or 20. The 7 in 327 has a value of 7 ones, or 7. There are 10 hundreds in 1 thousand The 1 is in the thousands place and has a value of 1 thousand. Share and Show Circle the value or the meaning of the red digit. Question 1. 702 Answer: The value of the red digit is 2 ones. Explanation: In the above-given question, given that, circle the value or the meaning of the red digit. The value of the red digit is 2 ones. Question 2. 459 Answer: The value of the red digit is 50. Explanation: In the above-given question, given that, circle the value or the meaning of the red digit. The value of the red digit is 5 tens. Question 3. 362 Answer: The value of the red digit is 300. Explanation: In the above-given question, given that, circle the value or the meaning of the red digit. The value of the red digit is 3 hundred. On Your Own Circle the value or the meaning of the red digit. Question 4. 549 Answer: The value of the red digit is 40. Explanation: In the above-given question, given that, circle the value or the meaning of the red digit. The value of the red digit is 4 tens. Question 5. 607 Answer: The value of the red digit is 7ones. Explanation: In the above-given question, given that, circle the value or the meaning of the red digit. The value of the red digit is 7 ones. Question 6. 1,000 Answer: The value of the red digit is 1 thousand. Explanation: In the above-given question, given that, circle the value or the meaning of the red digit. The value of the red digit is 1 thousand. Question 7. 914 Answer: The value of the red digit is 9 hundred. Explanation: In the above-given question, given that, circle the value or the meaning of the red digit. The value of the red digit is 9 hundred. Question 8. THINK SMARTER The value of the ones digit in George’s favorite number is 2. The value of the hundreds digit is 600 and the value of the tens digit is 90. Write George’s favorite number. _692___ Answer: George’s favorite number is 692. Explanation: In the above-given question, Given that, The value of the one-digit in George’s favorite number is 2. The value of the hundreds digit is 600. value of the tens digit is 90. George’s favorite number is 692. Question 9. GO DEEPER Write the number that matches the clues. • The value of my hundreds digit is 300. • The value of my tens digit is 0. • The value of my ones digit is an even number greater than 7. The number is _308___ Answer: The number is 308. Explanation: In the above-given question, given that, The value of my hundred digits is 300. value of my tens digit is 0. value of my one digit is an even number greater than 7 is 8. The number is 308. Problem Solving • Applications Question 10. THINK SMARTER Ty is making a Venn diagram. Where in the diagram should he write the other numbers? Answer: The numbers with a 5 in the tens place are 152, 454, 257, 352, and 250. The numbers with a 2 in the hundreds place are 215, 257, 205, and 250. Explanation: In the above-given figure, given that, The numbers are 152, 215, 454, 257, 352, 205, and 250. In a Venn diagram, The numbers with a 5 in the tens place are 152, 454, 257, 352, and 250. The numbers with a 2 in the hundreds place are 215, 257, 205, and 250. Question 11. MATHEMATICAL PRACTICE Apply Describe where 752 should be written in the diagram. Explain your answer. __________________ _________________________ _________________________ Answer: The number 752 should be written in the numbers with a 5 in the tens place. Explanation: In the above-given question, Given that, the number 752 should be written in the Venn diagram. The number 752 should be written in the numbers with a 5 in the tens place. Question 12. THINK SMARTER Fill in the bubble next to all the numbers that have the digit 4 in the tens place Answer: The numbers that have the digit 4 in the tens place are 149, 342. Explanation: In the above-given question, given that, the numbers that have the digit 4 in the tens place. The numbers that have the digit 4 in the tens place are 149, 342. TAKE HOME ACTIVITY • Ask your child to write 3-digit numbers, such as “a number with 2 hundreds” and “a number with a 9 in the ones place.” Place Value to 1,000 Homework & Practice 2.5 Circle the value or the meaning of the underlined digit. Question 1. Answer: The value of the underlined digit is 30. Explanation: In the above-given question, given that, circle the value or the meaning of the underlined digit. The value of the underlined digit is 3 tens. Question 2. Answer: The value of the underlined digit is 2 ones. Explanation: In the above-given question, given that, circle the value or the meaning of the underlined digit. The value of the underlined digit is 2 ones. Question 3. Answer: The value of the underlined digit is 5 hundred. Explanation: In the above-given question, given that, circle the value or the meaning of the underlined digit. The value of the underlined digit is 5 hundred. Question 4. Answer: The value of the underlined digit is 7 ones. Explanation: In the above-given question, given that, circle the value or the meaning of the underlined digit. The value of the underlined digit is 7 ones. Question 5. Answer: The value of the underlined digit is 5 hundred. Explanation: In the above-given question, given that, circle the value or the meaning of the underlined digit. The value of the underlined digit is 5 hundred. Problem Solving Question 6. Write the 3-digit number that answers the riddle. Answer: The number is 454. Explanation: In the above-given figure, Given that, I have the same hundreds of digits as one digit. The value of my tens digit is 50. The value of my ones digit is 4. So the number is 454. • I have the same hundreds digit as ones digit. • The value of my tens digit is 50. • The value of my ones digit is 4. The number is ____ Question 7. WRITE Math What is the value of 5 in 756? Write and draw to explain how you know. _________________________ _________________________ Answer: The value of 5 in 756 = 50. Explanation: In the above-given question, given that, the number is 756. 7 is in the hundreds place. 6 is in one place. so the value of 5 in 756 is tens place. Lesson Check Question 1. What is the value of the underlined digit? Answer: The value of the underlined digit is 3 hundred. Explanation: In the above-given question, given that, circle the value or the meaning of the underlined digit. The value of the underlined digit is 3 hundred. Question 2. What is the meaning of the underlined digit? Answer: The value of the underlined digit is 4 tens. Explanation: In the above-given question, given that, circle the value or the meaning of the underlined digit. The value of the underlined digit is 4 tens. Spiral Review Question 3. What number can be written as 40 + 5? _________45________________ Answer: The number can be written as 45. Explanation: In the above-given question, given that, the number is 40 + 5. so the number can be written as 45. Question 4. What number has the same value as 14 tens? ____140_____________________ Answer: The number can be written as 140. Explanation: In the above-given question, given that, the number is 100+ 40. so the number can be written as 140. Question 5. Write the number described by 1 ten 16 ones. _______26__________________ Question 6. Circle the even number. Answer: The even number is 16. Explanation: In the above-given question, given that the numbers are 7, 16, 21, and 25. 7, 21, and 25 are odd numbers. 16 is an even number. Lesson 2.6 Number Names Essential Question How do you write 3-digit numbers using words? Listen and Draw Write the missing numbers in the chart. Then find and circle the word form of these numbers below. Answer: The missing numbers in the chart are 11, 14, 29, 35, 46, and 52. Explanation: In the above-given figure, given that, The missing numbers are 11, 14, 29, 35, 46, and 52. circle the word form of the numbers below. HOME CONNECTION • In this activity, your child reviewed the word form of numbers less than 100. Math Talk MATHEMATICAL PRACTICES Explain Describe how to use words to write the number with a 5 in the tens place and a 7 in the ones place. Answer: The number is 57. Explanation: In the above-given figure, given that, the number with a 5 in the tens place and a 7 in the one’s place is 57. Model and Draw You can use words to write 3-digit numbers. First, look at the hundreds digit. Then, look at the tens digit and ones digit together. Share and Show MATH Board Write the number using words. Question 1. 506 Answer: The number is 506. Explanation: In the above-given figure, given that, the number is 506. so we have to write five hundred six. Question 2. 189 __One hundred____Eighty-nine.____ Answer: The number is 189. Explanation: In the above-given figure, given that, the number is 189. so we have to write one hundred eighty-nine. Question 3. 328 __________ Answer: The number is 328. Explanation: In the above-given figure, given that, the number is 328. so we have to write three hundred twenty-eight. Write the number Question 4. four hundred fifteen Answer: The number is 415 Explanation: In the above-given figure, given that, the number is 415 so we have to write 415. Question 5. two hundred ninety-one ___491_______ Answer: The number is 291. Explanation: In the above-given figure, given that, the number is 291. so we have to write 291. Question 6. six hundred three ____603______ Answer: The number is 603. Explanation: In the above-given figure, given that, the number is 603. so we have to write 603. Question 7. eight hundred forty-seven ___847_______ Answer: The number is 847. Explanation: In the above-given figure, given that, the number is 847. so we have to write 847. On Your Own Write the number Question 8. seven hundred seventeen __717____ Answer: The number is 717. Explanation: In the above-given figure, given that, the number is 717. so we have to write 717. Question 9. three hundred ninety __390____ Answer: The number is 390. Explanation: In the above-given figure, given that, the number is 390. so we have to write 390. Write the number using words. Question 10. 568 __five hundred sixty-eight.________ Answer: The number is five hundred sixty-eight Explanation: In the above-given figure, given that, the number is five hundred sixty-eight. so we have to write five hundred sixty-eight. Question 11. 321 __ three hundred twenty-one.________ Answer: The number is three hundred twenty-one. Explanation: In the above-given figure, given that, the number is three hundred twenty-one. so we have to write three hundred twenty one. Question 12. GO DEEPER My 3-digit number has a 4 in the hundreds place. It has a greater digit in the tens place than in the ones place. The sum of the digits is 6. What is my number? ___420___________ Write the number using words. _four hundred twenty.__________ Answer: The number is 420. Explanation: In the above-given question, given that, the 3-digit number has a 4 in the hundreds place. It has a greater digit in the tens place than in the ones place. The sum of digits is 6. The number is 420. Question 13. THINK SMARTER Alma counts two hundred sixty-eight leaves. Which is another way to write this number? Circle your answer. Answer: The number is 200 + 60 + 8. Explanation: In the above-given question, given that, Alma counts two hundred sixty-eight leaves. Another way to write this number is 200 + 60 + 8. Problem Solving • Applications Connect Symbols and Words Circle the answer for each problem. Question 14. Derek counts one hundred ninety cars. Which is another way to write this number? Answer: The number is 100 + 90 + 0. Explanation: In the above-given question, given that, Derek counts one hundred ninty. The another way to write this number is 100 + 90 + 0. Question 15. Beth counted three hundred fifty-six straws. Which is another way to write this number? 3 + 5 + 6 30 + 50 + 60 300 + 50 + 6 Answer: The number is 300 + 50 + 6. Explanation: In the above-given question, given that, Derek counts Three hundred fifty-six straws. The another way to write this number is 300 + 50 + 6. Question 16. THINK SMARTER There are 537 chairs at the school. Write this number using words. Show the number in two other ways. Answer: The number is 500 + 30 + 7. Explanation: In the above-given question, given that, Derek counts five hundred thirty-seven straws. The another way to write this number is 500 + 30 + 7. TAKE HOME ACTIVITY • Ask your child to write the number 940 using words. Number Names Homework & Practice 2.6 Write the number Question 1. two hundred thirty-two ____232______ Answer: The number is 232. Explanation: In the above-given figure, given that, the number is 232. so we have to write two hundred thirty-two. Question 2. five hundred forty-four _544_____ Answer: The number is 544. Explanation: In the above-given figure, given that, the number is 544. so we have to write five hundred forty-four. Question 3. one hundred fifty-eight ____158_____ Answer: The number is 158. Explanation: In the above-given figure, given that, the number is 158. so we have to write one hundred fifty-eight. Question 4. nine hundred fifty __950____ Answer: The number is 950. Explanation: In the above-given figure, given that, the number is 950. so we have to write nine hundred fifty. Question 5. four hundred twenty ___420________ Answer: The number is 420. Explanation: In the above-given figure, given that, the number is 420. so we have to write four hundred twenty. Question 6. six hundred seventy-eight __678____ Answer: The number is 678. Explanation: In the above-given figure, given that, the number is 678. so we have to write six hundred seventy eight. Write the number using words. Question 7. 317 _Three hundred seventeen._ Answer: The number is 317. Explanation: In the above-given figure, given that, the number is 317. so we have to write three hundred seventeen. Problem Solving Circle the answer. Question 8. Six hundred twenty-six children attend Elm Street School. Which is another way to write this number? Answer: The number is 600 + 20 + 6. Explanation: In the above-given question, given that, six hundred twenty-six attend EIm street school. Another way to write this number is 600 + 20 + 6. Question 9. WRITE Math Write a 3-digit number using the digits 5, 9, and 2. Then write your number using words. _________592.____________________________ Answer: The number is Five hundred ninety-two. Explanation: In the above-given question, given that, The number is Five hundred ninety-two. Another way to write this number is 500 + 90 + 2. Lesson Check Question 1. Write the number 851 in words. _eight hundred fifty-one.___________ Answer: The number is eight hundred fifty-one. Explanation: In the above-given question, given that, The number is Five hundred fifty-one. Another way to write this number is 500 + 50 + 1. Question 2. Write the number two hundred sixty using numbers. ___260_________ Answer: The number is 260. Explanation: In the above-given question, given that, The number is two hundred sixty. Another way to write this number is 200 + 60 + 0. Spiral Review Question 3. Write a number with the digit 8 in the tens place. ____284_________ Answer: The number is 284. Explanation: In the above-given question, given that, The number is two hundred eighty-four. Another way to write this number is 200 + 80 + 4. Question 4. Write the number shown with these blocks. Answer: The number is 245. Explanation: In the above-given figure, given that, number 245 with 2 hundred, 4 ten, 5 one. 200 + 40 + 5 = 245. Question 5. Count by fives. 650, 655, _660__, _665___, _670__ Answer: The numbers are 660, 665, and 670. Explanation: In the above-given figure, given numbers are, 650, 655. so the numbers are 660, 665, and 670. Question 6. Sam has 128 marbles. How many hundreds are in this number? _1_ hundred. Answer: One hundred. Explanation: In the above-given question, given that, Sam has 128 marbles. there is one hundred in this number. Lesson 2.7 Different Forms of Numbers Essential Question What are three ways to write a 3-digit number? Listen and Draw Write the number. Use the digits to write how many hundreds, tens, and ones. Math Talk MATHEMATICAL PRACTICES How many hundreds are in 368? Explain. Model and Draw You can use a quick picture to show a number. You can write a number in different ways. Read the number and draw a quick picture. Then write the number in different ways. Question 1. four hundred seven ___ hundreds __ tens ___ ones ___ + ___ + ___ ______ Answer: The number is 407. Explanation: In the above-given question, given that, the number is four hundred seven. 400 + 0 + 7. Question 2. three hundred twenty-five ___ hundreds __ tens ___ ones ___ + ___ + ___ ______ Answer: The number is 325. Explanation: In the above-given question, given that, the number is three hundred twenty-five. 300 + 20 + 5. Question 3. two hundred fifty-three _2__ hundreds _5_ tens _3__ ones 200___ + _50__ + _3__ __253____ Answer: The number is 253. Explanation: In the above-given question, given that, the number is two hundred fifty-three. 200 + 50 + 3. On Your Own Read the number and draw a quick picture. Then write the number in different ways. Question 4. one hundred seventy-two ___ hundreds __ tens ___ ones ___ + ___ + ___ ______ Answer: The number is 172. Explanation: In the above-given question, given that, the number is one hundred seventy-two. 100 + 70 + 2. Question 5. three hundred forty-six ___ hundreds __ tens ___ ones ___ + ___ + ___ ______ Answer: The number is 546. Explanation: In the above-given question, given that, the number is five hundred forty-six. 500 + 40 + 6. Question 6. THINK SMARTER Think of a 3-digit number with a zero in the ones place. Use words to write that number. ___Five__hundred_____forty.___________ Answer: The number is five hundred forty. Explanation: In the above-given question, given that, the number is five hundred forty. 500 + 40 + 0. Question 7. THINK SMARTER Ellen used these blocks to show 452. What is wrong? Cross out blocks and draw quick pictures for missing blocks. Answer: The number is four hundred fifty-two. Explanation: In the above-given question, given that, one hundred blocks are missing, no one’s block. 400 + 50 + 2. TAKE HOME ACTIVITY • Ask your child to show the number 315 in three different ways. Different Forms of Numbers Homework & Practice 2.7 Read the number and draw a quick picture. Then write the number in different ways. Question 1. two hundred fifty-one ___ hundreds ___ tens ___one ___ + ____ + _____ _________ Answer: The number is 2 hundreds 5 tens 1 ones. 200 + 50 + 1. Explanation: In the above-given question, given that, the number is two hundred fifty-one. 200 + 50 + 1. Question 2. three hundred twelve ___ hundreds ___ tens ___one ___ + ____ + _____ _________ Answer: The number is 3 hundreds 0 tens 12 ones. 300 + 0 + 12. 312. Explanation: In the above-given question, given that, the number is three hundred twelve. 300 + 0 + 12. Problem Solving Write the number another way. Question 3. 200 + 30 + 7 _237________ Answer: The number is 2 hundreds 30 tens 7 ones. 200 + 30 + 7. 237. Explanation: In the above-given question, given that, the number is two hundred thirty-seven. 200 + 30 + 7. Question 4. 895 __800 + 90 + 5_______ Answer: The number is 8 hundreds 9 tens 5 ones. 800 + 90 + 5. 895. Explanation: In the above-given question, given that, the number is eight hundred ninety-five. 800 + 90 + 5. Question 5. WRITE Math Draw a quick picture of 3 hundreds, 5 tens, and 7 ones. What number does your quick picture show? Write it in three different ways. Answer: The number is 3 hundreds 5 tens 7 ones. 300 + 50 + 7. 357. Explanation: In the above-given question, given that, the number is three hundred fifty-seven. 300 + 50 + 7. Lesson Check Question 1. Write the number 392 as hundreds, tens, and ones. __3__ hundreds __9_ tens _2_ ones Answer: The number is 3 hundreds 9 tens 2 ones. 300 + 90 + 2. Explanation: In the above-given question, given that, the number is three hundred ninety-two. 300 + 90 + 2. Question 2. What is another way to write the number 271? __2__ hundreds __7_ tens _1_ ones Answer: The number is 2 hundreds 7 tens 1 ones. 200 + 70 + 1. Explanation: In the above-given question, given that, the number is three hundred ninety-two. 200 + 70 + 1. Spiral Review Question 3. What is the value of the underlined digit? Answer: The value of the underlined digit is 5 tens. Explanation: In the above-given question, given that, circle the value or the meaning of the underlined digit. The value of the underlined digit is 5 tens. Question 4. What number is shown with these blocks? Answer: The number is two hundred twelve. Explanation: In the above-given question, given that, The number is two hundred twelve. Question 5. What is another way to write the number 75? __70__ + _5__ Answer: The number is 75. Explanation: In the above-given question: given that, the number is 75. 70 + 5 = 75. Question 6. What number can be written as 60 + 3? __63_____ Answer: The number is 63. Explanation: In the above-given question: given that, the number is 63. 60 + 3 = 63. Numbers to 1,000 Mid-Chapter Checkpoint Concepts and Skills Circle tens to make 1 hundred. Write the number in different ways. Question 1. Answer: the number is1 hundred 3 tens. Explanation: In the above-given figure, given that, the tens are 13. the number is i hundred 3 tens. Write how many hundreds, tens, and ones are in the model. Write the number in two ways. Question 2. Answer: the number is 2 hundred 4 tens 3 ones. Explanation: In the above-given figure, given that, the tens are 243. the number is 2 hundred 4 tens 3 ones. Circle the value or the meaning of the red digit. Question 3. Answer: The value of the red digit is 5 hundred. Explanation: In the above-given question, given that, circle the value or the meaning of the red digit. The value of the red digit is 5 hundred. Question 4. Answer: The value of the red digit is 4 ones. Explanation: In the above-given question, given that, circle the value or the meaning of the red digit. The value of the red digit is 4 ones. Question 5. THINK SMARTER Write the number six hundred forty-five in another way. Answer: The number is 645. Explanation: In the above-given question, given that, the number is six hundred forty-five. 600 + 40 + 5. Lesson 2.8 Algebra • Different Ways to Show Numbers Essential Question How can you use blocks or quick pictures to show the value of a number in different ways? Listen and Draw Draw quick pictures to solve. Write how many tens and ones. ____ tens ____ ones ___ tens __ ones Math Talk MATHEMATICAL PRACTICES Model Describe how you found different ways to show 35 books. Model and Draw Here are two ways to show 148. Share and Show Write how many hundreds, tens, and ones are in the model. Question 1. 213 Answer: a.There are 2 hundreds 1 tens 3 ones. Explanation: In the above-given figure, given that, the number is 213. There are 2 hundreds 0 tens 13 ones. Answer: b.There are 2 hundreds 0 tens 13 ones. Explanation: In the above-given figure, given that, the number is 213. There are 2 hundreds 0 ten13 ones. Question 2. 132 Answer: a.There are 1 hundreds 3 tens 2 ones. Explanation: In the above-given figure, given that, the number is 132. There are 1 hundreds 3 ten 2 ones. Answer: b.There are 1 hundreds 2 tens 12 ones. Explanation: In the above-given figure, given that, the number is 132 There are 1 hundreds 2 ten12 ones. On Your Own Write how many hundreds, tens, and ones are in the model. Question 3. 144 Answer: a.There are 1 hundred 4 tens 4 ones. Explanation: In the above-given figure, given that, the number is 144. There are 1 hundred 4 ten 4 ones. Answer: b.There are 1 hundred 3 tens 14 ones. Explanation: In the above-given figure, given that, the number is 144. There are 1 hundreds 3 ten14 ones. Question 4. 204 Answer: a.There are 1 hundreds 10 tens 4 ones. Explanation: In the above-given figure, given that, the number is 204. There are 1 hundreds 10 ten 4 ones. Answer: b.There are 2 hundreds 0 tens 4 ones. Explanation: In the above-given figure, given that, the number is 204. There are 2 hundreds 0 ten 4 ones. Question 5. MATHEMATICAL PRACTICE Make Arguments Sue said that 200 + 20 + 23 is the same as 200 + 30 + 3. Is she correct? Explain. _____________________ _____________________ _____________________ Answer: No sue was not correct. Explanation: In the above-given question, Given that, Sue said that 200 + 20 + 23 is the same as 200 + 30 + 3. 200 + 20 + 23 = 243. 200 + 30 + 3 = 233. No sue was not correct. Problem Solving • Applications WRITE Math Marbles are sold in boxes, in bags, or as single marbles. Each box has 10 bags of marbles in it. Each bag has 10 marbles in it. Answer: A number of marbles = 100. Explanation: In the above-given question, given that, Marbles are sold in boxes, in bags, or as single marbles. Each box has 10 bags of marbles in it. Each bag has 10 marbles in it. A number of marbles = 100. Question 6. THINK SMARTER Draw pictures to show two ways to buy 324 marbles. Answer: a.There are 3 hundreds 2 tens 4 ones. 300 + 20 + 4. Three hundred twenty-four. Explanation: In the above-given figure, given that, the number is 324. There are 3 hundreds 2 tens 4 ones. 300 + 20 + 4. Three hundred twenty-four. Question 7. THINK SMARTER There is only one box of marbles in the store. There are many bags of marbles and single marbles. Draw a picture to show a way to buy 312 marbles. How many boxes, bags, and single marbles did you show? _____________________________________ _____________________________________ Answer: A number of marbles = 312. Explanation: In the above-given question, given that, Marbles are sold in boxes, in bags, or as single marbles. Each box has 10 bags of marbles in it. Each bag has 10 marbles in it. A number of marbles = 312. TAKE HOME ACTIVITY • Write the number 156. Have your child draw quick pictures of two ways to show this number. Answer: The number is 156. Explanation: In the above-given question, given that, the number is 156. 100 + 50 + 6 = 156. 100 + 40 + 16 = 156. Algebra • Different Ways to Show Numbers Homework & Practice 2.8 Write how many hundreds, tens, and ones are in the model. Question 1. 135 Answer: a.There are 1 hundred 3 tens 5 ones. Explanation: In the above-given figure, given that, the number is 135. There are 1 hundred 3 tens 5 ones. Answer: b.There are 1 hundred 2 tens 15 ones. Explanation: In the above-given figure, given that, the number is 135. There are 1 hundreds 2 ten15 ones. Problem Solving Markers are sold in boxes, packs, or as single markers. Each box has 10 packs. Each pack has 10 markers. Question 2. Draw pictures to show two ways to buy 276 markers. Answer: A number of marbles = 276. Explanation: In the above-given question, given that, Marbles are sold in boxes, in bags, or as single marbles. Each box has 10 bags of marbles in it. Each bag has 10 marbles in it. A number of marbles = 276. Question 3. WRITE Math Draw quick pictures to show the number 326. Answer: The number is three hundred twenty-six. Explanation: In the above-given question, given that, The number is three hundred twenty-six. Lesson Check Question 1. Write the number that can be shown with this many hundreds, tens, and ones. Answer: the number is 1 hundred 2 tens 18 ones. one hundred thirty-eight. Explanation: In the above-given figure, given that, the tens are 138. the number is 1 hundred 2 tens 18 ones. one hundred thirty-eight. Question 2. Write the number that can be shown with this many hundreds, tens, and ones. Answer: the number is 2 hundred 15 tens 6 ones. two hundred twenty-one. Explanation: In the above-given figure, given that, the tens are 221. the number is 2 hundred 15 tens 6 ones. two hundred twenty-one. Spiral Review Question 3. What number can be written as 6 tens 2 ones? __62_____ Answer: The number is 62. Explanation: In the above-given question: given that, the number is 62. 60 + 2 = 62. Question 4. What number can be written as 30 + 2? ___32____ Answer: The number is 32. Explanation: In the above-given question: given that, the number is 32. 30 + 2 = 32. Question 5. Write the number 584 in words. _five hundred __eighty-four.___ Answer: the number is 5 hundred 8 tens 4 ones. five hundred eighty-four. Explanation: In the above-given figure, given that, the tens are 584. the number is 5 hundred 8 tens 4 ones. five hundred eighty-four. Question 6. Write the number 29 in words. __twenty- nine_______ Answer: The number is 29. Explanation: In the above-given question: given that, the number is 29. 20 + 9 = 29. Lesson 2.9 Count On and Count Back by 10 and 100 Essential Question How do you use place value to find 10 more, 10 less, 100 more, or 100 less than a 3-digit number? Listen and Draw Draw quick pictures for the numbers. Answer: 10 less than girls: The number of girls = 263. 10 less than boys: The number of boys = 142. Explanation: In the above-given question, given that, The number of girls = 273. 10 less than = 263. The number of boys = 152. 10 less than = 142. Math Talk MATHEMATICAL PRACTICES Describe how the two numbers are different. Model and Draw You can show 10 less or 10 more than a number by changing the digit in the tens place. You can show 100 less or 100 more than a number by changing the digit in the hundreds place. Share and Show Write the number Question 1. 10 more than 648 _658______ Answer: The number is 658. Explanation: In the above-given question: given that, 10 more than 648. The value in the 10’s digit is changed. The number is 658. Question 2. 100 less than 513 ___413___ Answer: The number is 413. Explanation: In the above-given question: given that, 100 less than 513. The value in the 100’s digit is changed. The number is 413. Question 3. 100 more than 329 ___429____ Answer: The number is 429. Explanation: In the above-given question: given that, 100 more than 429. The value in the 100’s digit is changed. The number is 429. Question 4. 10 less than 827 ____817_____ Answer: The number is 817. Explanation: In the above-given question: given that, 10 less than 827. The value in the 10’s digit is changed. The number is 817. On Your Own Question 5. 10 more than 471 _____481______ Answer: The number is 481. Explanation: In the above-given question: given that, 10 more than 471. The value in the 10’s digit is changed. The number is 481. Question 6. 10 less than 143 ____133______ Answer: The number is 133. Explanation: In the above-given question: given that, 10 less than 143. The value in the 10’s digit is changed. The number is 133. Question 7. 100 more than 555 ____655_________ Answer: The number is 655. Explanation: In the above-given question: given that, 100 more than 555. The value in the 100’s digit is changed. The number is 655. Question 8. 100 less than 757 _______657_____ Answer: The number is 657. Explanation: In the above-given question: given that, 100 less than 757. The value in the 100’s digit is changed. The number is 657. Question 9. 100 more than 900 ___1000___ Answer: The number is 1000. Explanation: In the above-given question: given that, 100 more than 900. The value in the 100’s digit is changed. The number is 1000. Question 10. 10 less than 689 ____679_____ Answer: The number is 679. Explanation: In the above-given question: given that, 10 less than 689. The value in the 10’s digit is changed. The number is 679. Question 11. 100 less than 712 ___612______ Answer: The number is 612. Explanation: In the above-given question: given that, 100 less than 712. The value in the 100’s digit is changed. The number is 612. Question 12. 10 less than 254 _____244____ Answer: The number is 244. Explanation: In the above-given question: given that, 10 less than 254. The value in the 10’s digit is changed. The number is 244. Question 13. THINK SMARTER Kyla wrote the riddle below. Fill in the blanks to make the sentence true. __938___ is 10 less than 948 and 10 more than 958_____ Answer: 10 less than: The number is 938. 10 more than: The number is 958. Explanation: In the above-given question: given that, 10 less than 948. The value in the 10’s digit is changed. The number is 938. 10 more than: The number is 958. Question 14. THINK SMARTER Rick has 10 more crayons than Lori. Lori has 136 crayons. Tom has 10 fewer crayons than Rick. How many crayons does each child have? Answer: Rick has 146 crayons. tom has 126 crayons. Lori has 136 crayons. Explanation: In the above-given question, given that, Lori has 136 crayons. Rick has 10 more crayons than Lori. tom has 10 fewer crayons than Rick. Rick has 146 crayons. tom has 126 crayons. Lori has 136 crayons. Problem Solving • Applications Analyze Relationships Question 15. Juan’s book has 248 pages. This is 10 more pages than there are in Kevin’s book. How many pages are in Kevin’s book? _238___ pages Answer: In Kevin’s book, there are 238. Explanation: In the above-given question, Given that, Juan’s book has 248 pages. This is more pages than there in kevin’s book. Question 16. There are 217 pictures in Tina’s book. There are 100 fewer pictures in Mark’s book. How many pictures are in Mark’s book? _317___ pages Answer: In mark’s book, there are 317 pictures. Explanation: In the above-given question, Given that, There are 217 pictures in Tina’s book. There are 100 fewer pictures in mark’s book. In mark’s book, there are 317 pictures. Question 17. GO DEEPER Use the clues to answer the question. • Shawn counts 213 cars. • Maria counts 100 fewer cars than Shawn. • Jayden counts 10 more cars than Maria. How many cars does Jayden count? _123__ cars Answer: Jayden counts 123 cars. Explanation: In the above-given question, given that, Shawn counts 213 cars. Maria counts 100 fewer cars than Shawn. Jayden counts 10 more cars than Maria. Jayden counts 123 cars. Question 18. THINK SMARTER Rico has 235 stickers. Gabby has 100 more stickers than Rico. Thomas has 10 fewer stickers than Gabby. Write the number of stickers each child has. Answer: Rico has 235 stickers. Gabby has 335 stickers. Thomas has 325 stickers. Explanation: In the above-given question, given that, Rico has 235 stickers. Gabby has 100 more stickers than Rico. Thomas has 10 fewer stickers than Gabby. Rico has 235 stickers. Gabby has 335 stickers. Thomas has 325 stickers. TAKE HOME ACTIVITY • Write the number 596. Have your child name the number that is 100 more than 596. Answer: The number is 696. Explanation: In the above-given question: given that, 100 more than 596. The value in the 100’s digit is changed. The number is 696. Count On and Count Back by 10 and 100 Homework & Practice 2.9 Write the number. Question 1. 10 more than 451 __461________ Answer: The number is 461. Explanation: In the above-given question: given that, 10 more than 451. The value in the 10’s digit is changed. The number is 461. Question 2. 10 less than 770 ___760______ Answer: The number is 760. Explanation: In the above-given question: given that, 10 less than 770. The value in the 10’s digit is changed. The number is 760. Question 3. 100 more than 367 __467_______ Answer: The number is 467. Explanation: In the above-given question: given that, 100 more than 367. The value in the 100’s digit is changed. The number is 467. Question 4. 100 less than 895 __795_______ Answer: The number is 795. Explanation: In the above-given question: given that, 100 less than 895. The value in the 100’s digit is changed. The number is 795. Question 5. 10 less than 812 __802______ Answer: The number is 802. Explanation: In the above-given question: given that, 10 less than 812. The value in the 10’s digit is changed. The number is 802. Question 6. 100 more than 543 ___553_______ Answer: The number is 553. Explanation: In the above-given question: given that, 100 more than 543. The value in the 100’s digit is changed. The number is 553. Question 7. 10 more than 218 ___228______ Answer: The number is 228. Explanation: In the above-given question: given that, 10 more than 218. The value in the 10’s digit is changed. The number is 228. Question 8. 100 more than 379 __389________ Answer: The number is 389. Explanation: In the above-given question: given that, 100 more than 379. The value in the 100’s digit is changed. The number is 389. Problem Solving Solve. Write or draw to explain. Question 9. Sarah has 128 stickers. Alex has 10 fewer stickers than Sarah. How many stickers does Alex have? _118___ stickers Answer: Alex has 118 stickers. Explanation: In the above-given question, given that, Sarah has 128 stickers. Alex has 10 fewer stickers than Sarah. Alex has 118 stickers. Question 10. WRITE Math Choose any 3-digit number. Describe how to find the number that is 10 more. ___373____ Answer: The number is 373. Explanation: In the above-given question: given that, 10 more than 363. The value in the 10’s digit is changed. The number is 373. Lesson Check Question 1. Write the number that is 10 less than 526. ___516______ Answer: The number is 516 Explanation: In the above-given question: given that, 10 less than 526. The value in the 10’s digit is changed. The number is 526. Question 2. Write the number that is 100 more than 487. __497_____ Answer: The number is 497. Explanation: In the above-given question: given that, 100 more than 487. The value in the 100’s digit is changed. The number is 497. Spiral Review Question 3. Write another way to describe 14 tens. Answer: The number is 0 hundred 14 tens. Explanation: In the above-given question: given that, the number is 104. 100 + 4 = 104. Question 4. What is the value of the underlined digit? Answer: The value of the underlined digit is 8 tens. Explanation: In the above-given question, given that, the value or the meaning of the underlined digit. The value of the underlined digit is 8 tens. Question 5. What number can be written as 30 + 5? ___35______ Answer: The number is 35. Explanation: In the above-given question: given that, the number is 35. 30 + 5 = 35. Question 6. What number can be written as 9 tens and 1 one? ___191_______ Answer: The number is 91. Explanation: In the above-given question: given that, the number is 91. 90 + 1 = 91. Lesson 2.10 Algebra • Number Patterns Essential Question How does place value help you identify and extend counting patterns? Listen and Draw Shade the numbers in the counting pattern. Math Talk MATHEMATICAL PRAACTICES Look for Structure What number is next in the counting pattern you see ? Explain. Model and Draw Look at the digits in the numbers. What two numbers are next in the counting pattern? The _100__ digit changes by one each time. The next two numbers are __514_ and __614_. Answer: The hundreds of digit changes by one each time. the next two numbers are 514, and 614. Explanation: In the above-given question, given that, the hundreds digit is increased. The next two numbers are 514, and 614. Share and Show Look at the digits to find the next two numbers. Question 1. The next two numbers are _177_ and _187__ Answer: The next two numbers are 177 and 187. Explanation: In the above-given question, given that, the numbers are increasing by 10 in 10’s place. The next two numbers are 177 and 187. Question 2. The next two numbers are 645__ and _745__ Answer: The next two numbers are 645 and 745. Explanation: In the above-given question, given that, the numbers are increasing by 100 in 100’s place. The next two numbers are 645 and 745. Question 3. The next two numbers are 461__ and _471__ Answer: The next two numbers are 461 and 471. Explanation: In the above-given question, given that, the numbers are increasing by 10 in 10’s place. The next two numbers are 461 and 471. Question 4. The next two numbers are _789_ and __889_ Answer: The next two numbers are 789 and 889. Explanation: In the above-given question, given that, the numbers are increasing by 100 in 100’s place. The next two numbers are 789 and 889. On Your Own Look at the digits to find the next two numbers. Question 5. The next two numbers are _593_ and _693__ Answer: The next two numbers are 593 and 693. Explanation: In the above-given question, given that, the numbers are increasing by 100 in 100’s place. The next two numbers are 593 and 693. Question 6. The next two numbers are _524_ and _534__ Answer: The next two numbers are 524 and 534. Explanation: In the above-given question, given that, the numbers are increasing by 10 in 10’s place. The next two numbers are 524 and 534. Question 7. The next two numbers are _900_ and _1000__ Answer: The next two numbers are 900 and 1000. Explanation: In the above-given question, given that, the numbers are increasing by 100 in 100’s place. The next two numbers are 900 and 1000. Question 8. The next two numbers are _695_ and _705__ Answer: The next two numbers are 695 and 705. Explanation: In the above-given question, given that, the numbers are increasing by 10 in 10’s place. The next two numbers are 695 and 705. Question 9. THINK SMARTER Mark read 203 pages. Laney read 100 more pages than Mark. Gavin read 10 fewer pages than Laney. How many pages did Gavin read? Answer: Gavin read 293 pages. Explanation: In the above-given question, Given that, Mark read 203 pages. Lane read 100 more pages than Mark. Gavin read 10 fewer pages than Laney. Gavin read 293 pages . Problem Solving • Applications Solve. Question 1. GO DEEPER There were 135 buttons in a jar. After Robin put more buttons into the jar, there were 175 buttons in the jar. How many groups of 10 buttons did she put into the jar? ___ groups of 10 buttons Explain how you solved the problem. _____________________________________ _____________________________________ _____________________________________ Answer: Robin put 3 groups of 10 buttons. Explanation: In the above-given question, Given that, There were 135 buttons in a jar. After robin put more buttons into the jar, there were 175 buttons in the jar. Robin put 3 groups of 10 buttons. Question 11. THINK SMARTER Write the next number in each counting pattern. 162, 262, 362, 462, _562____ Answer: Answer: The next number is 562. Explanation: In the above-given question, given that, the numbers are increasing by 100 in 100’s place. The next number is 562. 347, 357, 367, 377, _387___ Answer: The next number is 387. Explanation: In the above-given question, given that, the numbers are increasing by 10 in 10’s place. The next number is 387. 609, 619, 629, 639, _649__ Answer: The next number is 649. Explanation: In the above-given question, given that, the numbers are increasing by 10 in 10’s place. The next number is 649. TAKE HOME ACTIVITY • With your child, take turns writing number patterns in which you count on by tens or by hundreds. Algebra • Number Patterns Homework & Practice 2.10 Look at the digits to find the next two numbers. Question 1. The next two numbers are _272__ and _282__ Answer: The next two numbers are 272 and 282. Explanation: In the above-given question, given that, the numbers are increasing by 10 in 10’s place. The next two numbers are 272 and 282. Question 2. The next two numbers are _585__ and _685__ Answer: The next two numbers are 585 and 685. Explanation: In the above-given question, given that, the numbers are increasing by 100 in 100’s place. The next two numbers are 585 and 685. Question 3. The next two numbers are _828__ and _928__ Answer: The next two numbers are 828 and 928. Explanation: In the above-given question, given that, the numbers are increasing by 100 in 100’s place. The next two numbers are 828 and 928. Question 4. The next two numbers are _694__ and _704__ Answer: The next two numbers are 694 and 704. Explanation: In the above-given question, given that, the numbers are increasing by 10 in 10’s place. The next two numbers are 694 and 704. Problem Solving Question 5. What are the missing numbers in the pattern? The missing numbers are _471__ and _501__ Answer: The missing numbers are 471 and 501. Explanation: In the above-given question, given that, The numbers are 431, 441, 451, 461,481, 491. The missing numbers are 471 and 501. Question 6. WRITE Math How can you tell when a pattern shows counting on by tens? _____________ _____________ Lesson Check Question 1. What is the next number in this pattern? 453, 463, 473, 483, __493___ Answer: The next number is 493. Explanation: In the above-given question, given that, the numbers are increasing by 10 in 10’s place. The next number is 493. Question 2. What is the next number in this pattern? 295, 395, 495, 595, ___695___ Answer: The next number is 695. Explanation: In the above-given question, given that, the numbers are increasing by 100 in 100’s place. The next number is 695. Spiral Review Question 3. Write the number seven hundred fifty-one with digits. _751__ Answer: The number is 751. Explanation: In the above-given figure, given that, the number is 751. so we have to write 751. Question 4. What is the value of the underlined digit? ____ Answer: The value of the underlined digit is 1 hundred. Explanation: In the above-given question, given that, the value or the meaning of the underlined digit. The value of the underlined digit is 1 hundred. Question 5. What is another way to write 56? _5_ tens _6_ ones Question 6. Write the number 43 in tens and ones. _4_ tens _3_ ones Answer: The number is 4 tens and 3 ones. Explanation: In the above-given question, given that, the number is 4 tens and 3 ones. the number is 43. Lesson 2.11 Problem Solving • Compare Numbers Essential Question How can you make a model to solve a problem about comparing numbers? Children bought 217 boxes of chocolate milk and 188 boxes of plain milk. Did they buy more boxes of chocolate milk or plain milk? Unlock the Problem Answer: Children bought 217 boxes of chocolate milk. Children bought 188 boxes of plain milk. Explanation: In the above-given question, given that, They bought more boxes of chocolate milk. Children bought 217 boxes of chocolate milk. Children bought 188 boxes of plain milk. Show how to solve the problem. Model the numbers. Draw quick pictures of your models The children bought more boxes of ___ milk. Answer: Children bought 217 boxes of chocolate milk. Children bought 188 boxes of plain milk. Explanation: In the above-given question, given that, They bought more boxes of chocolate milk. Children bought 217 boxes of chocolate milk. Children bought 188 boxes of plain milk. HOME CONNECTION • Your child used base-ten blocks to represent the numbers in the problem. These models were used as a tool for comparing numbers to solve the problem. Try Another Problem Model the numbers. Draw quick pictures to show how you solved the problem. v Question 1. At the zoo, there are 137 birds and 142 reptiles. Are there more birds or more reptiles at the zoo? more _reptiles______ Answer: There are more reptiles. Explanation: In the above-given question, given that, there are 137 birds and 142 reptiles. there are more reptiles. Question 2. Tom’s book has 105 pages. Delia’s book has 109 pages. Whose book has fewer pages? __Tom’s____ book Answer: Tom’s book has 105 pages. Explanation: In the above-given question, given that, Tom’s book has 105 pages. Delia’s book has 109 pages. Tom’s book has 105 pages. Math Talk MATHEMATICAL PRACTICES Compare Explain what you did to solve the second problem. Share and Show MATH BOARD Model the numbers. Draw quick pictures to show how you solved the problem. Question 3. Mary’s puzzle has 164 pieces. Jake’s puzzle has 180 pieces. Whose puzzle has more pieces? __Jake’s____ puzzle Answer: Jake’s puzzle has more pieces. Explanation: In the above-given question, given that, Mary’s puzzle has 164 pieces. Jake’s puzzle has 180 pieces. Jake’s puzzle has more pieces. Question 4. There are 246 people at the game. There are 251 people at the museum. At which place are there fewer people? at the _game____ Answer: There are fewer people at the game. Explanation: In the above-given question, given that, There are 246 people at the game. there are 251 people at the museum. There are fewer people at the game. Question 5. There are 131 crayons in a box. There are 128 crayons in a bag. Are there more crayons in the box or in the bag? in the _box___ Answer: There are more crayons in the box. Explanation: In the above-given question, given that, There are 131 crayons in a box. There are 128 crayons in a bag. There are more crayons in the box. Question 6. There are 308 books in the first room. There are 273 books in the second room. In which room are there fewer books? in the _second__ room. Answer: In the second room, there are 273 books. Explanation: In the above-given question, given that, There are 308 books in the first room. There are 273 books in the second room. In the second room, there are 273 books. Problem Solving • Applications Question 7. THINK SMARTER There are 748 children at Dan’s school. There are 651 children at Karen’s school. There are 763 children at Jason’s school. Which school has more than 759 children? _Jason’s__ school Answer: In Jason’s school, there are 763 children. Explanation: In the above-given question, given that, There are 748 children at Dan’s school. There are 651 children at Karen’s school. There are 763 children at Jason’s school. In Jason’s school, there are 763 children. Question 8. MATHEMATICAL PRACTICE Analyze There are 136 crayons in a box. Use the digits 4, 1, and 2 to write a number that is greater than 136. __142_______ Answer: The number greater than 136 is 142. Explanation: In the above-given question, given that, There are 136 crayons in a box. The number greater than 136 is 142. Question 9. THINK SMARTER Becky has 134 stamps. Sara has 129 stamps. Who has more stamps? _____Becky________ Answer: Becky has more stamps. Explanation: In the above-given question, given that, Becky has 134 stamps. Sara has 129 stamps. Becky has more stamps. Sara buys 10 more stamps. Who has more stamps now? _____Sara________ Answer: Sara has more stamps. Explanation: In the above-given explanation, given that, Sara buys 10 more stamps. Sara has more stamps now. Draw quick pictures to show the stamps Becky and Sara have now. TAKE HOME ACTIVITY • Ask your child to explain how he or she solved one of the problems on this page. Problem Solving • Compare Numbers Homework & Practice 2.11 Model the numbers. Draw quick pictures to show how you solved the problem. Question 1. Lauryn has 128 marbles. Kristin has 118 marbles. Who has more marbles? __Lauryn_______ Answer: Lauryn has more marbles. Explanation: In the above-given question, given that, Lauryn has 128 marbles. Kristin has 118 marbles. Lauryn has more marbles. Question 2. Nick has 189 trading cards. Kyle has 198 trading cards. Who has fewer cards? __Nick_____ Answer: Nick has fewer cards. Explanation: In the above-given question, given that, Nick has 189 cards. Kyle has 198 cards. Nick has fewer cards. Question 3. A piano has 36 black keys and 52 white keys. Are there more black keys or white keys on a piano? __White Keys________ Answer: There are more white keys. Explanation: In the above-given question, given that, A piano has 36 black keys and 52 white keys. There are more white keys. Question 4. WRITE Math Draw to show how you can use models to compare 345 and 391. Lesson Check Question 1. Gina has 245 stickers. Circle the number less than 245. Answer: The number less than 245 is 239. Explanation: In the above-given question, given that, Gina has 245 stickers. The numbers are 285, 254, 245, and 239. Question 2. Carl’s book has 176 pages. Circle the number greater than 176. Answer: The number greater than 176 is 203. Explanation: In the above-given question, given that, Carl’s book has 176 pages. The numbers are 203, 174, 168, and 139. The number greater than 176 is 203. Spiral Review Question 3. Write 63 as a sum of tens and ones __6_ + _3__ Answer: The number has 6 tens and 3 ones. Explanation: In the above-given question: given that, the number is 63. 60 + 3 = 63. Question 4. Write the number 58 in tens and ones. __5_ tens _8_ ones Answer: The number has 5 tens and 8 ones. Explanation: In the above-given question: given that, the number is 58. 50 + 8 = 58. Question 5. Mr. Ford drove 483 miles during his trip. How many hundreds are in this number? __4__ Answer: They are 4 hundred in 483. Explanation: In the above-given question, given that, Mr. Ford drove 483 miles during his trip. They are 4 hundred in 483. Question 6. Write 20 in words. __twenty____ Answer: The number is twenty. Explanation: In the above-given question, given that, Write 20 in words. The number is twenty. Lesson 2.12 Algebra • Compare Numbers Essential Question How do you compare 3-digit numbers? Listen and Draw Draw quick pictures to solve the problem. More ___ were at the park. Math Talk MATHEMATICAL PRACTICES Explain how you compared the numbers. Share and Show Compare the numbers. Write >, <, or =. Question 1. Answer: 239 is greater than 179. Explanation: In the above-given question, given that, 179 is less than 239 Question 2. Answer: 435 is less than 437. Explanation: In the above-given question, given that, 435 is less than 437. Question 3. Answer: 764 is greater than 674. Explanation: In the above-given question, given that, 764 is greater than 674. Question 4. Answer: 519 is less than 572. Explanation: In the above-given question, given that, 519 is less than 572. On Your Own Compare the numbers. Write >, <, or =. Question 5. Answer: 378 is less than 504. Explanation: In the above-given question, given that, 378 is less than 504. Question 6. Answer: 821 is equal to 821. Explanation: In the above-given question, given that, 821 is equal to 821. Question 7. Answer: 560 is greater than 439. Explanation: In the above-given question, given that, 560 is greater than 439. Question 8. Answer: 934 is equal to 934. Explanation: In the above-given question, given that, 934 is equal to 934. THINK SMARTER Write the 3-digit numbers and compare the numbers. Use >, <, or =. Question 9. Answer: 475 is equal to 475. Explanation: In the above-given question, given that, 475 is equal to 475. Question 10. Answer: 736 is greater than 687. Explanation: In the above-given question, given that, 736 is greater than 687. MATHEMATICAL PRACTICE Use Reasoning Write a 3-digit number in the box that makes the comparison true. Question 11. Answer: 526 is less than 670. Explanation: In the above-given question, given that, 526 is less than 670. Question 12. Answer: 319 is greater than 500. Explanation: In the above-given question, given that, 319 is greater than 500. Question 13. Answer: 526 is less than 782. Explanation: In the above-given question, given that, 526 is less than 782. Question 14. Answer: 90 is less than 131. Explanation: In the above-given question, given that, 90 is less than 131. Problem Solving • Applications Solve. Write or draw to explain. Question 15. THINK SMARTER Mrs. York has 300 red stickers, 50 blue stickers, and 8 green stickers. Mr. Reed has 372 stickers. Who has more stickers? Answer: Mr. Reed has more stickers. Explanation: In the above-given question, given that, Mrs. York has 357 red stickers. Mr. Reed has 372 stickers. Mr. Reed has more stickers Question 16. MATHEMATICAL PRACTICE Analyze Jasmine has some number cards. Use the digits on these cards to make two 3-digit numbers. Use each digit only once. Compare the numbers. Answer: 125 is less than 638. Explanation: In the above-given question. given that, Jasmine has 125 and 638 number cards. 125 is less than 638. Question 17. THINK SMARTER Is the comparison true? Choose Yes or No. Answer: yes. No. No. yes. Explanation: In the above-given question, given that, 453 is greater than 354. 253 is less than 164. 391 is less than 417. 490 is less than 528. TAKE HOME ACTIVITY • Have your child explain how to compare the numbers 281 and 157. Algebra • Compare Numbers Homework & Practice 2.12 Compare the numbers. Write >, <, or =. Question 1. 489 605 Answer: 489 is less than 605. Explanation: In the above-given question, given that, 489 is less than 605. Question 2. 719 719 Answer: 719 is equal to 719. Explanation: In the above-given question, given that, 719 is equal to 719 Question 3. 370 248 Answer: 370 is greater than 248. Explanation: In the above-given question, given that, 370 is greater than 248. Question 4. 645 654 Answer: 645 is less than 654. Explanation: In the above-given question, given that, 645 is less than 654. Question 5. 205 250 Answer: 205 is less than 250 Explanation: In the above-given question, given that, 205 is less than 250 Question 6. 813 781 Answer: 813 is greater than 781 Explanation: In the above-given question, given that, 813 is greater than 781. Problem Solving Solve. Write or draw to explain. Question 7. Toby has 178 pennies. Bella has 190 pennies. Who has more pennies? _Bella___ has more pennies. Answer: Bella has more pennies. Explanation: In the above-given question, given that, Toby has 178 pennies. Bella has 190 pennies. Bella has more pennies. Question 8. WRITE Math Explain how comparing 645 and 738 is different from comparing 645 and 649. _____________________ _____________________ Lesson Check Question 1. Write >, <, or = to compare. Answer: 351 is greater than 315. Explanation: In the above-given question, given that, 315 is less than 351. Question 2. Write >, <, or = to compare. Answer: 401 is greater than 399. Explanation: In the above-given question, given that, 401 is less than 399. Spiral Review Question 3. What number has the same value as 50 tens? __5 tens 0 ones_______ Answer: The number has the same value as 50 is 5 tens 0 ones. Explanation: In the above-given question, given that, The number has the same value as 50 tens. Question 4. Write a number with an 8 in the hundreds place. ____803____ Answer: The number with an 8 in the hundreds place is 803. Explanation: In the above-given question, given that, The number with an 8 in the hundreds place is 803. Question 5. Ned counts by fives. He starts at 80. Which number should he say next? ____85______ Answer: He should say 85. Explanation: In the above-given question, given that, Ned counts by fives. He starts at 80. He should say 85. Question 6. Mr. Dean has an even number of cats and an odd number of dogs. Show how many dogs and cats he might have. 6 cats and _9_ dogs Answer: 6 cats and 9 dogs. Explanation: In the above-given question, given that, Mr. Dean has an even number of cats and an odd number of dogs. There are 6 cats and 9 dogs. Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers Are you seeing everywhere to find Go Math Grade 4 Answer Key Chapter 3 Multiply 2-Digit Numbers in pdf? If so, you have stepped onto the right page. On this page, we have compiled a pdf formatted HMH Go Math Grade 4 Chapter 3 Multiply 2-Digit Numbers Answer Key. Take the help of the Go Math Grade 4 Solution Key during your practice sessions and clear your queries. Assess your preparation standards and concentrate on the areas you are flagging. Go Math Grade 4 Solution Key Pdf Chapter 3 Multiply 2-Digit Numbers With the help of HMH Go Math Grade 4 Answer Key Ch 3, you can learn the easy methods to solve problems. Answer Key for HMH Go Math Grade 4 Chapter 3 Multiply 2-Digit Numbers consists of all the questions from practice tests, exercises, assessments tests. You guys are recommended to solve the 4th grade Go Math Answers of Chapter 3 Multiply 2-Digit Numbers regularly & attempt the exams with confidence. The topics covered in the Go Math HMH grade 4 Solutions are designed perfectly & in an understandable way. Lesson 1: Multiply by Tens Lesson 2: Estimate Products Lesson 3: Investigate • Area Models and Partial Products Lesson 4: Multiply Using Partial Products Mid-Chapter Checkpoint Lesson 5: Multiply with Regrouping Lesson 6: Choose a Multiplication Method Lesson 7: Problem Solving • Multiply 2-Digit Numbers Review/Test Common Core – Page No. 149 Multiply by Tens Choose a method. Then find the product. Question 1. 16 × 60 = 960 Use the halving-and-doubling strategy. Find half of 16: 16 ÷ 2 = 8. Multiply this number by 60: 8 × 60 = 480 Double this result: 2 × 480 = 960 Answer: 960 Explanation: Use the halving-and-doubling strategy. Find half of 16: 16 ÷ 2 = 8. Multiply this number by 60: 8 × 60 = 480 Double this result: 2 × 480 = 960 Question 2. 80 × 22 = ______ Answer: 1760 Explanation: By using the place value method, Multiply 80 x 22 You can think of 80 as 8 tens 80 x 22 = (22 x 8) tens = 176 tens = 176 x 10 = 1760 80 x 22 = 1760 Question 3. 30 × 52 = ______ Answer: 1560 Explanation: Use the Associative Property You can think of 30 as 3 x 10 30 x 52 = (3 x 10) x 52 = 3 x (10 x 52) = 3 x 520 = 1560 30 x 52 = 1560 Question 4. 60 × 20 = ______ Answer: 1200 Explanation: 60 x 20 Use the halving and doubling strategy half of the 60 to make the problem simpler 60/ 2 = 30 Multiply 30 with 20 30 x 20 = 600 Double the 600 2 x 600= 1200 60 x 20 = 1200 Question 7. 31 × 50 = ______ Answer: 1,550 Explanation: Use the place value method to multiply 31 x 50 You can think of 50 as 5 tens 31 x 50 = 31 x 5 tens = 155 tens = 1,550 31 x 50 = 1,550 Problem Solving Common Core – Page No. 150 Lesson Check Question 1. For the school play, 40 rows of chairs are set up. There are 22 chairs in each row. How many chairs are there in all? Options: a. 800 b. 840 c. 880 d. 8,800 Answer: c. 880 Explanation: As per the given data For the school play, 40 rows of chairs are available. 22 chairs are available in each row. Then total chairs in school play are = 22 x 40 By using the place value method You can think of 40 as 4 tens 22 x 40 = 22 x 4 tens = 88 tens = 880 Total chairs in school are = 880 Question 2. At West School, there are 20 classrooms. Each classroom has 20 students. How many students are at West School? Options: a. 40 b. 400 c. 440 d. 4,000 Answer: b. 400 Explanation: From the given data, Total classrooms in west school = 20 Number of students per each classroom = 20 Then, total students at West School = 20 x 20 By using the associative property You can think of 20 as 2 x 10 20 x 20 = 20 x (2 x 10) = (20 x 2) x 10 =(40) x 10 =400 Total number of students at West School = 400 Spiral Review Question 3. Alex has 48 stickers. This is 6 times the number of stickers Max has. How many stickers does Max have? Options: a. 6 b. 7 c. 8 d. 9 Answer: c. 8 Explanation: As per the give data, Alex has 48 stickers That means, X= 48 This is 6 times the number of stickers max has = Y = 6X = 48 Then, number of stickers with Max = Y = X = 48/6 = 8 Number of stickers with Max = Y = 8 Stickers. Question 4. Ali’s dog weighs 8 times as much as her cat. Together, the two pets weigh 54 pounds. How much does Ali’s dog weigh? Options: a. 6 pounds b. 42 pounds c. 46 pounds d. 48 pounds Answer: d. 48 pounds Explanation: From the given data, Ali’s cat weight = X Ali’s dog weight = 8 times as much as Ali’s cat = 8X Together, the two pets weight = (X+8X) = 54 pounds = 9X = 54 pounds = X = 54/9 pounds = 6 pounds Then, Ali’s dog weight = 8X =8 x 6 = 48 pounds. Question 5. Allison has 3 containers with 25 crayons in each. She also has 4 boxes of markers with 12 markers in each box. She gives 10 crayons to a friend. How many crayons and markers does Allison have now? Options: a. 34 b. 113 c. 123 d. 133 Answer: b. 113 Explanation: As per the given data, Allison has 3 containers with 25 crayons in each = X = 3 x 25 = 75 Allison has 4 boxes of markers with 12 markers in each box = Y = 4 x 12 = 48 Allison gives 10 crayons to a friend = Z = 75-10 = 65 Now, total number of crayons and markers with Allison = Y + Z = 48 + 65 = 113 Question 6. The state of Utah covers 82,144 square miles. The state of Montana covers 145,552 square miles. What is the total area of the two states? Options: a. 63,408 square miles b. 223,408 square miles c. 227,696 square miles d. 966,992 square miles Answer: c. 227,696 square miles Explanation: From the given data, The state of Utah covers 82,144 square miles The state of Montana covers 145,552 square miles Then, Total area of the two states = 82,144 + 145,552 The total area of two states = 227,696 square miles. Page No. 153 Question 1. To estimate the product of 62 and 28 by rounding, how would you round the factors? What would the estimated product be? about _____ Answer: 1800 Explanation: By using rounding and mental math Estimate 62 x 28 Firstly, round each factor 62 x 28 60 x 30 Use mental math 6 x 3 = 18 60 x 30 = 1800 So, estimated product of 62 and 28 = 1800 Estimate the product. Choose a method. Question 2. 96 × 34 Estimate: _____ Answer: 3000 Explanation: Use mental math and compatible numbers 96 x 34 100 x 30 Use mental math 1 x 30 = 30 100 x 30= 3000 Question 3. 47 ×$39
Estimate: $_____ Answer: 2000 Explanation: Round to the nearest ten 47 x$39

50 x $40 50 x$ 4 = $200 50 x$40 = 2000

Question 4.
78 × 72
Estimate: _____

5600

Explanation:
Use rounding and mental math
Round each factor
78 x 72

80 x 70
Use mental math
8 x 7 = 56
80 x 70 = 5600

Practice: Copy and Solve Estimate the product. Choose a method.

Question 8.
61 × 31
Estimate: _____

1800

Explanation:
Round to the nearest ten
61 x 31

60 x 30 = 1800

Question 9.
52 × 68
Estimate: _____

3500

Explanation:
Round each factor
52 x 68

50 x 70
Use mental math
5 x 7 =35
50 x 70 = 3500

Question 10.
26 × 44
Estimate: _____

1200

Explanation:
Round to the nearest tens
26 x 44

30 x 40 = 1200

Question 11.
57 × $69 Estimate:$ _____

$4200 Explanation: Round each factor 57 x$69

60 x $70 Use mental math 6 x$7 = $42 60 x$70 = $4200 Find two possible factors for the estimated product. Question 14. 5,600 Type below: ___________ Answer: 5,600 Explanation: Let us consider 7 x 8 = 56 70 x 80 = 5,600 Question 15. 2,400 Type below: ___________ Answer: 2,400 Explanation: Let us take 4 x 6 = 24 40 x 60 = 2400 Or 3 x 8 = 24 30 x 80 = 2,400 Question 16. Mr. Parker jogs for 35 minutes each day. He jogs 5 days in week 1, 6 days in week 2, and 7 days in week 3. About how many minutes does he jog? about _____ minutes Answer: about 630 minutes Explanation: From the given data, Mr. Parker jogs per day = 35 minutes He jogs 5 days in week 1 = 5 x 35 = 175 minutes 6 days in week 2 = 6 x 35 = 210 minutes 7 days in week 3 = 7 x 35 = 245 minutes Total minutes of jog by Mr. Parker = week 1 + week 2 + week 3 = 175 + 210 + 245 = 630 minutes So, total minutes of jog by Mr. Parker = 630 minutes Question 17. There are 48 beads in a package. Candice bought 4 packages of blue, 9 packages of gold, 6 packages of red, and 2 packages of silver beads. About how many beads did Candice buy? about _____ beads Answer: about 1008 beads Explanation: As per the given data, 48 beads are there in a package Candice bought 4 packages of blue beads = 4 x 48 = 192 9 packages of gold beads = 9 x 48 = 432 6 packages of red beads = 6 x 48 = 288 2 packages of silver beads = 2 x 48 = 96 Total beads bought by Candice = 192 + 432 + 288 + 96 = 1008 beads So, total beads bought by Candice = 1008. Page No. 154 Question 20. If Mel opens his refrigerator door 36 times every day, how many times will it be opened in April? Will the exact answer be more than or less than the estimate? Explain. Type below: ___________ Answer: 1200 Explanation: From the given data, Mel opens his refrigerator door per day = 36 times Number of days in April month = 30 days Refrigerator door opened in April month = 36 * 30 Round the factors 36 x 30 40 x 30 = 1200 Question 21. Represent a Problem What question could you write for this answer? The estimated product of two numbers, which are not multiples of ten, is 2,800. Type below: ___________ Answer: 2800 Explanation: Let us take 1. 38 × 21 ↓ ↓ 40 × 20 = 800 2,800 = 42 x 68 ↓ ↓ 40 x 70 = 2800 Question 22. Which is a reasonable estimate for the product? Write the estimate. An estimate may be used more than once. 26 × 48 __________ 28 × 21 __________ 21 × 22 __________ 51 × 26 __________ Answer: 25 x 50 = 1250 30 x 20 = 600 20 x 20 = 400 50 x 25 = 1250 Explanation: 26 x 48 -> 25 x 50 = 1250 28 x 21 -> 30 x 20 = 600 21 x 22 -> 20 x 20 = 400 51 x 26 -> 50 x 25 = 1250 Common Core – Page No. 155 Estimate Products Estimate the product. Choose a method. Question 1. 38 × 21 38 × 21 ↓ ↓ 40 × 20 800 Answer: 800 Explanation: 38 × 21 ↓ ↓ 40 × 20 800 Question 2. 63 × 19 Estimate: _____ Answer: 1200 Explanation: 63 x 19 60 x 20 = 1200 Estimated product of 63 x 19 = 1200 Question 5. 37 ×$44
Estimate:$_____ Answer:$1600

Explanation:
37 × $44 40 x$40 = $1600 Estimated Product of 37 x$44 = $1600 Question 6. 85 × 71 Estimate: _____ Answer: 6300 Explanation: 85 × 71 90 x 70 = 6300 Estimated Product of 85 x 71 = 6300 Question 7. 88 × 56 Estimate: _____ Answer: 4950 Explanation: 88 × 56 90 x 55 = 4950 Estimated Product of 90 x 55 = 4950 Question 8. 97 × 13 Estimate: _____ Answer: 1,000 Explanation: 97 × 13 100 x 10 = 1,000 Question 9. 92 × 64 Estimate: _____ Answer: 5850 Explanation: 92 × 64 90 x 65 = 5850 Problem Solving Common Core – Page No. 156 Lesson Check Question 1. Which is the best estimate for the product 43 × 68? Options: a. 3,500 b. 2,800 c. 2,400 d. 280 Answer: b. 2,800 Explanation: Round to the nearest tens 43 x 68 40 x 70 Use mental math 4 x 7 = 28 40 x 70 = 2800 Estimated product of 43 x 68 = 2800 Question 2. Marissa burns 93 calories each time she plays fetch with her dog. She plays fetch with her dog once a day. About how many calories will Marissa burn playing fetch with her dog in 28 days? Options: a. 4,000 b. 2,700 c. 2,000 d. 270 Answer: b. 2,700 Explanation: From the given data, Marissa burned calories each time when she plays fetch with her dog= 93 calories Then, Marissa burned calories in 28 days while playing fetch with her dog = 28 x 93 Round to the nearest tens 28 x 93 30 x 90 Then, estimated burned calories in 28 days by Marissa = 2700 calories Spiral Review Question 3. Use the model to find 3 × 126. Options: a. 368 b. 378 c. 468 d. 478 Answer: b. 378 Explanation: From the above Figure, 3 x 126 = 3 x 100 + 3 x 20 + 3 x 6 = 300 + 60 + 18 = 378 3 x 126 = 378 Question 4. A store sells a certain brand of jeans for$38. One day, the store sold 6 pairs of jeans of that brand. How much money did the store make from selling the 6 pairs of jeans?
Options:
a. $188 b.$228
c. $248 d.$288

b. $228 Explanation: As per the given data, A store sells a certain brand of jeans for rupees =$38
One day, the store sold 6 pairs of jeans of that brand = 6 x $38 6 x$38 = $228 The total amount of 6 pairs of jeans =$228

Question 5.
The Gateway Arch in St. Louis, Missouri, weighs about 20,000 tons. Which amount could be the exact number of tons the Arch weighs?
Options:
a. 31,093 tons
b. 25,812 tons
c. 17,246 tons
d. 14,096 tons

c. 17,246 tons

Explanation:
From the given data,
The Gateway Arch in St.Louis, Missouri weight = about 20,000 tons
From the available options, 17,246 tons is closer to 20,000 tons
Then, the exact number of tons the Arch weighs = 17,246 tons

Question 6.
Which is another name for 23 ten thousands?
Options:
a. 23,000,000
b. 2,300,000
c. 230,000
d. 23,000

c. 230,000

Explanation:
As per the data,
Another name for 23 ten thousands = 23 x 10,000
= 230,000
Another name for 23 ten thousand = 2,30,000

Page No. 159

Find the product.

Question 1.
16 × 19

16 × 19 = _____

304

Explanation:

16 x 19 = 304

Question 2.
18 × 26

18 × 26 = _____

468

Explanation:

200 + 160 + 60 + 48 = 468

Question 3.
27 × 39

27 × 39 = ______

1,053

Explanation:

600 + 210 + 180 +63 = 1053

Draw a model to represent the product.
Then record the product.

Question 4.
14 × 16 = ______

224

Explanation:

100 + 40 + 60 + 24 = 224

Question 5.
23 × 25 = ______

575

Explanation:

400 + 60 + 100 + 15 = 575

Question 6.
Explain how modeling partial products can be used to find the products of greater numbers.
Type below:
__________

You can use mental math to find the partial products and then find the sum of the partial products.

Explanation:

Question 7.
Emma bought 16 packages of rolls for a party. There were 12 rolls in a package. After the party there were 8 rolls left over. How many rolls were eaten? Explain.
______ rolls

184 rolls were eaten

Explanation:
From the given data,
Emma bought 16 packages of rolls for a party
There were 12 rolls in a package
Then, total rolls = 16 x 12 = 192

100 + 60 + 20 + 12 =192
After the party there were 8 rolls left over
Then, total eaten rolls are = 192 – 8 = 184

Page No. 160

Question 8.
Jamal and Kim used different ways to solve 12 × 15 by using partial products. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning.
Jamal’s Work

100 + 20 + 10 = 130

Kim’s Work

120 + 60 = 180
a. For the answer that is nonsense, write an answer that makes sense.
Type below:
__________

a. Jamal’s work makes nonsense.
100 + 20 + 50 + 10 = 180 it makes sense

Question 8.
b. Look at Kim’s method. Can you think of another way Kim could use the model to find the product? Explain.

Type below:
__________

Other method: 12 x 15
10 x 12 = 120
5 x 12 = 60
120 + 60 = 180.

Explanation:
Kim follows another method to find 12 x 15
That is, 100 + 50 = 150
20 + 10 = 30
Then, 150 + 30 =180
12 x 15 = 180

Question 9.
Look at the model in 8b. How would the partial products change if the product was 22 × 15? Explain why you think the products changed.
Type below:
__________

330

Explanation:
Following the 8b method
22 x 15 =330

200 + 100 = 300
20 + 10 = 30
Now, 300 + 30 = 330
Finally, 22 x 15 = 330
The factor of 15 is increased in present problem. So, the product also increases for 15 x 22.

Common Core – Page No. 161

Area Models and Partial Products

Draw a model to represent the product.
Then record the product.

Question 1.
13 × 42

Question 2.
18 × 34 = ______

300 + 40 + 240 + 32 = 612

Question 3.
22 × 26 = ______

400 + 120 + 40 + 12 = 572

Question 4.
1 5 × 33 = ______

300 + 30 + 150 + 15 = 495

Question 5.
23 × 29 = ______

400 + 180 + 60 + 27 = 667

Question 6.
19 × 36 = ______

300 + 60 + 270 + 54 = 684

Problem Solving

Question 7.
Sebastian made the following model to find the product 17 × 24.

Is his model correct? Explain.
a. yes
b. no

b. no

Explanation:

200 + 40 + 140 + 28 = 408

Question 8.
Each student in Ms. Sike’s kindergarten class has a box of crayons. Each box has 36 crayons. If there are 18 students in Ms. Sike’s class, how many crayons are
there in all?
______ crayons

648 crayons

Explanation:
From the given information,
Each student in Ms.Sike’s kindergarten class has a box of crayons
Crayons in each box = 36 Crayons
Number of students in Mr.Sike’s class = 18 students
Total crayons = 18 x 36

300 + 60 + 240 + 48 = 648

Common Core – Page No. 162

Lesson Check

Question 1.
Which product does the model below represent?

Options:
a. 161
b. 230
c. 340
d. 391

d. 391

Explanation:
200 + 30 + 140 + 21 = 391
17 x 23 = 391

Question 2.
Which product does the model below represent?

Options:
a. 219
b. 225
c. 244
d. 275

b. 225

Explanation:
130 + 20 + 65 + 10 = 225
15 x 15 = 225

Spiral Review

Question 3.
Mariah builds a tabletop using square tiles. There are 12 rows of tiles and 30 tiles in each row. How many tiles in all does Mariah use?
Options:
a. 100
b. 180
c. 360
d. 420

c. 360

Explanation:
From the given data,
Mariah builds a tabletop using square tiles
Square contains 12 rows of tiles and 30 tiles in each row = 12 x 30
12 x 30 = 360 tiles
Total tiles used by Mariah = 360 tiles

Question 4.
Trevor bakes 8 batches of biscuits, with 14 biscuits in each batch. He sets aside 4 biscuits from each batch for a bake sale and puts the rest in a jar. How many biscuits does Trevor put in the jar?
Options:
a. 112
b. 80
c. 50
d. 32

b. 80

Explanation:
As per the given data,
Number of biscuits baked by Trevor = 8 batches
Number of biscuits in each batch = 14 biscuits
So, total biscuits = 14 x 8 = 112
Trevor sets aside 4 biscuits from each batch for a bake = 8*4 = 32 biscuits are aside for a bake
Trevor kept rest of biscuits in a jar = 112 – 32 = 80
So, 80 biscuits are put in the jar by the Trevor

Question 5.
Li feeds her dog 3 cups of food each day. About how many cups of food does her dog eat in 28 days?
Options:
a. 60 cups
b. 70 cups
c. 80 cups
d. 90 cups

c. 80 cups

Explanation:
As per the given data,
Li feeds her dog per day = 3 cups of food
Then, Li feeds her dog for 28 days = 3 x 28
= 84 cups of food
So, Li feeds her dog with 84 cups of food in 28 days

Question 6.
Which symbol makes the number sentence true?
4 ■ 0 = 0
Options:
a. +
b. –
c. ×
d. ÷

c. ×

Explanation:
4 x 0 = 0

Page No. 165

Question 1.
Find 24 × 34.

_____

816

Explanation:

Question 2.
1 2
× 1 2
——–
_____

144

Explanation:

Question 3.
3 1
× 2 4
——-
_____

744

Explanation:

Question 4.
2 5
× 4 3
——-
_____

1,075

Explanation:

Question 5.
3 7
× 2 4
——-
_____

888

Explanation:

Question 6.
5 4
× 1 5
——-
_____

810

Explanation:

Question 7.
8 7
× 1 6
——-
_____

1,392

Explanation:

Question 8.
6 2
× 5 6
——-
_____

3,472

Explanation:

Question 9.
4 9
× 6 3
——-
_____

3,087

Explanation:

Practice: Copy and Solve Record the product.

Question 10.
38 × 47
_____

1,786

Explanation:

Question 11.
46 × 27
_____

1,242

Explanation:

Question 12.
72 × 53
_____

3,816

Explanation:

Question 13.
98 × 69
_____

6,762

Explanation:

Question 14.
53 × 68
_____

3,604

Explanation:

Question 15.
76 × 84
_____

6,384

Explanation:

Question 16.
92 × 48
_____

4,416

Explanation:

Question 17.
37 × 79
_____

2,923

Explanation:

Reason Abstractly Algebra Find the unknown digits. Complete the problem.

Question 18.

Type below:
___________

1,824

Explanation:

Question 19.

Type below:
___________

7,954

Explanation:

Question 20.

Type below:
___________

1,908

Explanation:

Question 21.

Type below:
___________

952

Explanation:

Page No. 166

Use the picture graph for 22–24.

Question 22.
Use Graphs A fruit-packing warehouse is shipping 15 boxes of grapefruit to a store in Santa Rosa, California. What is the total weight of the shipment?
______ pounds

1275 pounds

Explanation:
From the given data,
A fruit packing warehouse is shipping 15 boxes of grapefruit to store in Santa Rose, California
Grapefruit weight per box = 85 pounds
Total weight of the shipment = 85 x 15

So, the total weight of the shipment = 1275 pounds

Question 23.
How much less do 13 boxes of tangelos weigh than 18 boxes of tangerines?
______ pounds

450 pounds

Explanation:
As per the given data,
Tangelos weight per box = 90 pounds
Then, the weight of the 13 boxes of tangelos = 90 x 13

And, the weight of the 18 boxes of tangelos = 90 x 18

1620 – 1170 = 450
So, 13 boxes of tangelos weight are 450 pounds less than 18 boxes of tangelos weight

Question 24.
What is the weight of 12 boxes of oranges?
______ pounds

1,080 pounds

Explanation:
The weight of the oranges per box = 90 pounds
then, weight of 12 boxes oranges = 90 x 12

So, weight of 12 boxes oranges = 1,080 pounds

Question 25.
Each person in the United States eats about 65 fresh apples each year. Based on this estimate, how many apples do 3 families of 4 eat each year?
______ apples

780 apples

Explanation:
From the given data,
Each person in the united states eats fresh apples per year = 65
3 families of 4 persons = 3 x 4 = 12 persons
Then, the number of apples eat by 12 persons = 65 x 12

So, the total number of apples eat by 12 persons per year = 780

Question 26.
The product 26 × 93 is greater than 25 × 93. How much greater? Explain how you know without multiplying.
______

The difference is 93
26 x 93 is one more group of 93 than 25 x 93

Question 27.
Margot wants to use partial products to find 22 × 17. Write the numbers in the boxes to show 22 × 17.

Type below:
__________

Explanation:
22 x 17
(20 + 2) x 17
20 x 17 + 2 x 17
20 x (10 + 7) + 2 x (10 + 7)
(20 x 10) + (20 x 7) + (2 x 10) + (2 x 7)

Common Core – Page No. 167

Multiply Using Partial Products

Record the product.

Question 1.
2 3
× 7 9
———
1, 4 0 0
2 1 0
1 8 0
+ 2 7
——–
1, 8 1 7

1, 8 1 7

Explanation:
2 3
× 7 9
———
1, 4 0 0
2 1 0
1 8 0
+ 2 7
——–
1, 8 1 7

Question 2.
5 6
× 3 2
——-
_______

1,792

Explanation:

Question 3.
8 7
× 6 4
——-
_______

5,568

Explanation:

Question 4.
3 3
× 2 5
——-
_______

825

Explanation:

Question 5.
9 4
× 1 2
——-
_______

1,128

Explanation:

Question 6.
5 1
× 7 7
——-
_______

3,927

Explanation:

Question 7.
6 9
× 4 9
——-
_______

3,381

Explanation:

Question 8.
8 6
× 8 4
——-
_______

7,224

Explanation:

Question 9.
9 8
× 4 2
——-
_______

4,116

Explanation:

Question 10.
7 3
× 3 7
——-
_______

2,701

Explanation:

Question 11.
8 5
× 5 1
——-
_______

4,335

Explanation:

Problem Solving

Question 12.
Evelyn drinks 8 glasses of water a day, which is 56 glasses of water a week. How many glasses of water does she drink in a year? (1 year = 52 weeks)
_______ glasses

2,912 glasses

Explanation:
As per the given data,
Evelyn drinks 8 glasses of water a day
Evelyn drinks water per week = 56 glasses
Then, the number of glasses per 52 weeks = 52 x 56

Total number of glasses of water drink by Evelyn per year = 2912 glasses of water

Question 13.
Joe wants to use the Hiking Club’s funds to purchase new walking sticks for each of its 19 members. The sticks cost $26 each. The club has$480. Is this enough money to buy each member a new walking stick? If not, how much more money is needed?
Is the money enough? _______
How much more is needed? _______

This amount is not enough to buy walking sticks
Still, $14 amount is needed to buy walking sticks Explanation: From the given data, Joe wants to use the Hiking club funds to purchase new walking sticks for each of its 19 members Cost per each stick =$26
Total walking sticks cost per 19 members = $26 x 19 Total cost for walking sticks for 19 members =$494
The club has = $480 This amount is not enough to buy walking sticks Still,$14 amount is needed to buy walking sticks

Common Core – Page No. 168

Lesson Check

Question 1.
A carnival snack booth made $76 selling popcorn in one day. It made 22 times as much selling cotton candy. How much money did the snack booth make selling cotton candy? Options: a.$284
b. $304 c.$1,562
d. $1,672 Answer: d.$1,672

Explanation:
As per the given data,
A carnival snack booth made popcorn in one day = $76 It made 22 times as much selling cotton candy Then, total selling cotton candy made by snack booth =$76 x 22

So, $1672 money snack booth will get for selling cotton candy Question 2. What are the partial products of 42 × 28? Options: a. 800, 80, 40, 16 b. 800, 16 c. 800, 40, 320, 16 d. 80, 16 Answer: c. 800, 40, 320, 16 Explanation: So, partial products of 42 x 28 are 800, 40, 320, 16 Spiral Review Question 3. Last year, the city library collected 117 used books for its shelves. This year, it collected 3 times as many books. How many books did it collect this year? Options: a. 832 b. 428 c. 351 d. 72 Answer: c. 351 Explanation: From the given data, Last year, the number of used books collected by city library by its shelves = 117 books This year, it collected 3 times as many books = 3 x 117 =351 books Total number of books collected by the city library for this year = 351 books Question 4. Washington Elementary has 232 students. Washington High has 6 times as many students. How many students does Washington High have? Options: a. 1,392 b. 1,382 c. 1,292 d. 1,281 Answer: a. 1,392 Explanation: As per the given data, The number of students in Washington elementary = 232 students Washington High has 6 times as many students = 6 x 232 = 1392 Total number of students in Washington High = 1392 students Question 5. What are the partial products of 35 × 7? Options: a. 10, 12 b. 21, 35 c. 210, 35 d. 350, 21 Answer: c. 210, 35 Explanation: Partial products of 35 x 7 are 210, 35 Question 6. Shelby has ten$5 bills and thirteen $10 bills. How much money does Shelby have in all? Options: a.$15
b. $60 c.$63
d. $180 Answer: d.$180

Explanation:
From the given data,
Shelby has ten $5 bills and thirteen$10 bills = (10 x $5) + (13 x$10)
= ($50) + ($130)
=$180 Total money with Shelby =$180

Page No. 169

Question 1.
Explain how to find 40 × 50 using mental math.
Type below:
__________

200

Explanation:
40 x 50
By using mental math
4 x 5 = 20
40 x 50 = 200

Question 2.
What is the first step in estimating 56 × 27?
Type below:
__________

18 centimeters

Explanation:
Round to the nearest values.
So, the first step of the estimated 56 x 27 is rounding to the nearest value which is 60 x 30

Choose a method. Then find the product.

Question 5.
12 × 80 = _____

960

Explanation:
Use the halving and doubling strategy
half of the 80 to make the problem simpler
80/ 2 = 40
Multiply 40 with 12
40*12 = 480
Double the 480
2*480= 960
12*80 = 960

Question 6.
70 × 50 = _____

3,500

Explanation:
70 x 50
By using the place value method
You can take 50 as 5 tens
70 x 50 = 70 x 5 tens
= 350 tens
70 x 50 = 3,500

Question 7.
58 × 40 = _____

2,320

Explanation:
By using the associative property
You can think of 40 as (4 x 10)
58 x 40 = 58 x (4 x 10)
= (58 x 4) x 10
= 232 x 10
58 x 40 = 2,320

Question 8.
30 × 40 = _____

1,200

Explanation:
Use the halving and doubling strategy
half of the 40 to make the problem simpler
40/ 2 = 20
Multiply 20 with 30
20*30 = 600
Double the 600
2*600= 1200
30*40 = 1,200

Question 9.
14 × 60 = _____

840

Explanation:
By using the place value method
You can take 60 as 6 tens
14 x 60 = 14 x 6 tens
= 84 tens
14 x 60 = 840

Question 10.
20 × 30 = _____

600

Explanation:
By using the associative property
You can think of 30 as (3 x 10)
20 x 30 = 20 x (3 x 10)
= (20 x 3) x 10
= 60 x 10
20 x 30 = 600

Question 11.
16 × 90 = _____

1,440

Explanation:
Use the halving and doubling strategy
half of the 90 to make the problem simpler
90/ 2 = 45
Multiply 45 with 16
16*45 = 720
Double the 720
2*720= 1440
16*90 = 1,440

Estimate the product. Choose a method.

Question 14.
43 × 25
Estimate: _____

1,000

Explanation:
Round to the nearest tens.
43 is close to 40; 25 is close to 25;
40 x 25 = 1000
Estimated product of 43 x 25 = 1,000

Question 15.
76 × 45
Estimate: _____

3,200

Explanation:
Round to the nearest tens.
76 is close to 80; 45 is close to 40;
Use the mental math
8 x 4 = 32
80 x 40 = 3200
So, the estimated product of 76 x 45 = 3,200

Question 16.
65 × $79 Estimate: _____ Answer:$4,800

Explanation:
Round to the nearest tens.
65 is close to 60; $79 is close to$80;
Use the mental math
6 x $8 =$48
60 x $80 =$4800
So, estimated product of 65 x $79 =$4,800

Question 17.
92 × 38
Estimate: _____

3,600

Explanation:
Round to the nearest tens.
92 is close to 90; 38 is close to 40;
Use the mental math, then
9 x 4 = 36
90 x 40 = 3,600
So, estimated product of 92 x 38 = 3,600

Question 18.
37 × 31
Estimate: _____

1,200

Explanation:
Round to the nearest tens.
37 is close to 40; 31 is close to 30;
Use the mental math, then
4 x 3 = 12
40 x 30 = 1,200
So, estimated product of 37 x 31 = 1,200

Question 19.
26 × $59 Estimate: _____ Answer:$1,800

Explanation:
Round to the nearest tens.
26 is close to 30; $59 is close to$60;
Use the mental math, then
3 x $6 =$18
30 x $60 =$1,800
So, estimated product of 26 x $59 =$1,800

Question 20.
54 × 26
Estimate: _____

18 centimeters

Explanation:
Round to the nearest tens.
54 is close to 50; 26 is close to 30;
Use the mental math
5 x 3 = 15
50 x 30 = 1,500
So, estimated product of 54 x 26 = 1,500

Question 21.
52 × 87
Estimate: _____

4,500

Explanation:
Round to the nearest tens.
52 is close to 50; 87 is close to 90;
Use the mental math
5 x 9 = 45
50 x 90 = 4500
So, estimated product of 52 x 87 = 4,500

Question 22.
39 × 27
Estimate: _____

18 centimeters

Explanation:
Round to the nearest tens.
39 is close to 40; 27 is close to 30;
Use the mental math
4 x 3 = 12
40 x 30 = 1,200
So, estimated product of 39 x 27 = 1,200

Question 23.
63 × 58
Estimate: _____

3,600

Explanation:
Round to the nearest tens.
63 is close to 60; 58 is close to 60;
Use the mental math
6 x 6 = 36
60 x 60 = 3,600
So, estimated product of 63 x 58 = 3,600

Page No. 170

Question 25.
Tito wrote the following on the board. What is the unknown number?

______

400

Explanation:
An unknown number is 50 x 8 = 400

Question 26.
What are the partial products that result from multiplying 15 × 32?
Type below:
__________

Partial products are 300, 150, 20, 10

Explanation:

Partial products are 300, 150, 20, 10

Page No. 173

Question 1.
Look at the problem. Complete the sentences.
Multiply ____ and ____ to get 0.
Multiply ____ and ____ to get 1,620.
0 + 1,620 = ____

_____

Multiply 27 and 0 to get 0.
Multiply 27 and 6 to get 1,620.
Add the partial products. 0 + 1,620 = 1,620.

Estimate. Then find the product.

Question 2.
6 8
× 5 3
——-
Estimate: _________
Product: __________

Estimate: 3,500
Product: 3,604

Explanation:
68 is closer to 70 and 53 is closer to 50
Estimate: 70 x 50 = 3,500
60 x 53 = 3180
8 x 53 = 424
3180 + 424 = 3604
Product 3,604

Question 3.
6 1
× 5 4
——-
Estimate: _________
Product: __________

Estimate: 3,000
Product: 3,294

Explanation:
61 is closer to 60 and 54 is closer to 50
Estimate: 60 x 50 = 3,000
60 x 54 = 3240
1 x 54 = 54
3240 + 54 = 3294
Product 3,294

Question 6.
7 8
× 5 6
——-
Estimate: _________
Product: __________

Estimate: 4,800
Product: 4,368

Explanation:
78 is closer to 80 and 56 is closer to 60
Estimate: 80 x 60 = 4,800
70 x 56 = 3920
8 x 56 = 448
3920 + 448 = 4368
Product 4,368

Question 7.
2 7
× 2 5
——-
Estimate: _________
Product: __________

Estimate: 600
Product: 675

Explanation:
27 is closer to 30 and 25 is closer to 20
Estimate: 30 x 20 = 600
20 x 25 = 500
7 x 25 = 175
500 + 175 = 675
Product 675

Practice: Copy and Solve Estimate. Then find the product.

Question 8.
34 × 65
Estimate: _________
Product: __________

Estimate: 1,800
Product: 2,210

Explanation:
34 is closer to 30 and 65 is closer to 60
Estimate: 30 x 60 = 1,800
30 x 65 = 1950
4 x 65 = 260
1950 + 260 = 2210
Product 2,210

Question 9.
42 × $13 Estimate:$ _________
Product: $_________ Answer: Estimate:$400
Product: $546 Explanation: 42 is closer to 40 and 13 is closer to 10 Estimate: 40 x 10 = 400 40 x$13 = $520 2 x$13= $26$520 + $26 =$546
Product $546 Question 10. 60 × 17 Estimate: _________ Product: __________ Answer: Estimate: 1,200 Product: 1,020 Explanation: 17 is closer to 20 Estimate: 60 x 20 = 1,200 60 x 17 = 1020 Product = 1,020 Question 11. 62 × 45 Estimate: _________ Product: __________ Answer: Estimate: 2,400 Product: 2,790 Explanation: 62 is closer to 60 and 45 is closer to 40 Estimate: 60 x 40 = 2,400 60 x 45 = 2700 2 x 45= 90 2700 + 90 = 2790 Product 2,790 Question 12. 57 ×$98
Estimate: $_________ Product:$ _________

Estimate: 6,000
Product: 5,586

Explanation:
57 is closer to 60 and 98 is closer to 100
Estimate: 60 x 100 = 6,000
50 x 98 = 4900
7 x 98= 686
4900 + 686 = 5586
Product 5,586

Look for a Pattern Algebra Write a rule for the pattern.
Use your rule to find the unknown numbers.

Question 13.

Rule _____________
Type below:
_________

Explanation:
1 hour = 60 min
Then, 5hr = 5 x 60 = 300 min
10hr = 10 x 60 = 600 min
15hr = 15 x 60 = 900 min
20hr = 20 x 60 = 1200 min
25hr = 25 x 60 = 1500 min

Question 14.
Owners of a summer camp are buying new cots for their cabins. There are 16 cabins. Each cabin needs 6 cots. Each cot costs $92. How much will the new cots cost?$ _______

$8,832 Explanation: As per the given data, Owners pf a summer camp are buying new cots for their cabins Number of cabins = 16 Each cabin needs 6 cots Then, total cots = 16 x 6 = 96 Each cot cost =$92
Then, cost for total cots = $92 x 96 92 is closer to 90 and 96 is closer to 100 Estimate = 90 x 100 = 9,000 90 x 96 = 8640 2 x 96 = 192 8640 + 192 = 8832 Product = 8,832 Page No. 174 Question 16. Machine A can label 11 bottles in 1 minute. Machine B can label 12 bottles in 1 minute. How many bottles can both machines label in 15 minutes? a. What do you need to know? Type below: __________ Answer: number of bottles labeled by Machine A and Machine B in 15 minutes Question 16. b. What numbers will you use? Type below: __________ Answer: 15x 11 and 15 x 12 Question 16. c. Tell why you might use more than one operation to solve the problem. Type below: __________ Answer: To find out the total number of bottle made by both machines A & B Question 16. d. Solve the problem. So, both machines can label ____ bottles in ____ minutes. Type below: __________ Answer: Machine A can label 11 bottles in 1 minute Then, the number of bottles labeled by machine A in 15 minutes = 15 x 11 = 165 Machine B can label 12 bottles in 1 minute Then, number of bottles labelled by Machine B in 15 minutes = 15 x 12 = 180 Total bottles labelled by both the machines in 15 minutes = 165 + 180 = 345 Question 17. Make Sense of Problems A toy company makes wooden blocks. A carton holds 85 blocks. How many blocks can 19 cartons hold? ______ blocks Answer: 1,615 blocks Explanation: From the given data, A toy company makes wooden blocks A carton holds 85 blocks Then, number of blocks hold by 19 cartons = 19 x 85 = 1615 Total number of blocks held by 19 cartons = 1,615 Question 19. Mr. Garcia’s class raised money for a field trip to the zoo. There are 23 students in his class. The cost of the trip will be$17 for each student. What is the cost for all the students? Explain how you found your answer.
$______ Answer:$391

Explanation:
As per the given data,
Mr. Garcia’s class raised money for a field trip to the zoo
Total number of students in his class = 23 students
Cost of the trip for each student = $17 Then, total cost for all the students =$17 x 23 = $391 Common Core – Page No. 175 Multiply with Regrouping Estimate. Then find the product. Question 1. Estimate: 2,700 Think: 87 is close to 90 and 32 is close to 30. 90 × 30 = 2,700 Answer: 2,784 Explanation: Think: 87 is close to 90 and 32 is close to 30. 90 × 30 = 2,700 Question 2. 7 3 × 2 8 ——– Estimate: ______ Product: _______ Answer: Estimate: 2,100 Product: 2,044 Explanation: Estimate: 73 is close to 70; 28 is close to 30. So, 70 x 30 = 2,100. Product: Write 73 as 7 tens and 3 ones. Multiply 28 by 3 ones. 2 28 x 73 ——– 84 <– 3 x 28 Multiply 28 by 7 tens 5 28 x 73 ——– 1960 <– 70 x 28 Add the partial products. 84 + 1960 = 2,044. So, 73 x 28 = 2,044. Question 3. 4 8 × 3 8 ——– Estimate: ______ Product: _______ Answer: Estimate: 2,000 Product: 1,824 Explanation: 48 is close to 50 and 38 is close to 40. Estimate: 50 × 40 = 2,000 40 x 38 = 1520 8 x 38 = 304 1520 + 304 = 1824. Product: 1,824 Question 4. 5 9 × 5 2 ——– Estimate: ______ Product: _______ Answer: Estimate: 3,000 Product: 3,068 Explanation: 59 is close to 60 and 52 is close to 50. Estimate: 60 × 50 = 3,000 50 x 52 = 2600 9 x 52 = 468 2600 + 468 = 3068. Product: 3,068. Question 7. 9 1 × 1 9 ——– Estimate: ______ Product: _______ Answer: Estimate: 1,800 Product: 1,729 Explanation: 91 is close to 90 and 19 is close to 20. Estimate: 90 × 20 = 1,800 90 x 19 = 1,710 1 x 19 = 19 1,710+ 19 = 1,729. Product: 1,729. Problem Solving Question 8. Baseballs come in cartons of 84 baseballs. A team orders 18 cartons of baseballs. How many baseballs does the team order? _______ baseballs Answer: 1,512 baseballs Explanation: To find total baseballs, 84 x 18 80 x 18 = 1,440 4 x 18 = 72 84 x 18 = 1,512 Question 9. There are 16 tables in the school lunchroom. Each table can seat 22 students. How many students can be seated at lunch at one time? _______ students Answer: 352 students Explanation: Total Students = 16 x 22 10 x 22 = 220 6 x 22 = 132 220 + 132 = 352. 352 students can be seated at lunch at one time Common Core – Page No. 176 Lesson Check Question 1. The art teacher has 48 boxes of crayons. There are 64 crayons in each box. Which is the best estimate of the number of crayons the art teacher has? Options: a. 2,400 b. 2,800 c. 3,000 d. 3,500 Answer: c. 3,000 Explanation: 1. Total number of crayons = 48 x 64 48 is close to 50; 64 is close to 60 50 x 60 = 3,000. The art teacher has about to 3, 000 crayons. Question 2. A basketball team scored an average of 52 points in each of 15 games. How many points did the team score in all? Options: a. 500 b. 312 c. 780 d. 1,000 Answer: c. 780 Explanation: Total Points = 52 x 15 50 x 15 = 750 2 x 15 = 30 750 + 30 = 780. The basketball team scored 780 points in total. Spiral Review Question 3. On Saturday, an orchard sold 83 bags of apples. There are 27 apples in each bag. Which expression represents the total number of apples sold? Options: a. 16 + 6 + 56 + 21 b. 160 + 60 + 56 + 21 c. 160 + 60 + 560 + 21 d. 1,600 + 60 + 560 + 21 Answer: d. 1,600 + 60 + 560 + 21 Explanation: Total number of apples sold = 83 x 27 80 x 27 = 2,160 3 x 27 = 81 2,160 + 81 = 2,241. The total number of apples sold = 2,241. 16 + 6 + 56 + 21 = 99 not equal to 2,241 160 + 60 + 56 + 21 = 297 not equal to 2,241 160 + 60 + 560 + 21 = 801 not equal to 2,241 1,600 + 60 + 560 + 21 = 2,241 equal to 2,241 1,600 + 60 + 560 + 21 = 2,241 is correct. Question 4. Hannah has a grid of squares that has 12 rows with 15 squares in each row. She colors 5 rows of 8 squares in the middle of the grid blue. She colors the rest of the squares red. How many squares does Hannah color red? Options: a. 40 b. 140 c. 180 d. 220 Answer: b. 140 Explanation: Hannah has a grid of squares that has 12 rows with 15 squares in each row = 12 x 15 = 180. The grid of squares in blue = 5 x 8 = 40. The grid of squares in red = 180 – 40 = 140. Question 5. Gabriella has 4 times as many erasers as Leona. Leona has 8 erasers. How many erasers does Gabriella have? Options: a. 32 b. 24 c. 12 d. 2 Answer: a. 32 Explanation: Gabriella has 4 x 8 = 32 erasers. Question 6. Phil has 3 times as many rocks as Peter. Together, they have 48 rocks. How many more rocks does Phil have than Peter? Options: a. 36 b. 24 c. 16 d. 12 Answer: b. 24 Explanation: Phil has 3 times as many rocks as Peter. Together, they have 48 rocks If Peter has x rocks, Phil has 3x rocks 3x + x = 48. 4x = 48. x = 48/4 = 12. Peter has 12 rocks. Phil has 3 x 12 = 36 rocks. Phil has 36 – 12 = 24 more rocks than Peter. Page No. 179 Question 1. Find the product. Estimate: ______ Product: _______ Answer: Estimate: 1,500 Product: 1,566 Explanation: 54 x 29 Estimate: Think 54 is close to 50; 29 is close to 30. 50 x 30 = 1,500 Product: 20 x 5 tens = 100 tens 20 x 4 ones = 80 ones 9 x 5 tens = 45 tens 9 x 4 ones = 36 ones. Add partial products. 1000 + 80 + 450 + 36 = 1,566. Estimate. Then choose a method to find the product. Question 3. 6 3 × 4 2 ——- Estimate: ______ Product: _______ Answer: Estimate: 2,400 Product: 2646 Explanation: 63 x 42 Estimate: Think 63 is close to 60; 42 is close to 40. 60 x 40 = 2400 Product: 40 x 6 tens = 240 tens 40 x 3 ones = 120 ones 2 x 6 tens = 12 tens 2 x 3 ones = 6 ones. Add partial products. 2400 + 120 + 120 + 6 = 2646. Question 4. 8 4 × 5 3 ——- Estimate: ______ Product: _______ Answer: Estimate: 4,000 Product: 4,452 Explanation: 84 x 53 Estimate: Think 84 is close to 80; 53 is close to 50. 80 x 50 = 4,000 Product: 50 x 8 tens = 400 tens 50 x 4 ones = 200 ones 3 x 8 tens = 24 tens 3 x 4 ones = 12 ones. Add partial products. 4000 + 200 + 240 + 12 = 4,452. Question 5. 7 1 × 1 3 ——- Estimate: ______ Product: _______ Answer: Estimate: 700 Product: 923 Explanation: 71 x 13 Estimate: Think 71 is close to 70; 13 is close to 10. 70 x 10 = 700 Product: 10 x 7 tens = 70 tens 10 x 1 ones = 10 ones 3 x 7 tens = 21 tens 3 x 1 ones = 3 ones. Add partial products. 700 + 10 + 210 + 3 = 923. Practice: Copy and Solve Estimate. Find the product. Question 6. 29 ×$82
Estimate: $_______ Product:$ _______

Estimate: $2,400 Product:$2,378

Explanation:
29 x $82 Estimate: Think 29 is close to 30;$82 is close to $80. 30 x$80 = $2,400 Product:$80 x 2 tens = $160 tens$80 x 9 ones = $720 ones$2 x 2 tens = $4 tens$2 x 9 ones = $18 ones. Add partial products.$1600 + $720 +$40 + $18 =$2,378.

Question 7.
57 × 79
Estimate: _______
Product: _______

Estimate: 4,800
Product: 4,503

Explanation:
57 x 79
Estimate: Think 57 is close to 60; 79 is close to 80.
60 x 80 = 4,800
Product:
70 x 5 tens = 350 tens
70 x 7 ones = 490 ones
9 x 5 tens = 45 tens
9 x 7 ones = 63 ones.
3500 + 490 + 450 + 63 = 4,503.

Question 8.
80 × 27
Estimate: _______
Product: _______

Estimate: 2,400
Product: 2,160

Explanation:
80 x 27
Estimate: Think 27 is close to 30.
30 x 80 = 2,400
Product:
20 x 8 tens = 160 tens
20 x 0 ones = 0 ones
7 x 8 tens = 56 tens
7 x 0 ones = 0 ones.
1600 + 0 + 560 + 0 = 2,160.

Question 9.
32 × $75 Estimate:$ _______
Product: $_______ Answer: Estimate:$2,100
Product: $2,400 Explanation: 32 ×$75
Estimate: Think 32 is close to 30; $75 is close to$70.
30 x $70 =$2,100
Product:
$70 x 3 tens =$210 tens
$70 x 2 ones =$140 ones
$5 x 3 tens =$15 tens
$5 x 2 ones =$10 ones.
$2100 +$140 + $150 +$10 = $2,400. Question 10. 55 × 48 Estimate: _______ Product: _______ Answer: Estimate: 2,750 Product: 2,640 Explanation: 55 × 48 Estimate: Think 48 is close to 50. 55 x 50 = 2,750 Product: 40 x 5 tens = 200 tens 40 x 5 ones = 200 ones 8 x 5 tens = 40 tens 8 x 5 ones = 40 ones. Add partial products. 2000 + 200 + 400 + 40 = 2,640. Question 11. 19 ×$82
Estimate: $_______ Product:$ _______

Estimate: $1,600 Product:$1,558

Explanation:
19 × $82 Estimate: Think 19 is close to 20;$82 is close to $80. 20 x$80 = $1,600 Product:$80 x 1 tens = $80 tens$80 x 9 ones = $720 ones$2 x 1 tens = $2 tens$2 x 9 ones = $18 ones. Add partial products.$800 + $720 +$20 + $18 =$1,558.

Question 12.
25 × $25 Estimate:$ _______
Product: $_______ Answer: Estimate:$625
Product: $625 Explanation: 25 ×$25
Estimate:
25 x $25 =$625
Product:
$20 x 2 tens =$40 tens
$20 x 5 ones =$100 ones
$5 x 2 tens =$10 tens
$5 x 5 ones =$25 ones.
$400 +$100 + $100 +$25 = $625. Question 13. 41 × 98 Estimate: _______ Product: _______ Answer: Estimate: 4,000 Product: 4,018 Explanation: 41 × 98 Estimate: Think 41 is close to 40; 98 is close to 100. 40 x 100 = 4,000 Product: 90 x 4 tens = 360 tens 90 x 1 ones = 90 ones 8 x 4 tens = 32 tens 8 x 1 ones = 8 ones. Add partial products. 3600 + 90 + 320 + 8 = 4,018. Identify Relationships Algebra Use mental math to find the number. Page No. 180 Question 18. Martin collects stamps. He counted 48 pages in his collector’s album. The first 20 pages each have 35 stamps in 5 rows. The rest of the pages each have 54 stamps. How many stamps does Martin have in his album? a. What do you need to know? Type below: _________ Answer: The total stamps in the first 20 pages + The total stamps in the remaining pages. Question 18. b. How will you use multiplication to find the number of stamps? Type below: _________ Answer: The first 20 pages each have 35 stamps in 5 rows. So, 35 x 5 = 175 stamps. Question 18. c. Tell why you might use addition and subtraction to help solve the problem. Type below: _________ Answer: As mentioned that the number of stamps available in the first 20 pages and the number of stamps available in the rest of the pages. We need to add all pages to get 48 pages stamps. Question 18. d. Show the steps to solve the problem. Type below: _________ Answer: Martin has 48 pages in his collector’s album. The first 20 pages each have 35 stamps in 5 rows. So, 35 x 5 = 175 stamps. The first 20 pages have 175 stamps. The rest of the pages each have 54 stamps. So, total stamps = 175 + 54 = 229 stamps. Question 18. e. Complete the sentences. Martin has a total of _____ stamps on the first 20 pages. There are _____ more pages after the first 20 pages in Martin’s album. There are _____ stamps on the rest of the pages. There are _____ stamps in the album. Type below: _________ Answer: Martin has a total of __175___ stamps on the first 20 pages. There are __24___ more pages after the first 20 pages in Martin’s album. There are __54___ stamps on the rest of the pages. There are ___229__ stamps in the album. Question 19. Select the expressions that have the same product as 35 × 17. Mark all that apply. Options: a. (30 × 10) + (30 × 7) + (5 × 10) + (5 × 7) b. (30 × 17) + (5 × 17) c. (35 × 30) + (35 × 5) + (35 × 10) + (35 × 7) d. (35 × 10) + (35 × 7) e. (35 × 10) + (30 × 10) + (5 × 10) + (5 × 7) f. (35 × 30) + (35 × 5) Answer: a. (30 × 10) + (30 × 7) + (5 × 10) + (5 × 7) b. (30 × 17) + (5 × 17) d. (35 × 10) + (35 × 7) Explanation: 35 × 17 30 x 10 =300 30 x 7 = 210 5 x 10 = 50 5 x 7 = 35 300 + 210 + 50 + 35 = 595. a. (30 × 10) + (30 × 7) + (5 × 10) + (5 × 7) = 300 + 210 + 50 + 35 = 595 equal to 595. b. (30 × 17) + (5 × 17) = 510 + 85 = 595 equal to 595. c. (35 × 30) + (35 × 5) + (35 × 10) + (35 × 7) = 1050 + 175 + 350 + 245 = 1820 not equal to 595. d. (35 × 10) + (35 × 7) = 350 + 245 = 595 equal to 595 e. (35 × 10) + (30 × 10) + (5 × 10) + (5 × 7) = 350 + 300 + 50 + 35 = 735 not equal to 595. f. (35 × 30) + (35 × 5) = 1050 + 175 = 1,225 not equal to 595. Common Core – Page No. 181 Choose a Multiplication Method Estimate. Then choose a method to find the product. Question 1. Estimate: 1,200 3 1 × 4 3 ——- 9 3 + 1, 2 4 0 ———— 1, 3 3 3 Answer: Estimate: 1,200 Product: 1, 3 3 3 Explanation: Estimate: 1,200 3 1 × 4 3 ——- 9 3 + 1, 2 4 0 ———— 1, 3 3 3 Question 2. 6 7 × 8 5 ——- Estimate: _____ Product: ______ Answer: Estimate: 6,300 Product: 5,695 Explanation: Estimate: 67 is close to 70; 85 is close to 90. 70 x 90 = 6,300. Product: 67 x 85 80 x 6 tens = 480 tens 80 x 7 ones = 560 ones 5 x 6 tens = 30 tens 5 x 7 ones = 35 ones. Add partial products. 4800 + 560 + 300 + 35 = 5,695. Question 3. 6 8 × 3 8 ——- Estimate: _____ Product: ______ Answer: Estimate: 2,800 Product: 2,584 Explanation: Estimate: 68 is close to 70; 38 is close to 40. 70 x 40 = 2,800. Product: 68 x 38 30 x 6 tens = 180 tens 30 x 8 ones = 240 ones 8 x 6 tens = 48 tens 8 x 8 ones = 64 ones. Add partial products. 1800 + 240 + 480 + 64 = 2,584. Question 4. 9 5 × 1 7 ——- Estimate: _____ Product: ______ Answer: Estimate: 1,700 Product: 1,615 Explanation: Estimate: 95 is close to 100. 100 x 17 = 1,700. Product: 95 x 17 10 x 9 tens = 90 tens 10 x 5 ones = 50 ones 7 x 9 tens = 63 tens 7 x 5 ones = 35 ones. Add partial products. 900 + 50 + 630 + 35 = 1,615. Question 5. 4 9 × 5 4 ——- Estimate: _____ Product: ______ Answer: Estimate: 2,500 Product: 2,646 Explanation: Estimate: 49 is close to 50; 54 is close to 50. 50 x 50 = 2,500. Product: 49 x 54 50 x 4 tens = 200 tens 50 x 9 ones = 450 ones 4 x 4 tens = 16 tens 4 x 9 ones = 36 ones. Add partial products. 2000 + 450 + 160 + 36 = 2,646. Question 6. 9 1 × 2 6 ——- Estimate: _____ Product: ______ Answer: Estimate: 2,700 Product: 2,366 Explanation: Estimate: 91 is close to 90; 26 is close to 30. 90 x 30 = 2,700. Product: 49 x 54 20 x 9 tens = 180 tens 20 x 1 ones = 20 ones 6 x 9 tens = 54 tens 6 x 1 ones = 6 ones. Add partial products. 1800 + 20 + 540 + 6 = 2,366. Question 7. 8 2 × 1 9 ——- Estimate: _____ Product: ______ Answer: Estimate: 1,600 Product: 1,558 Explanation: Estimate: 82 is close to 80; 19 is close to 20. 80 x 20 = 1,600. Product: 82 x 19 10 x 8 tens = 80 tens 10 x 2 ones = 20 ones 9 x 8 tens = 72 tens 9 x 2 ones = 18 ones. Add partial products. 800 + 20 + 720 + 18 = 1,558. Question 8. 4 6 × 2 7 ——- Estimate: _____ Product: ______ Answer: Estimate: 1,500 Product: 1,242 Explanation: Estimate: 46 is close to 50; 27 is close to 30. 50 x 30 = 1,500. Product: 46 x 27 20 x 4 tens = 80 tens 20 x 6 ones = 120 ones 7 x 4 tens = 28 tens 7 x 6 ones = 42 ones. Add partial products. 800 + 120 + 280 + 42 = 1,242. Question 9. 4 1 × 3 3 ——- Estimate: _____ Product: ______ Answer: Estimate: 1,200 Product: 1,353 Explanation: Estimate: 41 is close to 40; 33 is close to 30. 40 x 30 = 1,200. Product: 41 x 33 30 x 4 tens = 120 tens 30 x 1 ones = 30 ones 3 x 4 tens = 12 tens 3 x 1 ones = 3 ones. Add partial products. 1200 + 30 + 120 + 3 = 1,353. Question 10. 9 7 × 1 3 ——- Estimate: _____ Product: ______ Answer: Estimate: 1,300 Product: 1,261 Explanation: Estimate: 97 is close to 100. 100 x 13 = 1,300. Product: 97 x 13 10 x 9 tens = 90 tens 10 x 7 ones = 70 ones 3 x 9 tens = 27 tens 3 x 7 ones = 21 ones. Add partial products. 900 + 70 + 270 + 21 = 1,261. Question 11. 7 5 × 6 9 ——- Estimate: _____ Product: ______ Answer: Estimate: 5,600 Product: 5,195 Explanation: Estimate: 75 is close to 80; 69 is close to 70. 80 x 70 = 5,600. Product: 75 x 69 60 x 7 tens = 420 tens 60 x 5 ones = 300 ones 9 x 7 tens = 63 tens 9 x 5 ones = 45 ones. Add partial products. 4200 + 300 + 630 + 45 = 5,195. Problem Solving Common Core – Page No. 182 Lesson Check Question 1. A choir needs new robes for each of its 46 singers. Each robe costs$32. What will be the total cost for all 46 robes?
Options:
a. $1,472 b.$1,372
c. $1,362 d.$230

a. $1,472 Explanation: 46 x$32
40 x $32 =$1,280
6 x $32 =$192
$1,280 +$192 = $1,472 Question 2. A wall on the side of a building is made up of 52 rows of bricks with 44 bricks in each row. How many bricks make up the wall? Options: a. 3,080 b. 2,288 c. 488 d. 416 Answer: b. 2,288 Explanation: 52 x 44 50 x 44 = 2,200 2 x 44 = 88 2,200 + 88 = 2,288. 2,288 bricks make up the wall. Spiral Review Question 3. Which expression shows how to multiply 4 × 362 by using place value and expanded form? Options: a. (4 × 3) + (4 × 6) + (4 × 2) b. (4 × 300) + (4 × 600) +(4 × 200) c. (4 × 300) + (4 × 60) + (4 × 20) d. (4 × 300) + (4 × 60) + (4 × 2) Answer: d. (4 × 300) + (4 × 60) + (4 × 2) Explanation: 4 × 362 = 1,448 a. (4 × 3) + (4 × 6) + (4 × 2) = 12 + 24 + 8 = 44 not equal to 1,448. b. (4 × 300) + (4 × 600) +(4 × 200) = 1200 + 2400 + 800 = 4,400 not equal to 1,448. c. (4 × 300) + (4 × 60) + (4 × 20) = 1200 + 240 + 80 = 1,520 not equal to 1,448. d. (4 × 300) + (4 × 60) + (4 × 2) = 1200 + 240 + 8 = 1,448 equal to 1,448. Question 4. Use the model below. What is the product 4 x 492? Options: a. 16 + 36 + 8 = 60 b. 160 + 36 + 8 = 204 c. 160 + 360 + 8 = 528 d. 1,600 + 360 + 8 = 1,968 Answer: d. 1,600 + 360 + 8 = 1,968 Explanation: 1,600 + 360 + 8 = 1,968 Question 5. What is the sum 13,094 + 259,728? Options: a. 272,832 b. 272,822 c. 262,722 d. 262,712 Answer: c. 262,722 Explanation: 13,094 + 259,728 = 262,722 Question 6. During the 2008–2009 season, there were 801,372 people who attended the home hockey games in Philadelphia. There were 609,907 people who attended the home hockey games in Phoenix. How much greater was the home attendance in Philadelphia than in Phoenix that season? Options: a. 101,475 b. 191,465 c. 201,465 d. 202,465 Answer: b. 191,465 Explanation: 801,372 – 609,907 = 191,465 Philadelphia attendance is 191,465 greater than in Phoenix that season. Page No. 185 Question 1. An average of 74 reports with bird counts were turned in each day in June. An average of 89 were turned in each day in July. How many reports were turned in for both months? (Hint: There are 30 days in June and 31 days in July.) First, write the problem for June. Type below: __________ Answer: Given that An average of 74 reports with bird counts was turned in each day in June. For June Month, there are 30 days = 30 x 74 = 2,220. Question 1. Next, write the problem for July. Type below: __________ Answer: An average of 89 reports with bird counts was turned in each day in July. For July Month, there are 31 days = 31 x 89 = 2,759. Question 1. Last, find and add the two products. ____________ reports were turned in for both months. Type below: __________ Answer: Given that An average of 74 reports with bird counts was turned in each day in June. For June Month, there are 30 days = 30 x 74 = 2,220. An average of 89 reports with bird counts was turned in each day in July. For July Month, there are 31 days = 31 x 89 = 2,759. Add two products to get the total number of reports that were turned in for both months. 2,220 + 2,759 = 4,979. Question 2. What if an average of 98 reports were turned in each day for the month of June? How many reports were turned in for June? Describe how your answer for June would be different. ______ reports Answer: 720 more reports Explanation: Given that an average of 98 reports was turned in each day for the month of June. June has 30 days. Total number of reports were turned in for June = 30 x 98 = 2, 940. From the above answer, 98 − 74 = 24. So, there would be 30 × 24, or 720 more reports. Question 3. There are 48 crayons in a box. There are 12 boxes in a carton. Mr. Johnson ordered 6 cartons of crayons for the school. How many crayons did he get? ______ crayons Answer: 3,456 crayons Explanation: There are 48 crayons in a box. There are 12 boxes in a carton. So, 1 carton = 48 x 12 = 576 crayons. If Mr. Johnson ordered 6 cartons of crayons for the school, 6 x 576 crayons = 3,456 crayons. He gets 3,456 crayons. Question 4. Make Sense of Problems Each of 5 birdwatchers reported seeing 15 roseate spoonbills in a day. If they each reported seeing the same number of roseate spoonbills over 14 days, how many would be reported? ______ roseate spoonbills Answer: 1,050 roseate spoonbills Explanation: Given that, 1 day –>5 birdwatchers reported 15 roseate spoonbills = 5 x 15 = 75 roseate spoonbills. So, in 14 days –> 5 birdwatchers reported 75 x 14 = 1,050 roseate spoonbills. Page No. 186 Question 7. Lydia is having a party on Saturday. She decides to write a riddle on her invitations to describe her house number on Cypress Street. Use the clues to find Lydia’s address. ______ Cypress Street Answer: 14827 Cypress Street Explanation: Given that tens digit is 5 less than 7 = 7 – 5 = 2. 2 is the tens digit. The thousands digit is twice the digit in the tens place = 2 x 2 = 4. The hundreds digit is the greatest even number that is less than 10 i.e, 8. The ones digit is the product of 7 and 1 = 7 x 1 = 7. The ten thousands digit is the difference between the hundreds digit and the ones digit. So, 8 – 7 = 1. Add the products to get the final answer = 14827. Lydia’s address ( house number ) is 14827 Cypress Street. Question 8. A school is adding 4 rows of seats to the auditorium. There are 7 seats in each row. Each new seat costs$99. What is the total cost for the new seats? Show your work.
$______ Answer:$2,772

Explanation:
Given that A school is adding 4 rows of seats to the auditorium. There are 7 seats in each row.
So, 7 x 4 = 28 seats are available in an auditorium.
Each new seat costs $99. 28 x$99 = $2,772 for total cost of the new seats. Common Core – Page No. 187 Problem Solving Multiply 2 – Digit numbers Solve each problem. Use a bar model to help. Question 1. Mason counted an average of 18 birds at his bird feeder each day for 20 days. Gloria counted an average of 21 birds at her bird feeder each day for 16 days. How many more birds did Mason count at his feeder than Gloria counted at hers? Birds counted by Mason: 18 × 20 = 360 Birds counted by Gloria: 21 × 16 = 336 Draw a bar model to compare. Subtract. 360 – 336 = 24 So, Mason counted 24 more birds. Answer: Birds counted by Mason: 18 × 20 = 360 Birds counted by Gloria: 21 × 16 = 336 Draw a bar model to compare. Subtract. 360 – 336 = 24 So, Mason counted 24 more birds. Question 2. The 24 students in Ms. Lee’s class each collected an average of 18 cans for recycling. The 21 students in Mr. Galvez’s class each collected an average of 25 cans for recycling. How many more cans were collected by Mr. Galvez’s class than Ms. Lee’s class? ______ more cans Answer: The number of cans collected by Ms. Lee’s class = 18 x 24 = 432. The number of cans collected by Mr. Galvez’s class = 25 x 21 = 525. Use Bar Model Subtract. 525 – 432 = 93 more cans. So, Mr. Galvez’s class collected 93 more cans than Ms. Lee’s class. Question 3. At East School, each of the 45 classrooms has an average of 22 students. At West School, each of the 42 classrooms has an average of 23 students. How many more students are at East School than at West School? ______ more students Answer: Students in East school = 45 x 22 = 990. Students in West School = 42 x 23 = 966. Use Bar Model Subtract. 990 – 966 = 24. So, East School has 24 students more than West School. Question 4. A zoo gift shop orders 18 boxes of 75 key rings each and 15 boxes of 80 refrigerator magnets each. How many more key rings than refrigerator magnets does the gift shop order? ______ more key rings Answer: Number of Key Rings = 75 x 18 = 1,350. Number of Refrigerator Magnets= 80 x 15 = 1,200. Use Bar Model Subtract. 1,350 – 1,200 = 150. So, key rings are 150 more than refrigerator magnets. Common Core – Page No. 188 Lesson Check Question 1. Ace Manufacturing ordered 17 boxes with 85 ball bearings each. They also ordered 15 boxes with 90 springs each. How many more ball bearings than springs did they order? Options: a. 5 b. 85 c. 90 d. 95 Answer: d. 95 Explanation: Number of ball bearings = 85 x 17 = 1,445. Number of springs = 90 x 15 = 1,350. Use Bar Model Subtract. 1,445 – 1,350 = 95. So, ball bearings are 95 more than springs. Question 2. Elton hiked 16 miles each day on a 12-day hiking trip. Lola hiked 14 miles each day on her 16-day hiking trip. In all, how many more miles did Lola hike than Elton hiked? Options: a. 2 miles b. 18 miles c. 32 miles d. 118 miles Answer: c. 32 miles Explanation: Hiking trip by Elton = 12 x 16 = 192. Hiking trip by Lola = 16 x 14 = 224. Use Bar Model Subtract. 224 – 192 = 32. So, the Hiking trip by Lola is 32 times more than the Hiking trip by Elton. Spiral Review Question 3. An orchard has 24 rows of apple trees. There are 35 apple trees in each row. How many apple trees are in the orchard? Options: a. 59 b. 192 c. 740 d. 840 Answer: d. 840 Explanation: An orchard has 24 rows of apple trees. There are 35 apple trees in each row. 24 x 35 = 840 apple trees are in the orchard. Question 4. An amusement park reported 354,605 visitors last summer. What is this number rounded to the nearest thousand? Options: a. 354,600 b. 355,000 c. 360,000 d. 400,000 Answer: b. 355,000 Explanation: An amusement park reported 354,605 visitors last summer. 4,605 is close to 5,000. So, the answer is 355,000. Question 5. Attendance at the football game was 102,653. What is the value of the digit 6? Options: a. 6 b. 60 c. 600 d. 6,000 Answer: c. 600 Explanation: Digit 6 is at hundreds of positions. So, the answer is 6 x 100 = 600. Question 6. Jill’s fish weighs 8 times as much as her parakeet. Together, the pets weigh 63 ounces. How much does the fish weigh? Options: a. 7 ounces b. 49 ounces c. 55 ounces d. 56 ounces Answer: d. 56 ounces Explanation: Let Jill’s parakeet = X. Jill’s fish weighs 8 times as much as her parakeet = 8X. Together, the pets weigh 63 ounces. X + 8X = 63. 9X = 63. X = 63/9 = 7. So, Jill’s parakeet =7. Jill’s fish = 7 x 8 = 56 ounces. Review/Test – Page No. 189 Mrs. Traynor’s class is taking a field trip to the zoo. The trip will cost$26 for each student. There are 22 students in her class.

Question 2.
Part A
Round each factor to estimate the total cost of the student’s field trip.
$______ Answer:$600

Explanation:
Total cost of the students’ field trip = 22 x $26. 22 x$26
20 x $30 =$600
The total cost would be about $600. Question 2. Part B Use compatible numbers to estimate the total cost of the field trip.$ ______

$500 Explanation: If we use compatible numbers to estimate the total cost of the field trip. 22 x$26
20 × 25 = 500
The total cost would be about $500. Question 2. Part C Which do you think is the better estimate? Explain. Better estimate: _________ Answer: Using rounded numbers is a better estimate. When rounded numbers are used, one estimated factor was$4 more than the actual factor and the other estimated factor was $2 that is less than the actual factor. So, the estimate should be close to the actual one. When compatible numbers are used both estimated factors were less than the actual factors. So, the product will be an underestimate. Review/Test – Page No. 190 For numbers 3a–3e, select Yes or No to show if the answer is correct. Question 3. 3a. 35 × 10 = 350 i. yes ii. no Answer: i. yes Explanation: 35 x 10 = 350 30 x 10 = 300. 5 x 10 = 50. 300 + 50 = 350. Question 3. 3b. 19 × 20 = 380 i. yes ii. no Answer: i. yes Explanation: 19 × 20 = 380 19 x 20 = 19 x 2 tens. 19 x 20 = 38 tens = 380. Question 3. 3c. 12 × 100 = 120 i. yes ii. no Answer: ii. no Explanation: 12 x 100 = 120. 10 x 100 = 1000 2 x 100 = 200. 1000 + 200 = 1200. Question 3. 3d. 70 × 100 = 7,000 i. yes ii. no Answer: i. yes Explanation: 70 x 100 = 7,000 100 x 7 tens = 700 tens = 7,000 Question 3. 3e. 28 × 30 = 2,100 i. yes ii. no Answer: ii. no Explanation: 28 × 30 20 x 30 = 600 8 x 30 = 240 600 + 240 = 840 Question 5. Which would provide a reasonable estimate for each product? Write the estimate beside the product. An estimate may be used more than once 23 × 38 __________ 31 × 32 __________ 46 × 18 __________ 39 × 21 __________ Answer: 23 × 38 –> 25 x 40 31 x 32 –> 30 × 30 46 × 18 –> 50 × 20 39 × 21 –> 25 × 40 Explanation: 23 × 38; 23 is close to 25; 38 is close to 40. So, the estimated product is 25 x 40 31 x 32; 31 is close to 30; 32is close to 30. So, the estimated product is 30 × 30 46 × 18; 46 is close to 50; 18 is close to 20. So, the estimated product is 50 × 20 39 × 21; 39 is close to 40; 21 is close to 25. So, the estimated product is 25 × 40 Question 6. There are 26 baseball teams in the league. Each team has 18 players. Write a number sentence that will provide a reasonable estimate for the number of players in the league. Explain how you found your estimate. Type below: __________ Answer: There are 26 baseball teams in the league. Each team has 18 players. 26 x 18 25 x 20 We Rounded each factor to its close factor, then simplified the multiplication. Question 7. The model shows 48 × 37. Write the partial products. Type below: __________ Answer: Partial Products are 1200, 240, 280, 56 Review/Test – Page No. 191 Question 8. Jess made this model find the product 32 × 17. Her model is incorrect. Part A What did Jess do wrong? Type below: __________ Answer: Jess added the numbers in the model instead of multiplying. Question 8. Part B Redraw the model so that it is correct. Type below: __________ Answer: Question 8. Part C What is the actual product 32 × 17? ______ Answer: 544 Explanation: 32 × 17 10 x 32 = 320 7 x 32 = 224 320 + 224 = 544. Question 9. Tatum wants to use partial products to find 15 × 32. Write the numbers in the boxes to show 15 × 32. Type below: __________ Answer: Review/Test – Page No. 192 Question 10. Which product is shown by the model? Write the letter of the product on the line below the model. Type below: __________ Answer: C A B 10 + 3 = 13 10 + 3 = 13 13 x 13 2. 10 + 7 = 17 30 + 6 = 36 17 x 36 3. 20 + 4 = 24 10 + 4 = 14 24 x 14 Question 12. Write the unknown digits. Use each digit exactly once. Type below: __________ Answer: 90 x 40 = 3,600 90 x 6 = 540 3 x 40 = 120 3 x 6 = 18. 3,600 + 540 + 120 + 8 = 4,278. Question 13. Mike has 16 baseball cards. Niko has 17 times as many baseball cards as Mike does. How many baseball cards does Niko have? ________ baseball cards Answer: 272 baseball cards Explanation: Mike has 16 baseball cards. Niko has 17 times as many baseball cards as Mike does. Niko have 16 x 17 = 272 baseball cards. Question 14. Multiply. 36 × 28 = ________ Answer: 1,008 Explanation: 36 x 28 20 x 30 = 600 20 x 6 = 120 8 x 30 = 240 8 x 6 = 48 600 + 120 + 240 + 48 = 1,008 Review/Test – Page No. 193 Question 16. Select another way to show 25 × 18. Mark all that apply. Options: a. (20 × 10) + (20 × 8) + (5 × 10) + (5 × 8) b. (25 × 20) + (25 × 5) + (25 × 10) + (25 × 8) c. (20 × 18) + (5 × 10) + (5 × 8) d. (25 × 10) + (25 × 8) e. (25 × 20) + (25 × 5) Answer: a. (20 × 10) + (20 × 8) + (5 × 10) + (5 × 8) c. (20 × 18) + (5 × 10) + (5 × 8) d. (25 × 10) + (25 × 8) Explanation: 25 × 18 10 x 25 = 250 8 x 25 = 200 250 + 200 = 450. a. (20 × 10) + (20 × 8) + (5 × 10) + (5 × 8) = 200 + 160 + 50 + 40 = 450 b. (25 × 20) + (25 × 5) + (25 × 10) + (25 × 8) = 500 + 125 + 250 + 200 = 1,075 c. (20 × 18) + (5 × 10) + (5 × 8) = 360 + 50 + 40 = 450 d. (25 × 10) + (25 × 8) = 250 + 200 = 450 e. (25 × 20) + (25 × 5) = 500 + 125 = 625 Question 17. Terrell runs 15 sprints. Each sprint is 65 meters. How many meters does Terrell run? Show your work. ______ meters Answer: 975 meters Explanation: Terrell run 15 x 65 = 975 meters. Question 18. There are 3 new seats in each row in a school auditorium. There are 15 rows in the auditorium. Each new seat cost$74. What is the cost for the new seats? Explain how you found your answer.
$______ Answer:$3,330

Explanation:
Given that There are 3 new seats in each row in a school auditorium. There are 15 rows in the auditorium. Each new seat cost $74. So, 3 x 15 = 45 seats are available in an auditorium. Each new seat costs$74.
45 x $74 =$3,330 for total cost of the new seats.

Question 19.
Ray and Ella helped move their school library to a new building. Ray packed 27 boxes with 25 books in each box. Ella packed 23 boxes with 30 books in each box. How many more books did Ella pack? Show your work.
______ books

15 books

Explanation:
Ray packed 27 x 25 = 675 books.
Ella packed 23 x 30 = 690 books
Ella packed 690 – 675 = 15 books more than Ray.

Review/Test – Page No. 194

Question 20.
Julius and Walt are finding the product of 25 and 16.

Part A
Julius’ answer is incorrect. What did Julius do wrong?
Type below:
__________

Julius multiplied 25 by 10 and then multiplied 25 by 6 correctly. He added the two partial products incorrectly.

Question 20.
Part B
What did Walt do wrong?
Type below:
__________

Walt multiplied 6 by 5 and got 300 instead of 30

Question 20.
Part C
What is the correct product?
Type below:
__________

25 x 16 = 400

Question 21.
A clothing store sells 26 shirts and 22 pairs of jeans. Each item of clothing costs $32. Part A What is a reasonable estimate for the total cost of the clothing? Show or explain how you found your answer.$ ______

$1500 Explanation: A clothing store sells 26 shirts and 22 pairs of jeans. 26 + 22 = 48 clothes. Each item of clothing costs$32.
48 x $32 50 x$30 = $1500 Question 21. Part B What is the exact answer for the total cost of the clothing? Show or explain how you found your answer.$ ______

$1,536 Explanation: 48 x$32
40 x $32 =$1,280
8 x $32 =$256
$1,280 +$256 = $1,536 Page No. 199 Question 1. A restaurant has 68 chairs. There are six chairs at each table. About how many tables are in the restaurant? Estimate. 68 ÷ 6 Think: What number times 6 is about 68? 10 × 6 = ___ 11 × 6 = ___ 12 × 6 = ___ 68 is closest to ______, so the best estimate is about _______ tables are in the restaurant. Type below: __________ Answer: 68 is close to 70 and 6 is close to 5. So, 70/5 = 12. 10 × 6 = __60_ 11 × 6 = _66__ 12 × 6 = _72__ 68 is closest to ___66___, so the best estimate is about 11 x 6 = 66 tables are in the restaurant. Find two numbers the quotient is between. Then estimate the quotient. Find two numbers the quotient is between. Then estimate the quotient. Question 4. 90 ÷ 7 between _______ and _______ Answer: between 12 and 13 about 13 Explanation: 12 x 7 = 84; 13 x 7 = 91. The quotient of 90 ÷ 7 is between 12 and 13. Question 5. 67 ÷ 4 between _______ and _______ Answer: between 16 and 17 about 17 Explanation: 16 x 4 = 64; 17 x 4 = 68. The quotient of 67 ÷ 4 is between 16 and 17. Question 6. 281 ÷ 9 between _______ and _______ Answer: between 30 and 40 about 30 Explanation: 30 x 9 = 270; 40 x 9 = 360. The quotient of 281 ÷ 9 is between 30 and 40. Question 7. 102 ÷ 7 between _______ and _______ Answer: between 14 and 15 about 15 Explanation: 14 x 7 = 98; 15 x 7 = 105. The quotient of 102 ÷ 7 is between 14 and 15. Question 8. 85 ÷ 6 between _______ and _______ Answer: between 14 and 15 about 14 Explanation: 14 x 6 = 84; 15 x 6 = 90. The quotient of 85 ÷ 6 is between 14 and 15. Question 9. 220 ÷ 8 between _______ and _______ Answer: between 20 and 30 about 30 Explanation: 20 x 8 = 160; 30 x 8 = 240. The quotient of 220 ÷ 8 is between 20 and 30. Decide whether the actual quotient is greater than or less than the estimate given. Write < or >. Question 10. 83 ÷ 8 _______ 10 Answer: > Explanation: 83 ÷ 8 = 10.375 > 10 Question 11. 155 ÷ 4 _______ 40 Answer: < Explanation: 155 ÷ 4 = 38.75 < 40 Question 12. 70 ÷ 6 _______ 11 Answer: > Explanation: 70 ÷ 6 = 11.666 > 11 Question 13. What’s the Question? A dolphin’s heart beats 688 times in 6 minutes. Answer: about 100 times. Type below: __________ Answer: About how many times does a dolphin’s heart beats in 1 minute? Question 14. Analyze A mother bottlenose ate about 278 pounds of food in one week. About how much food did she eat in a day? about _____ pounds Answer: about 40 pounds Explanation: 278 ÷ 7 The quotient of 278 ÷ 7 is between 39 and 40. Page No. 200 Question 16. If a bottlenose dolphin can eat 175 pounds of fish, squid, and shrimp in a week, how many pounds of food does it eat in a day? Milo says the answer is about 20 pounds. Leah says the answer is about 30 pounds. Who is correct? Explain. ________ Answer: The bottlenose dolphin can eat 25 pounds in 1 day. Both answers are correct. Because 25 pounds is between 20 and 30 pounds. Explanation: 1 week = 7 days. The bottlenose dolphin can eat 175 pounds for 7 days. For 1 day = 175 ÷ 7 = 25 pounds. The bottlenose dolphin can eat 25 pounds in 1 day. Both answers are correct. Because 25 pounds is between 20 and 30 pounds. Question 17. Four families went out for lunch. The total food bill came to$167. The families also left a $30 tip for the waitress. If each family spent the same amount, how much did each family spend on dinner? Explain how you found your answer.$ ______

$98.5 Explanation: Four families went out for lunch. The total food bill came to$167. The families also left a $30 tip for the waitress. So, total amount =$167 + $30 =$197.
If each family spent the same amount = $197 ÷ 2 =$98.5
Each family spent \$98.5.

Question 18.
There are 6 showings of a film about Van Gogh at the Art Museum. A total of 459 people saw the film. The exact number of people were at each show. About how many people were at each show? Circle the numbers the quotient is between. Then explain how you found your answer.
40 50 60 70 80
Type below:
_________

40 50 60 70 80
I found multiples of 6 that 459 is between. 70 × 6 = 420 and 80 × 6 = 480. Since 459 is closer to 480, 459 ÷ 6 is about 80.

Conclusion

Hope the data shared about Go Math Grade 4 Answer Key Chapter 3 Multiply 2- Digit Number has helped you in your preparation. If you feel any learning is missing do give us your suggestions and we will consider them if possible. Just keep on visiting our site to get the latest update on Grade 4 Go Math HMH Answer Keys for other chapters as well.

3-Digit Addition and Subtraction Show What You Know

Model Subtracting Tens
Write the difference.
Question 1.

5 tens − 3 tens = ______ tens
50 − 30 = _____
20

Explanation:
There are 5 tens if we subtract 3 tens only 2 tens will remain.Therefore 50‐30 =20.

Question 2.

7 tens − 2 tens = ______ tens
70 − 20 = _____
50

Explanation:
There are 7 tens if we subtract 2 tens only 5 tens will remain.Therefore 70‐20 =50.

Write the sum.
Question 3.

Explanation:
In the above picture there are 7 tens and 9 ones.So, 54+25=79

Question 4.

Explanation:
In the above picture there are 4 tens and 13 ones.13 ones is 1 tens and 3 ones.Finally there are 5 tens and 3 ones.So, 35+18=83

Question 5.

Explanation:
In the above picture there are 14 tens and 9 ones.14 tens means 1 hundreds and 4 tens.Finally there are 1 hundreds, 4 tens and 9 ones.So, 82+67=149.

Question 6.

Explanation:
In the above picture there are 10 tens and 10 ones.10 tens means 1 hundreds and 10 ones means 1 tens.Finally there are 1 hundreds and 1 tens. So, 29+81=110

Hundreds, Tens, and Ones
Write the hundreds, tens, and ones shown. Write the number.
Question 7.

Explanation:
In the above picture there are 2 hundreds, 5 tens and 3 ones.So, the number is 253.

Question 8.

Explanation:
In the above picture there are 3 hundreds, 5 tens and 1 ones.So, the number is 351.

3-Digit Addition and Subtraction Vocabulary Builder

Visualize It
Fill in the graphic organizer by writing examples of ways to regroup.

Understand Vocabulary
Question 1.
Write a number that has a hundreds digit that is greater than its tens digit. _________
540

Explanation:
In the number 540 the tens digit is 4 and the hundreds digit is 5.As 5 is greater than 4 the number has a hundreds digit that is greater than its tens digit.

Question 2.
Write an addition sentence that has a sum of 20. ______
10+10=20

Explanation:
There are 10 ones and 10 ones in the above picture.10 ones means 1 tens.Finally there are 2 tens.So, 10+10=20.

Question 3.
Write a subtraction sentence that has a difference of 10. ________
20-10=10

Explanation:
There are 2 tens in above picture if we subtract 1 tens from it we get 1 tens.So, 20‐10=10.

3-Digit Addition and Subtraction Game 2-Digit Shuffle

Materials

• number cards 10–50

Play with a partner.

1. Shuffle the number cards. Place them face down in a pile.
2. Take two cards. Say the sum of the two numbers.
4. If your sum is correct, place a counter on a button. If you regrouped to solve, place a counter on another button.
5. Take turns. Cover all the buttons. The player with more counters on the board wins.
6. Repeat the game, saying the difference between the two numbers for each turn.

3-Digit Addition and Subtraction Vocabulary Game

Picture It

For 3 to 4 players
Materials

• timer

How to Play

1. Take turns to play.
2. Choose a math word from the Word Box. Do not say the word.
3. Set the timer for 1 minute.
4. Draw pictures and numbers to give clues about the math word.
5. The first player to guess the word gets 1 point. If he or she use the word in a sentence, they get 1 more point. That player gets the next turn.
6. The first player to score 5 points wins.

The Write Way
Reflect
Choose one idea. Write about it on the lines below.

• Tell how to solve this problem.
42 – 25 = _____
• Write a paragraph that uses at least three of these words.
• Explain something you know about regrouping.

Lesson 6.1 Draw to Represent 3-Digit Addition

Essential Question How do you draw quick pictures to show adding 3-digit numbers?

Listen and Draw

Draw quick pictures to model the problem. Then solve.

MATHEMATICAL PRACTICES
Use Tools Explain how your quick pictures show the problem.

Explanation:
Manuel read 45 pages in a book and then he read 31 morw pages.As shown in the above picture there are 7 tens and 6 ones.It is 76.Therefore manuel read 76 pages in all.

Share and Show

Draw quick pictures. Write how many hundreds, tens, and ones in all. Write the number.
Question 1.

_____ hundreds _____ tens _____ ones
______

4 hundreds 6 tens and 9 ones is 469.

Explanation:
In the above picture there are 4 hundreds, 6 tens and 9 ones.So, the number is 469.

Question 2.

_____ hundreds _____ tens _____ ones
______

5 hundreds 5 tens and 8 ones is 558

Explanation:
In the above picture there are 5 hundreds, 5 tens and 8 ones.So, the number is 558.

Draw quick pictures. Write how many hundreds, tens, and ones in all. Write the number.
Question 3.

_____ hundreds _____ tens _____ ones
______

4 hundreds 4 tens and 9 ones is 449.

Explanation:
In the above picture there are 4 hundreds, 4 tens and 9 ones.So, the number is 449.

Question 4.

_____ hundreds _____ tens _____ ones
______

3 hundreds 8 tens and 2 onea is 382

Explanation:
In the above picture there are 3 hundreds, 8 tens and 2 ones.So, the number is 382.

Question 5.
THINK SMARTER
Use the quick pictures to find the two numbers being added. Then write how many hundreds, tens, and ones in all. Write the number.

_____ hundreds _____ tens _____ ones
______
There are 3 hundreds, 5 tens and 8 ones.So, the sum of 153 and 205 is 358.
3 hundreds 5 tens and 8 ones.

Problem Solving • Applications

Question 6.
MATHEMATICAL PRACTICE Represent a Problem
There are 125 poems in Carrie’s book and 143 poems in Angie’s book. How many poems are in these two books? Draw a quick picture to solve.
______ poems

Explanation:
There are 2 hundreds, 6 tens and 8 ones.So, the sum of 125 and 143 is 268.
2 hundreds 6 tens and 8 ones.

Question 7.
THINK SMARTER+
Rhys wants to add 456 and 131.
Help Rhys solve this problem. Draw quick pictures. Write how many hundreds, tens, and ones in all. Write the number.

_____ hundreds _____ tens _____ ones
______

Explanation:
In the above picture there are 5 hundreds, 8 tens and 7 ones.So the number is 587.
5 hundreds 8 tens 7 ones

TAKE HOME ACTIVITY • Write 145 + 122. Have your child explain how he or she can draw quick pictures to find the sum.

Explanation:
There are 2 hundreds, 6 tens and 7 ones in the above picture.So, the sum of 145 and 122 is 267.
2 hundred 6 tens 7 ones.

Draw to Represent 3-Digit Addition Homework & Practice 6.1

Draw quick pictures. Write how many hundreds, tens, and ones in all. Write the number.
Question 1.

_____ hundreds _____ tens _____ ones
______

Explanation:
In the above picture add the hundreds, tens and ones.There are 3 hundreds, 5 tens and 7 ones.So the sum of 142 and 215 is 357.
3 hundreds 5 tens 7 ones.

Problem Solving
Solve. Write or draw to explain.
Question 2.
A farmer sold 324 lemons and 255 limes. How many pieces of fruit did the farmer sell altogether?
______ pieces of fruit

Explanation:
In the above picture add the hundreds,tens and ones.There are 5 hundreds 7 tens and 9 ones.So the sum of 324 and 255 is 579.
5 hundreds 7 tens 9 ones.

Question 3.
WRITE
Draw quick pictures and write to tell how you would add 342 and 416.

Explanation:
In the above picture add the hundreds,tens and ones.There are 7 hundreds, 5 tens and 8 ones.So, the sum of 342 and 416 is 758.
7 hundreds 5 tens and 8 ones.

Lesson Check
Question 1.
Ms. Carol sold 346 child tickets and 253 adult tickets. How many tickets did Ms. Carol sell?
______ tickets

Explanation:
In the above picture add the humdreds, tens and ones.There are 5 hundreds, 9 tens and 9 ones.So, the sum of 346 and 253 is 599.
5 hundreds 9 tens 9 ones.

Question 2.
Mr. Harris counted 227 gray pebbles and 341 white pebbles. How many pebbles did Mr. Harris count?
_______ pebbles

Explanation:
In the above picture add the hundreds, tens and ones.There are 5 hundreds,6 tens and 8 ones.So the sum of 227 and 341 is 568.
5 hundreds 6 tens 8 ones.

Question 3.
Pat has 3 rows of shells. There are 4 shells in each row. How many shells does Pat have?
_____ shells

Explanation:
Add the shells in the above picture.There are 3 rows of shells and each row has 4 shells each.So, there are 12 shells in all.
1 tens and 2 ones.

Question 4.
Kara counted 32 red pens, 25 blue pens, 7 black pens, and 24 green pens. How many pens did Kara count?
______ pens

Explanation:
Add the number of pens kara counts.Add the tens and ones.There are 7 tens and 18 ones.So, the number of pens kara counted is 7 tens and 18 ones ie 8 tens and 8 ones.Therefore the sum of 32,25,7 and 24 is 88.
8 tens and 8 ones.

Question 5.
Kai had 46 blocks. He gave 39 blocks to his sister. How many blocks does Kai have left?
46 – 39 = ______ blocks

Explanation:
In the above picture 39 is removed from 46.So, the difference of 46 and 39 is 7.
7 ones.

Question 6.
A shop has 55 posters for sale. 34 posters show sports. The rest of the posters show animals. How many posters show animals?
_______ posters

Explanation:
In the above picture 34 is removed from 55.So, the difference of 55 and 34 is 21.
2 tens 1 ones.

Lesson 6.2 Break Apart 3-Digit Addends

Essential Question How do you break apart addends to add hundreds, tens, and then ones?

Listen and Draw

Write the number. Draw a quick picture for the number. Then write the number in different ways.
_______
______ hundreds ______ tens _____ ones
_____ + _____ + ______
258
2 hundreds 5 tens 8 ones
200+50+8

_______
______ hundreds ______ tens _____ ones
_____ + _____ + ______
325
3 hundreds 2 tens 5 ones
300+20+8

MATHEMATICAL PRACTICES
Make Connections
What number can be written as 400 + 20 + 9?
400+20+9
=4 hundreds 2 tens and 9 ones
400+20+9=429

Model and Draw

Break apart the addends into hundreds, tens, and ones. Add the hundreds, the tens, and the ones. Then find the total sum.

Explanation:
Add 538 and 216.Add the hundreds, tens and ones from the above picture.There are 7 hundreds,4 tens and 14 ones.So, the sum of 538 and 216 is 754.
7 hundreds 5 tens 4 ones.

Share and Show

Break apart the addends to find the sum.
Question 1.

Explanation:
Add 321 and 457.Add the hundreds, tens and ones from the above picture.There are 7 hundreds,7 tens and 8 ones.So, the sum of 321 and 457 is 778
7 hundreds 7 tens 8 ones.

Question 2.

Explanation:
Add 744 and 162.Add the hundreds, tens and ones from the above picture.There are 8 hundreds,1 tens and 6 ones.So, the sum of 744 and 162 is 906.
9 hundreds 0 tens 6 ones.

Question 3.

Explanation:
Add 254 and 536.Add the hundreds, tens and ones from the above picture.There are 7 hundreds,8 tens and 10 ones.So, the sum of 254 and 536 is 790.
7 hundreds 9 tens 0 ones.

Break apart the addends to find the sum.
Question 4.

Explanation:
Add 538 and 216.Add the hundreds, tens and ones from the above picture.There are 7 hundreds,4 tens and 14 ones.So, the sum of 538 and 216 is 754.
7 hundreds 5 tens 4 ones.

Question 5

Explanation:
Add 425 and 232.Add the hundreds, tens and ones from the above picture.There are 5 hundreds,5 tens and 7 ones.So, the sum of 538 and 216 is 557.
5 hundreds 5 tens 7 ones.

Question 6.

Explanation:
Add 849 and 123.Add the hundreds, tens and ones from the above picture.There are 9 hundreds,6 tens and 12 ones.So, the sum of 538 and 216 is 972.
9 hundreds 7 tens 2 ones.

Question 7.
THINK SMARTER+
Mr. Jones has many sheets of paper. He has 158 sheets of blue paper, 100 sheets of red paper, and 231 sheets of green paper. How many sheets of paper does he have?

______ sheets of paper

Explanation:
Add 158,100 and 231.Add the hundreds, tens and ones from the above picture.There are 4 hundreds,8 tens and 9 ones.So, the sum of 158,100 and 231 is 489.
4 hundreds 8 tens 9 ones.

Problem Solving • Applications

Question 8.
GO DEEPER
Wesley added in a different way.

Explanation:
As in the above example add hundreds,tens and ones seperately and the sum of hundreds,tens and ones is 786.
7 hundreds 8 tens 6 ones

Question 9.
THINK SMARTER
There are 376 children at one school. There are 316 children at another school. How many children are at the two schools?

Select one number from each column to solve the problem.

Explanation:
Add 376 and 316.Add the hundreds, tens and ones from the above picture.There are 6 hundreds,8 tens and 12 ones.So, the sum of 376 and 316 is 692.
6 hundreds 9 tens 2 ones.

TAKE HOME ACTIVITY • Write 347 + 215. Have your child break apart the numbers and then find the sum.

Break Apart 3-Digit Addends Homework & Practice 6.2

Break apart the addends to find the sum.
Question 1.

Question 2.

Problem Solving
Solve. Write or draw to explain.
Question 3.
There are 126 crayons in a bucket. A teacher puts 144 more crayons in the bucket. How many crayons are in the bucket now?
______ crayons

Explanation:
There are 126 crayons in a bucket and the teacher adds 144 more to the bucket.To find the totqal number of crayons in the bucket, Add 126 and 144.Add the hundreds, tens and ones from the above picture.There are 2 hundreds,7 tens and 0 ones.So, the sum of 126 and 144 is 270.Therefore there are total 260 crayons in the bucket.
2 hundreds 6 tens 0 ones.

Question 4.
WRITE
Draw quick pictures and write to explain how to break apart addends to find the sum of 324 + 231.

Explanation:
Add 324 and 231.Add the hundreds, tens and ones from the above picture.There are 5 hundreds,5 tens and 5 ones.So, the sum of 324 and 231 is 555.
5 hundreds 5 tens 5 ones.

Lesson Check
Question 1.
What is the sum?

Explanation:
Add 218 and 145.Add the hundreds, tens and ones from the above picture.There are 3 hundreds,5 tens and 13 ones.So, the sum of 218 and 145 is 363.
3 hundreds 6 tens 3 ones.

Question 2.
What is the sum?

Explanation:
Add 664 and 223.Add the hundreds, tens and ones from the above picture.There are 8 hundreds,8 tens and 7 ones.So, the sum of 664 and 223 is 887.
8 hundreds 8 tens 7 ones.

Spiral Review
Question 3.
Ang found 19 berries and Barry found 21 berries. How many berries did they find altogether?
19 + 21 = ______ berries

Explanation:
Ang found 19 berries and Barry found 21 berries.Add 19 and 21.There are 3 tens and 10 ones in the above picture.So, the sum of 19 and 21 is 40.
4 tens and 0 ones.

Question:
Write a subtraction fact related to 9 + 6 = ______
20-5=15

Explanation:
In the above question the sum of 9 and 6 is 15.So, the subtraction fact for 15 is 20-5=15.

Question 5.
There are 25 goldfish and 33 betta fish. How many fish are there?
25 + 33 = _____ fish

Explanation:
There are 25 goldfish and 33 betta fish.Add 25 and 33.Add the tens and ones from the above picture.There are 5 tens and 8 ones.So the sum of

Question 6.
Subtract 16 from 41. What is the difference?

Lesson 6.3 3-Digit Addition: Regroup Ones

Essential Question When do you regroup ones in addition?

Listen and Draw

Use to model the problem. Draw quick pictures to show what you did.

MATHEMATICAL PRACTICES
Describe how you modeled the problem.

Explanation:
To find the sum of 213 and 356.There are 5 hundreds,6 tens and 9 ones in the above picture.So. the sum of 213 and 356 is 569.5 hundreds 6 tens 9 ones.

Model and Draw

Share and Show

Write the sum.
Question 1.

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 328 and 134 is 462.

Question 2.

Explanation:
In the above picture the ones,tens and hundreds are added seperately without regrouping.The sum of 445 and 23 is 468.

Write the sum.
Question 3.

Explanation:
In the above picture the ones,tens and hundreds are added seperately without regrouping.The sum of 526 and 103 is 629.

Question 4.

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 348 and 19 is 367.

Question 5.

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 628 and 347 is 975.

Question 6.

Question 7.

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 562 and 329 is 891.

Question 8.

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 147 and 125 is 272.

Question 9.
THINK SMARTER
On Thursday, there were 326 visitors at the zoo. There were 200 more visitors at the zoo on Friday than on Thursday. How many visitors were at the zoo on both days?

______ visitors

Explanation:
In the above picture the ones,tens and hundreds are added seperately without regrouping.The sum of 326 and 200 is 526.

Problem Solving • Applications

Solve. Write or draw to explain.
Question 10.
MATHEMATICAL PRACTICE Model with Mathematics
The gift shop is 140 steps away from the zoo entrance. The train stop is 235 steps away from the gift shop. How many total steps is this?

______ steps

Explanation:
In the above picture the ones,tens and hundreds are added seperately without regrouping.The sum of 140 and 235is 375.

Question 11.
THINK SMARTER
Katina’s class used 249 noodles to decorate their bulletin board. Gunter’s class used 318 noodles. How many noodles did the two classes use?
________ noodles
Did you have to regroup to solve? Explain.

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 249 and 318 is 567.

TAKE HOME ACTIVITY • Ask your child to explain why he or she regrouped in only some of the problems in this lesson.

3-Digit Addition: Regroup Ones Homework & Practice 6.3

Write the sum.
Question 1.

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 148 and 234 is 382.

Question 2.

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 321 and 318 is 639.

Question 3.

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 414 and 179 is 593.

Question 4.

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 602 and 258 is 860.

Problem Solving
Solve. Write or draw to explain.
Question 5.
In the garden, there are 258 yellow daisies and 135 white daisies. How many daisies are in the garden altogether?
______ daisies

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 258 and 135 is 393.

Question 6.
WRITE
Find the sum of 136 + 212. Explain why you did or did not regroup.

Explanation:
In the above picture the ones,tens and hundreds are added seperately without regrouping.The sum of 136 and 212 is 348.

Leson Check
Question 1.
What is the sum?

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 435 and 146 is 581.

Question 2.
What is the sum?

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 436 and 306 is 742.

Spiral Review
Question 3.
What is the difference?
9 – 4 = _______

Explanation:
In the above picture there are 9 ones.Subtract 4 ones from ir.There are 5 ones remained after subracting.Therefore the difference of 9 and 4 is 5.

Question 4.
What is the sum?

Explanation:
There are 13 tens and 11 ones in the above picture.Regroup 11 ones as 1 tens 1 ones.Add the tens and ones.Therefore there are 14 tens and 1 ones.Regroup 14 tens as 1 hundreds 4 tens.So,the sum of 82 and 59 is 1 hundreds 4 tens 1 ones.

Question 5.
What is the sum?
26 + 7 = ____

Explanation:
There are 2 tens and 13 ones in the above picture.regroup 13 ones as 1 tens 3 ones.Add the tens and ones.Therefore the sum of 26 and 7 is 33

Question 6.
Add 243 and 132. How many hundreds, tens, and ones are there in all?
______ hundreds _____ tens _____ ones

Explanation:
In the above picture the ones,tens and hundreds are added seperately by regrouping the ones.The sum of 243 and 132 is 375.

Lesson 6.4 3-Digit Addition: Regroup Tens

Essential Question When do you regroup tens in addition?

Listen and Draw

Use to model the problem. Draw quick pictures to show what you did.

MATHEMATICAL PRACTICES
Explain how your quick pictures show what happened in the problem.

Model and Draw

Share and Show

Write the sum.
Question 1.

Question 2.

Question 3.

Write the sum.
Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.
GO DEEPER
In a bowling game, Jack scored 116 points and 124 points. Hal scored 128 points and 134 points. Who scored more points? How many more points were scored?
_____ ______ more points

MATHEMATICAL PRACTICE Attend to Precision
Question 11.
760 + 178

Question 12.
216 + 346

Question 13.
423 + 285

Problem Solving • Applications
Question 14.
THINK SMARTER
These lists show the pieces of fruit sold. How many pieces of fruit did Mr. Olson sell?

_______ pieces of fruit

Question 15.
GO DEEPER
Who sold more pieces of fruit?
_______________
How many more?
_______ more pieces of fruit

Question 16.
THINK SMARTER
At the city park theater, 152 people watched the morning play. Another 167 watched the afternoon play.
How many people watched the two plays? ______ people
Fill in the bubble next to each true sentence about how to solve the problem.

TAKE HOME ACTIVITY • Have your child choose a new combination of two fruits on this page and find the total number of pieces of the two types of fruit.

3-Digit Addition: Regroup Tens Homework & Practice 6.4

Write the sum.
Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Problem Solving
Solve. Write or draw to explain.
Question 7.
There are 142 blue toy cars and 293 red toy cars at the toy store. How many toy cars are there?
_______ toy cars

Question 8.
WRITE
Find the sum of 362 + 265. Explain why you did or did not regroup.

Lesson Check
Question 1.
What is the sum?

Question 2.
Annika has 144 pennies and Yahola has 284 pennies. How many do they have altogether?

Spiral Review
Question 3.
What is the sum?

Question 4.
What is the sum?

Question 5.
Francis had 8 toy cars, then his brother gave him 9 more. How many toy cars does Francis have now?
8 + 9 = ______ cars

Question 6.
What is the difference?

Lesson 6.5 Addition: Regroup Ones and Tens

Essential Question How do you know when to regroup in addition?

Listen and Draw

Use mental math. Write the sum for each problem.

10 + 30 + 40 = _____
100 + 400 + 200 = _____
10 + 50 + 40 = _____
600 + 300 = _____

Explanation:
Add the tens digits  and hundreds digits in the above sums.

Explanation:
Add the tens digits and the hundreds digits in the above sums.

MATHEMATICAL PRACTICES
Analyze Were some problems easier to solve than other problems? Explain.

Share and Show

Write the sum.
Question 1.

Explanation:
4 ones+ 9 ones=13 ones
1 ten + 8 tens +2 tens=11 tens
1 hundred + 1 hundred + 3 hundreds=5 hundreds.

Question 2.

Explanation:
6 ones+ 8 ones=14 ones
1 ten + 4 tens +7 tens=12 tens
1 hundred + 5 hundred + 2 hundreds=8 hundreds.

Question 3.

Explanation:
7 ones+ 3 ones=10 ones
1 ten + 2 tens +5 tens=11 tens
3 hundreds + 3 hundreds=6 hundreds.

Question 4.

Explanation:
4 ones+ 2 ones=6 ones
3 tens +5 tens=8 tens
2 hundred + 1 hundreds=3 hundreds.

Question 5.

Explanation:
5 ones+ 2 ones=7 ones
7 tens +7 tens=14 tens
1 hundred + 3 hundreds + 2 hundreds=6 hundreds.

Question 6.

Explanation:
9 ones+ 3 ones=12 ones
1 ten + 8 tens +2 tens=11 tens
1 hundred + 1 hundred + 6 hundreds=8 hundreds.

Write the sum.
Question 7.

Explanation:
4 ones+ 1 one=5 ones
7 tens +8 tens=15 tens
1 hundred + 5 hundreds + 2 hundreds=8 hundreds.

Question 8.

Explanation:
6 ones+ 3 ones=9 ones
1 ten + 8 tens =9 tens
4 hundreds + 4 hundreds=8 hundreds.

Question 9.

Explanation:
6 ones+ 7 ones=13 ones
1 ten + 4 tens +9 tens=14 tens
1 hundred + 3 hundreds + 5 hundreds=9 hundreds.

Question 10.

Explanation:
5 ones+ 3 ones=8 ones
6 tens +8 tens=14 tens
1 hundred + 3 hundreds + 2 hundreds=6 hundreds.

Question 11.

Explanation:
7 ones+ 9 ones=16 ones
1 ten + 4 tens +0 tens=5 tens
6 hundred + 1 hundreds=5 hundreds.

Question 12.

Explanation:
6 ones+ 6 ones=12 ones
1 ten + 4 tens +5 tens=10 tens
1 hundred + 5 hundreds + 3 hundreds=9 hundreds.

Question 13.

Explanation:
8 ones+ 1 ones=9 ones
4 tens +3 tens=7 tens
3 hundreds + 6 hundreds=9 hundreds.

Question 14.

Explanation:
5 ones+ 9 ones=14 ones
1 ten + 5 tens +3 tens=9 tens
4 hundreds + 1 hundred=5 hundreds.

Question 15.

Explanation:
3 ones+ 5 ones=8 ones
6 tens +4 tens=10 tens
1 hundred + 5 hundreds + 2 hundreds=8 hundreds.

Question 16.
THINK SMARTER
Miko wrote these problems. What are the missing digits?

TAKE HOME ACTIVITY • Have your child explain how to solve 236 + 484.

Explanation:
6 ones+ 4 ones=10 ones
1 ten + 3 tens +8 tens=12 tens
1 hundred + 2 hundreds + 4 hundreds=7 hundreds.

Addition: Regroup Ones and Tens Homework & Practice 6.5

Write the sum.
Question 1.

Explanation:
7 ones+ 5 ones=12 ones
1 ten + 4 tens +3 tens=8 tens
5 hundreds + 4 hundreds=9 hundreds.

Question 2.

Explanation:
7 ones+ 4 ones=11 ones
1 ten + 6 tens +8 tens=15 tens
1 hundred + 3 hundreds + 2 hundreds=6 hundreds.

Question 3.

Explanation:
5 ones+ 6 ones=11 ones
1 ten + 8 tens +5 tens=14 tens
1 hundred + 4 hundred + 4 hundreds=5 hundreds.

Question 4.

Explanation:
7 ones+ 6 ones=13 ones
1 ten + 8 tens +0 tens=9 tens
1 hundred + 3 hundreds=4 hundreds.

Question 5.

Explanation:
7 ones+ 8 ones=15 ones
1 ten + 4 tens +2 tens=7 tens
6 hundreds + 1 hundred=7 hundreds.

Question 6.

Explanation:
4 ones+ 9 ones=13 ones
1 ten + 8 tens +2 tens=11 tens
1 hundred + 1 hundred + 3 hundreds=5 hundreds.

Problem Solving
Solve. Write or draw to explain.
Question 7.
Saul and Luisa each scored 167 points on a computer game. How many points did they score together?
_______ points

Explanation:
Saul and luisa has 167 points each on a computer game.Add points of both saul and luisa.There are 3 hundreds 2 tens and 14 ones.So, the sum of 167 and 167 is 3 hundred 3 tens and 4 ones.
7 ones+ 7 ones=14 ones
1 ten + 6 tens +6 tens=13 tens
1 hundred + 1 hundred + 1 hundred=3 hundreds.

Question 8.
WRITE
Write the addition problem for 275 plus 249 and find the sum. Then draw quick pictures to check your work.

Explanation:
5 ones+ 9 ones=14 ones
1 ten + 7 tens +4 tens=12 tens
1 hundred + 2 hundreds + 2 hundreds=5 hundreds.

Lesson Check
Question 1.
What is the sum?

Explanation:
8 ones+ 2 ones=10 ones
1 ten + 4 tens +7 tens=12 tens
1 hundred + 3 hundreds + 2 hundreds=6 hundreds.

Question 2.
What is the sum?

Explanation:
3 ones+ 7 ones=10 ones
1 ten + 2 tens +1 tens=11 tens
1 hundred + 2 hundreds=3 hundreds.

Spiral Review
Question 3.
Which addition fact has the same sum as 9 + 4.
10 + _____
9+4=13
10+3=13

Explanation:
The sumof 9 and 4 is 13.So, if we add 3 to 10 we get the same sum 13.Therefore the addition fact that has the same sum as 9+4 is 10+3.

Question 4.
What is the sum?

Explanation:
2 ones+ 5 ones + 6 ones=13 ones
1 ten + 3 tens +1 tens +4 tens=9 tens

Question 5.
Add 29 and 35. What is the sum?

Question 6.
Tom had 25 pretzels. He gave away 12 pretzels. How many pretzels does Tom have left?
25 – 12 = ______ pretzels

Explanation:
There are 25 blocks in the above picture.Subtract 1 tens and 2 ones from the above picture.Therefore 13 blocks are left.
So, the difference of 25 and 12 is 13.

3-Digit Addition and Subtraction Mid-Chapter Checkpoint

Concepts and Skills

Break apart the addends to find the sum.
Question 1.

Explanation:
Add 567 and 324.Add the hundreds, tens and ones from the above picture.There are 8 hundreds,8 tens and 11 ones.So, the sum of 567 and 324 is 363.
8 hundreds 9 tens 1 ones

write the sum.

Question 2.

Explanation:
8 ones+ 6 ones=14 ones
1 ten + 4 tens +4 tens=9 tens
2 hundreds + 3 hundreds=5 hundreds.

Question 3.

Explanation:
0 ones+ 4 ones=4 ones
1 ten +6 tens=11 tens
6 hundreds + 2 hundreds=8 hundreds.

Question 4.

Explanation:
1 ones+ 7 ones=8 ones
9 tens +3 tens=12 tens
1 hundred + 3 hundreds + 5 hundreds=9 hundreds.

Question 5.
THINK SMARTER
There are 148 small sand dollars and 119 large sand dollars on the beach. How many sand dollars are on the beach?

______ sand dollars

Explanation:
8 ones+ 9 ones=17 ones
1 ten + 4 tens +1 tens=6 tens
1 hundred + 1 hundred=2 hundreds.

Lesson 6.6 Problem Solving • 3-Digit Subtraction

Essential Question How can making a model help when solving subtraction problems?

There were 436 people at the art show. 219 people went home. How many people stayed at the art show?

Unlock the Problem

Show how to solve the problem.
Make a model. Then draw a quick picture of your model.
______ people

HOME CONNECTION • Your child used a model and a quick picture to represent and solve a subtraction problem.

Try Another Problem

Make a model to solve. Then draw a quick picture of your model.
Question 1.
There are 532 pieces of art at the show. 319 pieces of art are paintings. How many pieces of art are not paintings?
______ pieces of art

Question 2.
245 children go to the face-painting event. 114 of the children are boys. How many of the children are girls?
_______ girls

MATHEMATICAL PRACTICES

Share and Show

Make a model to solve. Then draw a quick picture of your model.
Question 3.
There were 237 books on the table. Miss Jackson took 126 books off the table. How many books were still on the table?

______ books

Question 4.
There were 232 postcards on the table. The children used 118 postcards. How many postcards were not used?

_______ postcards

Question 5.
THINK SMARTER
164 children and 31 adults saw the movie in the morning. 125 children saw the movie in the afternoon. How many fewer children saw the movie in the afternoon than in the morning?

______ fewer children

MATHEMATICAL PRACTICE Make Sense of Problems
Question 6.
There were some grapes in a bowl. Clancy’s friends ate 24 of the grapes. Then there were 175 grapes in the bowl. How many grapes were in the bowl before?

______ grapes

Question 7.
THINK SMARTER
At Gregory’s school, there are 547 boys and girls. There are 246 boys. How many girls are there?
Draw a quick picture to solve.

TAKE HOME ACTIVITY • Ask your child to choose one of the problems in this lesson and solve it in a different way.

Problem Solving • 3-Digit Subtraction Homework & Practice 6.6

Make a model to solve. Then draw a quick picture of your model.
Question 1.
On Saturday, 770 people went to the snack shop. On Sunday, 628 people went. How many more people went to the snack shop on Saturday than on Sunday?
______ more people

Question 2.
There were 395 lemon ice cups at the snack shop. People bought 177 lemon ice cups. How many lemon ice cups are still at the snack shop?
______ cups

Question 3.
There were 576 bottles of water at the snack shop. People bought 469 bottles of water. How many bottles of water are at the snack shop now?
_______ bottles

Question 4.
WRITE
Draw quick pictures to show how to subtract 314 and 546.

Lesson Check
Question 1.
There are 278 math and science books. 128 of them are math books. How many science books are there?
______ books

Question 2.
A book has 176 pages. Mr. Roberts has read 119 pages. How many pages does he have left to read?
_____ pages

Spiral Review
Question 3.
What is the sum?
1 + 6 + 2 = _____

Question 4.
What is the difference?
54 – 8 = _____

Question 5.
What is the sum?

Question 6.
What is the sum?

Lesson 6.7 3-Digit Subtraction: Regroup Tens

Essential Question When do you regroup tens in subtraction?

Listen and Draw

Use to model the problem.
Draw a quick picture to show what you did.

MATHEMATICAL PRACTICES
Describe what to do when there are not enough ones to subtract from.

Share and Show

Solve. Write the difference.
Question 1.

Question 2.

Solve. Write the difference.
Question 3.

Question 4.

Question 5.

Question 6.

Question 7.
GO DEEPER
A bookstore has 148 books about people and 136 books about places. Some books were sold. Now there are 137 books left. How many books were sold?
_______ books

Question 8.
THINK SMARTER
There were 287 music books and 134 science books in the store. After some books were sold, there are 159 books left. How many books were sold?

Problem Solving • Applications

MATHEMATICAL PRACTICE Make Sense of Problems
Solve. Write or draw to explain.
Question 9.
There are 235 whistles and 42 bells in the store. Ryan counts 128 whistles on the shelf. How many whistles are not on the shelf?

______ whistles

Question 10.
THINK SMARTER
He sells 107 stamps. How many stamps does he have now? ______ stamps
Would you do these things to solve the problem?
Choose Yes or No.

TAKE HOME ACTIVITY • Ask your child to explain why he or she regrouped in only some of the problems in this lesson.

3-Digit Subtraction: Regroup Tens Homework & Practice 6.7

Solve. Write the difference.
Question 1.

Question 2.

Question 3.

Question 4.

Problem Solving
Solve. Write or draw to explain.
Question 5.
There were 985 pencils. Some pencils were sold. Then there were 559 pencils left. How many pencils were sold?
______ pencils

Question 6.
WRITE
Choose one exercise from above. Draw quick pictures to check your work.

Lesson Check
Question 1.
What is the difference?

Question 2.
What is the difference?

Spiral Review
Question 3.
What is the difference?
45 – 7 = _____

Question 4.
Leroy has 11 cubes. Jane has 15 cubes. How many cubes do they have altogether?
______ cubes

Question 5.
Mina puts 5 flowers in each vase. How many flowers will she put in 3 vases?
______ flowers

Question 6.
Mr. Hill had 428 pencils. He gave away 150 pencils. How many pencils did he keep?
______ pencils

Lesson 6.8 3-Digit Subtraction: Regroup Hundreds

Essential Question When do you regroup hundreds in subtraction?

Listen and Draw

Draw quick pictures to show the problem

MATHEMATICAL PRACTICES
Describe what to do when there are not enough tens to subtract from.

Share and Show

Solve. Write the difference.
Question 1.

Question 2.

Solve. Write the difference.
Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

MATHEMATICAL PRACTICE Make Arguments
Question 9.
Choose one exercise above. Describe the subtraction that you did. Be sure to tell about the values of the digits in the numbers.
______________________
_______________________

Problem Solving • Applications

Question 10.
THINK SMARTER
Sam made two towers. He used 139 blocks for the first tower. He used 276 blocks in all. For which tower did he use more blocks? ______

Explain how you solved the problem.

Question 11.
THINK SMARTER
This is how many points each class scored in a math game.

How many more points did Mr. Chang’s class score than Mr. Pagano’s class? Draw a picture and explain how you found your answer.
_______ more points

TAKE HOME ACTIVITY • Have your child explain how to find the difference for 745 − 341.

3-Digit Subtraction: Regroup Hundreds Homework & Practice 6.8

Solve. Write the difference.
Question 1.

Question 2.

Question 3.

Question 4.

Problem Solving
Solve. Write or draw to explain.
Question 5.
There were 537 people in the parade. 254 of these people were playing an instrument. How many people were not playing an instrument?
_______ people

Question 6.
WRITE
Write the subtraction problem for 838 – 462 and find the difference. Then draw quick pictures to check your difference.

Lesson Check
Question 1.
What is the difference?

Question 2.
What is the difference?

Spiral Review
Question 3.
What is the difference?
52 – 15 = ______

Question 4.
Wallace has 8 crayons and Alma has 7. How many do the have together?
8 + 7 = _____ crayons

Question 5.
What is the sum?

Question 6.
Mrs. Lin’s class read 392 books in February. Mr. Hook’s class read 173 books. How many more books did Mrs. Lin’s class read?

Lesson 6.9 Subtraction: Regroup Hundreds and Tens

Essential Question How do you know when to regroup in subtraction?

Listen and Draw

Use mental math. Write the difference for each problem.

90 − 40 = _____
700 − 500 = _____
70 − 60 = _____
800 − 300 = _____

Explanation:
Subtract the tens amd hundreds from the above sums to find the difference.

Explanation:
Subtract the tens and hundreds from the above sums to find the difference.

MATHEMATICAL PRACTICES
Were some problems easier to solve than other problems? Explain.
Yes some problems wre easy to solve than the other problems as theur was no need of any regrouping for some problems.

Share and Show

Solve. Write the difference.
Question 1.

Explanation:
Regroup 2 tens 1 ones as 1 tens 11 ones.Subtract the ones.
Regroup 4 hundreds 1 tens as 3 hundreds 11 tens.Subtract the tens
Subtract the hundreds.

Question 2.

Explanation:
Subtract the ones.
Regroup 1 hundreds 7 tens as 1 hundreds 17 tens.Subtract the tens
Subtract the hundreds.

Question 3.

Explanation:
Regroup 4 tens 6 ones as 3 tens 16 ones.Subtract the ones.
Regroup 5 hundreds 3 tens as 4 hundreds 13 tens.Subtract the tens
Subtract the hundreds.

Question 4.

Explanation:
Subtract the hundreds,tens and ones as there is no need of regrouping.

Question 5.

Explanation:
Regroup 4 tens 7 ones as 3 tens 17 ones.Subtract the ones.
Regroup 7 hundreds 3 tens as 6 hundreds 13 tens.Subtract the tens
Subtract the hundreds.

Question 6.

Explanation:
Subtract the ones.
Regroup 9 hundreds 3 tens as 8 hundreds 13 tens.Subtract the tens
Subtract the hundreds.

Solve. Write the difference.
Question 7.

Explanation:
Regroup 4 tens 2 ones as 3 tens 12 ones.Subtract the ones.
Subtract the tens
Subtract the hundreds.

Question 8.

Explanation:
Subtract the ones.
Regroup 4 hundreds 6 tens as 3 hundreds 16 tens.Subtract the tens
Subtract the hundreds.

Question 9.

Explanation:
Regroup 5 tens 5 ones as 4 tens 15 ones.Subtract the ones.
Regroup 4 hundreds 1 tens as 3 hundreds 1 tens.Subtract the tens
Subtract the hundreds.

Question 10.

Explanation:
Subtract the ones.
Regroup 6 hundreds 5 tens as 5 hundreds 15 tens.Subtract the tens
Subtract the hundreds.

Question 11.

Explanation:
Regroup 2 tens 1 ones as 1 tens 11 ones.Subtract the ones.
Regroup 5 hundreds 1 tens as 4 hundreds 11 tens.Subtract the tens
Subtract the hundreds.

Question 12.

Explanation:
Regroup 5 tens 8 ones as 4 tens 18 ones.Subtract the ones.
Subtract the tens
Subtract the hundreds.

Question 13.

Explanation:
Regroup 4 tens 2 ones as 3 tens 12 ones.Subtract the ones.
Regroup 5 hundreds 3 tens as 4 hundreds 13 tens.Subtract the tens
Subtract the hundreds.

Question 14.

Explanation:
Subtract the ones.
Regroup 8 hundreds 2 tens as 7 hundreds 12 tens.Subtract the tens
Subtract the hundreds.

Question 15.

Explanation:
Regroup 4 tens 7 ones as 3 tens 17 ones.Subtract the ones.
Regroup 9 hundreds 3 tens as 8 hundreds 13 tens.Subtract the tens
Subtract the hundreds.

Question 16.
THINK SMARTER
Alex wrote these problems. What are the missing digits?

Explanation:
The missing numbers in the first sum are 5 and 5 because only when the numbers are 5 tens and 5 ones if we regroup them they become 4 tens and 15 ones.
The missing numbers in the second sum are 8, 3 and 6 because only when the numbers are 8 hundreds and 3 tens if we regroup them they become 7 hundreds and 13 ones.And 6 ones because if we subtract only 6 ones from 7 ones we get the answer as 1 ones.

Problem Solving • Applications

Question 17.
GO DEEPER
This is how Walter found the difference for 617 − 350.

Find the difference for 843 − 270 using Walter’s way.

Explanation:
As shown in the above picture the difference between 270 and 300 is 30, 800 and 300 is 500 and 843 and 800 is 43.So, when we add 30,500 and 43 is sum wiil be 573.Therefore the difference between 543 and 270 is 573.

Question 18.
MATHEMATICAL PRACTICE Analyze
There are 471 children at Caleb’s school. 256 children ride buses to get to school.

How many children do not ride buses to get to school?
_____ children

Explanation:
Regroup 7 tens 1 ones as 6 tens 11 ones.Subtract the ones.
Subtract the tens
Subtract the hundreds.

Question 19.
THINK SMARTER
Mrs. Herrell had 427 pinecones. She gave 249 pinecones to her children.
How many pinecones does she still have?
_______ pinecones

Explanation:
Regroup 2 tens 7 ones as 1 tens 17 ones.Subtract the ones.
Regroup 4 hundreds 1 tens as 3 hundreds 11 tens.Subtract the tens
Subtract the hundreds.

TAKE HOME ACTIVITY • Ask your child to find the difference when subtracting 182 from 477.

Explanation:
Subtract the ones.
Regroup 4 hundreds 7 tens as 3 hundreds 17 tens.Subtract the tens
Subtract the hundreds.

Subtraction: Regroup Hundreds and Tens Homework & Practice 6.9

Solve. Write the difference.
Question 1.

Explanation:
Regroup 1 tens 6 ones as 0 tens 16 ones.Subtract the ones.
Regroup 8 hundreds 0 tens as 7 hundreds 10 tens.Subtract the tens
Subtract the hundreds.

Question 2.

Explanation:
Regroup 0 tens 2 ones as 9 tens 12 ones.Subtract the ones.
Regroup 9 hundreds 9 tens as 8 hundreds 19 tens.Subtract the tens
Subtract the hundreds.

Question 3.

Explanation:
Regroup 9 tens 6 ones as 8 tens 16 ones.Subtract the ones.
Subtract the tens
Subtract the hundreds.

Problem Solving
Solve.
Question 4.
Mia’s coloring book has 432 pages. She has already colored 178 pages. How many pages in the book are left to color?
______ pages

Explanation:
Regroup 3 tens 2 ones as 2 tens 12 ones.Subtract the ones.
Regroup 4 hundreds 2 tens as 3 hundreds 12 tens.Subtract the tens
Subtract the hundreds.

Question 5.
WRITE
Draw quick pictures to show how to subtract 546 from 735.

Explanation:
Regroup 3 tens 5 ones as 2 tens 15 ones.Subtract the ones.
Regroup 7 hundreds 2 tens as 6 hundreds 12 tens.Subtract the tens
Subtract the hundreds.

Lesson Check
Question 1.
What is the difference?

Explanation:
Subtract the ones.
Regroup 3 hundreds 4 tens as 2hundreds 14 tens.Subtract the tens
Subtract the hundreds.

Question 2.
What is the difference?

Explanation:
Regroup 3 tens 6 ones as 2 tens 16 ones.Subtract the ones.
Regroup 3 hundreds 2 tens as 2 hundreds 12 tens.Subtract the tens
Subtract the hundreds.

Spiral Review
Question 3.
What is the sum?

Explanation:
6 ones + 3 ones=19 ones
1 tens +4 tens + 3 tens=7 tens
2 hundreds + 5 hundreds=7 hundreds.
7 hundreds 7 tens 9 ones.

Question 4.
What is the difference?

Explanation:
Regroup 3 tens 8 ones as 2 tens 18 ones.Subtract the ones.
Subtract the tens

Question 5.
What is the difference?
17 – 9 = _____

Question 6.
Lisa had 15 daisies. She gave away 7 daisies. Then she found 3 more daisies. How many daisies does Lisa have now?
15 – 7 + 3 = ______

Lesson 6.10 Regrouping with Zeros

Essential Question How do you regroup when there are zeros in the number you start with?

Listen and Draw

Draw or write to show how you solved the problem.

MATHEMATICAL PRACTICES
Describe another way that you could solve the problem.

Share and Show

Solve. Write the difference.
Question 1.

Question 2.

Question 3.

Solve. Write the difference.
Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 11.

Question 12.

Question 13.
THINK SMARTER
Miguel has 125 more baseball cards than Chad. Miguel has 405 baseball cards. How many baseball cards does Chad have?

_____ baseball cards

Problem Solving • Applications

Question 14.
MATHEMATICAL PRACTICE
Analyze Claire has 250 pennies. Some are in a box and some are in her bank. There are more than 100 pennies in each place. How many pennies could be in each place?
_____ pennies in a box
_______ pennies in her bank
Explain how you solved the problem.
________________
_________________

Question 15.
THINK SMARTER
There are 404 people at the baseball game. 273 people are fans of the blue team. The rest are fans of the red team. How many people are fans of the red team?
Does the sentence describe how to find the answer?
Choose Yes or No.

There are ________ fans of the red team.

TAKE HOME ACTIVITY • Ask your child to explain how he or she solved one of the problems in this lesson.

Regrouping with Zeros Homework & Practice 6.10

Solve. Write the difference.
Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Problem Solving
Solve.
Question 7.
There are 303 students. There are 147 girls. How many boys are there?
_______ boys

Question 8.
WRITE
Write the subtraction problem 604 – 357. Describe how you will subtract to find the difference.
_______________
________________

Lesson Check
Question 1.
What is the difference?

Question 2.
What is the difference?

Spiral Review
Question 3.
What is the sum?

Question 4.
There are 555 students at Roosevelt Elementary School and 282 students at Jefferson Elementary. How many students are at the two schools altogether?

Question 5.
What is the difference?
10 – 2 = _____

Question 6.
Gabriel’s goal is to read 43 books this year. So far he has read 11 books. How many books does he have left to meet his goal?

Question 1.
Mr. Kent’s art class used 234 craft sticks. Ms. Reed’s art class used 358 craft sticks. How many craft sticks did the two classes use?
______ craft sticks

Question 2.
At the library, there are 668 books and magazines. There are 565 books at the library. How many magazines are there?
Circle the number that makes the sentence true.

Question 3.
There are 176 girls and 241 boys at school. How many children are at school?

Select one number from each column to solve the problem.

Question 4.
THINK SMARTER+
Anna wants to add 246 and 132.
Help Anna solve this problem. Draw quick pictures. Write how many hundreds, tens, and ones in all. Write the number.

_____ hundreds _____ tens _____ ones
_________

Question 5.
Mrs. Preston had 513 leaves. She gave 274 leaves to her students. Draw to show how you found your answer.
How many leaves does she still have?
______ leaves

Question 6.
A farmer has 112 pecan trees and 97 walnut trees. How many more pecan trees does the farmer have than walnut trees?
Fill in the bubble next to all the sentences that describe what you would do.

Question 7.
Amy has 408 beads. She gives 322 beads to her sister. How many beads does Amy have now?
Does the sentence describe how to find the answer?
Choose Yes or No

Question 8.
GO DEEPER
Raul used this method to find the sum 427 + 316.

Use Raul’s method to find this sum.

Describe how Raul solves addition problems.
_____________________
____________________

Question 9.
ally scores more points in a game than Ty. Sally uses 900 – 500 to estimate how many more points.
Fill in the bubble next to all the problems she may have been estimating for.

Question 10.
Use the numbers on the tiles to solve the problem.

Describe how you solved the problem.
___________________________
__________________________

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Curious George

How many kittens can you add to the group to have 10 kittens? Explain.

The kittens we can add to the group to have 10 kittens = 8.

Explanation:
In the above-given question,
given that,
there are 2 kittens in the picture,
we can add 8 kittens to make 10 kittens.
2 + 8 = 10.
The kittens we can add to the group to have 10 kittens = 8.

Addition Concepts Show What You Know

Explore Numbers 1 to 4

Use to show the number. Draw the

Question 1.

The number is 4.

Explanation:
In the above-given question,
given that,
the number is 4.
so we have to draw the 4 buttons.

Question 2.

The number is 3.

Explanation:
In the above-given question,
given that,
the number is 3.
so we have to draw the 3 buttons.

Numbers 1 to 10
How many objects are in each group?

Question 3.

The number of chicks = 7.

Explanation:
In the above-given question,
given that,
there are 7 chicks,
so the number of chicks = 7.

Question 4.

The number of eggs= 5.

Explanation:
In the above-given question,
given that,
there are 5 eggs,
so the number of eggs = 5.

Question 5.

The number of flowers = 4.

Explanation:
In the above-given question,
given that,
there are 4 flowers,
so the number of flowers = 4.

Numbers 0 to 10
How many spots are on the ladybug?

Question 6.

The number of spots on the ladybug = 0.

Explanation:
In the above-given question,
given that,
there are no spots on the bug.
so the number of spots on the ladybug = 0.

Question 7.

The number of spots on the ladybug = 6.

Explanation:
In the above-given question,
given that,
there are 6 spots on the bug.
so the number of spots on the ladybug = 6.

Question 8.

The number of spots on the ladybug = 10.

Explanation:
In the above-given question,
given that,
there are ten spots on the bug.
so the number of spots on the ladybug = 10.

Question 9.

The number of spots on the ladybug = 2.

Explanation:
In the above-given question,
given that,
there are 2 spots on the bug.
so the number of spots on the ladybug = 2.

Visualize It

Draw to show 1 more. Draw to show adding to.

The number of love shapes = 4.

Explanation:
In the above-given question,
given that,
there are 3 love shapes and also given that 1 more.
3 + 1 = 4.
so the number of love shapes = 4.

The number of boxes = 4.

Explanation:
In the above-given question,
given that,
there are 3 boxes and also given that 1 more.
3 + 1 = 4.
so the number of love shapes = 4.

Understand Vocabulary

Complete the sentences with review words.

Question 1.
Sue wants to know how many counters are in two groups. She can _use__ Addition__to find out.

She can use addition to find out.

Explanation:
In the above-given question,
given that,
Sue wants to know how many counters are in two groups.
She can use addition to find out.

Question 2.
Pete has 2 apples. May has 3 apples. May has _1 _ apple than Pete.

May has 1 more apple than Pete.

Explanation:
In the above-given question,
given that,
Peter has 2 apples.
May has 3 apples.
2 + 1 = 3.
May has 1 more apple than Pete.

Materials
• 2 sets of Numeral Cards 0–4

Play with a partner.
1. Mix the cards in each set. Put both sets facedown.
2. Take a card from each set. Join and to add.
4. If you are correct, cover the answer with a
5. The other player takes a turn.
6. The first player to cover 3 spaces in a row wins.

The number is = 5.

Explanation:
In the above-given question,
given that,
player 1 red and player 2 blue.
player 1 = 2 and player 2 = 3
we have to add 2 + 3 = 5.
The number is 5.

Going Places with GOMATH! words

Going to the Zoo

Materials

How to Play
1. Each player puts a on START.
2. Toss the to take a turn. Move your that many spaces.
3. If you land on these spaces:
White Space Read the math word or symbol. Tell its meaning. If you are correct, jump ahead to the next space with the same word. If not, stay where you are.
Green Space Follow the directions. If there are no directions, stay where you are.
4. The first player to reach FINISH wins.

Game
HOW TO PLAY
Materials

2. Toss the and move your that many spaces.
3. If you land on one of these spaces:
Blue Space Explain the math word or use it in a sentence. If your answer is correct, jump ahead to the next space with that word.