# Big Ideas Math Answers Grade 3 Chapter 7 Round and Estimate Numbers

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## Big Ideas Math Book 3rd Grade Answer Key Chapter 7 Round and Estimate Numbers

Lesson 1: Place value

Lesson 2: Round Numbers Using a Number Line

Lesson 3: Round Numbers Using Place Value

Lesson 4: Estimate Sums

Lesson 5: Estimate Differences

### Lesson 7.1 Place value

Explore and Grow
Model each number. Write each number in expanded form.

130
310
103

100+30+0=130
300+10+0=310
100+00+3=103
Reasoning
Which number is the greatest? How do you know?

Answer: 310 is the greatest number because the number value of the digit in hundreds place is great compared to others numbers i.e 103 and 130.

Think and Grow: Place value

Find the value of the underlined digit.
Example
253

Expanded form: 200 + 50 + 3
The digit 5 has a value of _5 tens_, or __50__.

Example
517

Expanded form: _500__ + __10__ + ___7__
The digit 5 has a value of __5 hundreds___, or ___500__.

Show and Grow
Circle the value of the underlined digit.

Question.

Circle the value of the underlined digit.

Question.

Write the value of the underlined digit

Question 8.
152

The value of the place of  one digit in the number 152.
The digit 1 has a place value of  100 because its in the hundreds place.
Question 9.
725

The value of the place of the five digit in the number 725.
The digit 5 has a place value of one’s because its in the one’s place.

Question 10.
2o7

The value of the place of the digit in the number 207.
The digit 0 has a place value of  tens because its in the tens place.

Identify the value of each digit.

Question 11.

The value of 3 in 386 = 300
The value of 8 in 386 = 80
The value of 6 in 386 = 6
Question 12.

The value of 5 in 569 = 500
The value of 6 in 569 = 60
The value of 9 in 569 = 9

Question 13.
Reasoning
Use each number card once to write the greatest three-digit number. Then use each number card once to write the least three-digit number.

Among three digits given hundreds place= 8( its greater than other 2 three digits)
Among 2 digits three digits given tens place= 5 (its greater than other  2)
Last ones place = 2(its left out digit)

Think and Grow: Modeling Real Life
Newton spends two hundred two dollars atthe grocery store.Descartes spends $220. Who spends more money? Make quick sketches: _____ spends more money. Answer: Newton amount spent value= 2 hundred and 2 dollar =$200+ $2=$202
Descartes amount spent value= $220$202   <    $220 Hence, Descartes spends more money. Show and Grow Question 4. Newton spends one hundred forty-two dollars at the pet store. Descartes spends$124. Who spends more money?

Newton amount spent value= 1 hundred and forty two dollar
= $100+$40+$2=$142
Descartes amount spent value= $124$142   >    $124 Hence, Newton spends more money. Question 15. DIG DEEPER! Order the weights of the zoo animals from least to greatest. Which animal weighs the least? Which animal weighs the most? Answer: Lion weighs the least of a weighting of 404 pounds. Zebra weighs the most of weighting of 474 pounds. ### Place value Property Homework & Practice 7.1 Circle the value of the underlined digit. Question. Answer: The value of 2 in 325= 20 The value of 1 in 541= 1 The value of 6 in 653= 600 The value of 4 in 194= 4 Write the value of the underlined digit Question 5. 736 Answer: 7 X 100 +3 X 10 +6 X 1=700+30+6 = 736 The value of 3 digit in the number 736 is 3 tens or 30. Question 6. 962 Answer: 9 X 100+6 X 10+2 X 1=900+60+2 = 962 The value of 9 digit in the number 962 is 9 hundreds or 900. Question 7. 897 Answer: 8 X 100+9 X 10+7 X 1=800+90+7 = 897 The value of 7 digit in the number 897 is 7 one’s or 7. Identify the value of each digit. Question 8. Answer: Question 9. Answer: Question 10. DIG DEEPER! Descartes is thinking of a number. What is his number? The three digits of my number are 2, 7, and 5. My number is even. My number is less than 750. Answer: The three digits numbers are 2,7,5 CONDITIONS : The three digits numbers are 2,7,5 My number is even. My number is less than 750. So, Among three digits 2 is even, the last digit is “2” Out of 7 and 5 digits,5 < 7. so the first digit in my number is 5. The middle digit is going to be 7. Hence,the three-digit my number= 572. Question 11. Modeling Real Life A skating rink gives out three hundred thirty glow sticks on Friday and 303 glow sticks on Saturday. On which day does the skating rink give out more glow sticks? Answer: Glow sticks given on Friday = three hundred thirty =3 x 100+3 x 10=300+30=330 Glow sticks given on Saturday=303 Comparison: 330 > 303 Hence, the day the skating rink given out more glow sticks is on Friday. Question 12. DIG DEEPER! Order the basketball field goals made in a season of the basketball players from least to greatest. Which player made the least number of field goals? Which made the most number of field goals? Answer: Player who made the least number of field goals is D player. Player who made the most number of field goals is C player. Review & Refresh Complete the related facts Question 13. 9 ÷ 3 = ____ 3 × ____ = 9 Answer: 9 ÷ 3 = 3 3 × __3__ = 9 Question 14. 40 ÷ 8 = __5___ 8 × ___5_ = 40 Answer: 40 ÷ 8 = __5___ 8 × ___5_ = 40 Question 15. 63 ÷ 7 = __9__ 7 × ___9_ = 63 Answer: 63 ÷ 7 = __9__ 7 × __9___ = 63 ### Lesson 7.2 Round Numbers Using a Number Line Explore and Grow Plot 32 on the number line. Circle the two closest multiples of ten. Which multiple of ten is 32 closer to? Answer: The two closest multiples of 32 ten is 30 and 40. Hence, the multiple of ten close to 32 is 30. Repeated Reasoning Which multiple of ten is closer to 38? 31? 36? How did you decide? Explain. Answer: 38 is between 30 and 40. 38 is closer to 40 than it is to 30. So, 38 is rounded to the nearest ten to 40. Think and Grow: Round Numbers Using a Number Line To round a number to the nearest ten, replace the number with its nearest multiple of ten. When a number is half way between two multiples of ten, use the greater number. Example Round 23 to the nearest ten. 23 is between 20 and 30. 23 is closer to ___ than it is to _____. So, 23 rounded to the nearest ten is _____ Answer: 23 is between 20 and 30. 23 is closer to 20 than it is to 30. So, 23 rounded to the nearest ten is 20. Example Round 175 to the nearest ten 175 is halfway between 170 and 180. So, 175 rounded to the nearest ten is _____. You can round a number to the nearest hundred in a similar way. Answer: 175 is halfway between 170 and 180. 175 rounded to the Nearest Ten is 180. So, the Nearest Hundred Value of 175 is 200. Example Round 465 to the nearest hundred 465 is close to ____ than it is to ____. So, 465 rounded to the nearest hundred is _____. Answer: 465 is halfway in between 460 and 470. So, the Nearest Hundred Value of 465 is 500. Show and Grow Question 1. Round 59 to the nearest ten _____. Answer: The Nearest Ten of 59 is 60. Question 2. Round 350 to the nearest ten _____. Answer: The Nearest Ten is 350 is 350. Apply and Grow: Practice Round the number to the nearest ten and to the nearest hundred/ Question 3. 203 Answer: Nearest Ten: 200 Nearest Hundred: 200 Question 4. 75 Answer: Nearest Ten of 75 is 80. The nearest Hundred of 75 is 100. Question 5. 961 Nearest ten: ______ Nearest hundred: _____ Answer: Nearest Ten of 961 is 960. Nearest Hundred of 961 is 1000 Question 6. 47 Nearest ten: _______ Nearest hundred: _____ Answer: Nearest Ten of 47 is 50. Nearest Hundred of 47 is 0. Question 7. DIG DEEPER! Round ? to the nearest ten and to the nearest hundred Nearest ten: ____ Nearest hundred: ______ Answer: Nearest Ten is 550 Nearest Hundred is 600. Think and Grow: Modeling Real Life On which days does the school collect about 90 food items? The school collects about 90 food and items on _____ and _____ Answer: The school collects about 90 food and items on Monday and Thursday because they are nearest to 90 on number line. Show and Grow Question 8. Use the table above to and on which days the school collects about 80 food items. Answer: The school collects about 80 food and items on Wednesday and Friday because they are nearest to 80 on number line. Question 9. Your teacher wants you to read a book with about 200 pages. Circle the books you can read. Explain. Answer: Books contains 200 about pages are 272 pages and 238 pages because these books having pages of 200 pages and above. Question 10. DIG DEEPER! There are 9 rows and 9 columns of soup cans on a shelf. Round the number of soup cans in all to the nearest ten and to the nearest hundred. Answer: Number of rows of soups=9 Number of columns of soups=9 Total number of cans of soups in all shelf=9 x 9=81 Nearest Ten of 81= 80 Nearest Hundred of 81=100 ### Round Numbers Using a Number Line Homework & Practice 7.2 Round the number to the nearest ten and to the nearest hundred. Question 1. 39 Answer: 39 lies between 30 and 40. So, the Nearest Ten of 39 is 40. 39 lies between 0 and 100. So, the Nearest Hundred of 39 is 100. Question 2. 156 Answer: 156 lies in between 150 and 160. So, the Nearest ten of 156 is 160. 156 lies in between 100 and 200. So, the Nearest Hundred of 156 is 200. Round the number to the nearest ten and to the nearest hundred. Question 3. 402 Nearest ten: _____ Nearest hundred: _____ Answer: 402 lies in between 400 and 410. So, the Nearest Ten of 402 is 400. 402 lies in between 400 and 500. So, the Nearest Hundred of 402 is 400. Question 4. 627 Nearest ten: _____ Nearest hundred: ______ Answer: 627 lies in between 620 and 630. So, the Nearest Ten of 627 is 630. 627 lies in between 600 and 700. So, the Nearest Hundred of 627 is 600. Question 5. Writing Explain how to use a number line to round 24 to the nearest ten. Answer: A line on which numbers are marked at intervals used to illustrate simple numerical operations is known as a number line. 24 is closest to 20 because the number does not cross half way between 20 and 30 on the line. Hence, rounded 24 to the nearest ten is 20. Question 6. Modeling Real Life Your class is painting stones for a garden mosaic. On which days does your class paint about 30 stones? Answer: The class paint about 30 stones on Monday and Friday because on these days the paints are above and about 30. Question 7. Modeling Real Life A giant panda eats about 300 pounds of bamboo every week. Which weights of bamboo can a zookeeper buy to feed a giant panda for a week? Answer: Weight of bamboo eats the giant panda per week= 300 pounds Hence,weights of bamboo a zookeeper buys to feed the giant panda for a week= 310 and 340 pounds(because these two are more than 300 pounds). Review & Refresh Tell whether the product is even or odd. Question 8. 3 × 5 ______ Answer: 3 x 5 = 15 So,15 is odd number. Question 9. 10 × 8 ______ Answer: 10 x 8 = 80 So, 80 is even number. Question 10. 7 × 2 _____ Answer: 7 x 2 = 14 So, 14 is even number. ### Lesson 7.3 Round Numbers Using Place Value Explore and Grow Plot 376 on each number line. Round the number to the nearest ten and to the nearest hundred. Nearest ten: ______ Nearest hundred: ______ Answer: Nearest Ten of 376 is 380 Nearest Hundred of 376 is 400. Reasoning How can you round the number without using the number line? Answer: We can round the number without using the number line by checking if it is less than 5, then the digit in the place you are rounding decreases by 1. If it is 5 or greater, then the digit in the place you are rounding increases by 1 . Think and Grow: Round Numbers Using Place Value Use Place Value to Round Numbers • Find the place to which you are rounding. • Look at the digit to the right. If it is less than 5, then the digit in the place you are rounding stays the same. If it is 5 or greater, then the digit in the place you are rounding increases by 1. • Write Zeros for the digits to the right of the place you are rounding. Example Round 68 to the nearest ten. 68 rounded to the nearest ten is ______. Answer: The Nearest Ten of 68 is 70. Example Round 235 to the nearest hundred and to the nearest ten. 235 rounded to the nearest hundred is ____. 235 rounded to the nearest ten is ____. Answer: The Nearest Hundred of 235 is 200. The Nearest Ten of 235 is 240. Show and Grow Round the number to the nearest ten. Question 1. 41 _____ Answer: 41 lies in between 40 and 50. So, Nearest Ten of 41 is 40. Question 2. 85 _____ Answer: 85 lies in between 80 and 90. 85 is the half way of 80 and 90. So,Nearest Ten of 85 is 90. Question 3. 153 _____ Answer: 153 lies in between 150 and 160. Nearest Ten of 153: 150. Round the number to the nearest hundred. Question 4. 749 _____ Answer: 749 lies between 700 and 800. Nearest hundred of 749 is 700. Question 5. 372 ______ Answer: 372 lies in between 300 and 400. Nearest Hundred of 372 is 400. Question 6. 94 _____ Answer: 94 lies in between 0 and 100. The nearest Hundred of 94 is 100. Apply and Grow: Practice Round the number to the nearest ten. Question 7. 17 ____ Answer: 17 lies in between 10 and 20. So, the Nearest Ten of 17 is 20. Question 8. 52 _____ Answer: 52 lies in between 50 and 60. So, Nearest Ten of 52 is 50. Question 9. 79 _____ Answer: 79 lies in between 70 and 80. So, Nearest Ten of 79 is 80. Question 10. 673 _____ Answer: 673 lies in between 670 and 680. So, Nearest Ten of 673 is 670. Question 11. 521 ____ Answer: 521 lies in between 520 and 530. So, Nearest Ten of 521 of 520. Question 12. 208 ___ Answer: 208 lies in between 200 and 210. So, Nearest Ten of 208 is 210. Round the number to the nearest hundred. Question 13. 161 ____ Answer: 161 lies in between 100 and 200. So, the Nearest Hundred of 161 is 200. Question 14. 738 _____ Answer: 738 lies in between 700 and 800. So, the Nearest Hundred of 738 is 700. Question 15. 504 ____ Answer: 504 lies in between 500 and 600. So, Nearest Hundred of 504 is 500. Question 16. 50 ____ Answer: 50 lies in between 0 and 100. So, Nearest Hundred of 50 is 100. Question 17. 22 ____ Answer: 22 lies in between 0 and 100. So, Nearest Hundred of 22 is 0. Question 18. 999 _____ Answer: 999 lies in between 900 and 1000. So, the Nearest Hundred of 999 is 1000. Round the number to the nearest ten to the nearest hundred. Question 19. 836 Nearest ten: ______ Nearest hundred: ____ Answer: The nearest Ten of 836 is 840. The nearest Hundred of 836 is 800. Question 20. 945 Nearest ten: ______ Nearest hundred: ____ Answer: Nearest Ten of 945 is 950. Nearest Hundred of 945 is 900. Question 21. 72 Nearest ten: ______ Nearest hundred: ____ Answer: Nearest Ten of 72 is 70. Nearest Hundred of 72 is 100. Question 22. Number Sense Newton rounds 587 to 590. To what place does he round? Answer: Newton rounds 587 to 590. Newton rounds 587 to its Nearest ten-value 590. Question 23. Number Sense Which numbers round to 400 when rounded to the nearest hundred? Answer: Numbers rounded to 400 when rounded to the nearest hundreds are 356 and 437. Think and Grow: Modeling Real Life On which day do about 800 people attend the concert? Explain. About 800 people attend the concert on ______ Explain: About 800 people attend the concert on all the days because in all the days people count is about n above 800. Show and Grow Question 24. Use the table above to find on which days about 940 people attend the concert. Explain. Answer: About 940 people attend the concert on Friday and Sunday because in these days the people count is about n above 940. DIG DEEPER! Round the time to the nearest ten minutes. Question 25. Answer: The nearest Ten minutes of 7:23 is 7:20. Question 26. Answer: The nearest Ten minutes of 3:05 is 3:10. Question 27. Explain how using place value to round is similar to using a number line to round. Answer: In math, every digit in a number has a place value. Place value can be defined as the value represented by a digit in a number on the basis of its position in the number. number line is a line on which numbers are placed in intervals, to show basic numerical calculations. Using place value to round is similar to using a number line to round is THE SAME. If we’re rounding the number 111 to the nearest ten, it’s between 110 and 120 on the number line, and it’s closer to 110. Furthermore, the process is the same when we’re rounding to the nearest hundred–only now we’re asking which two multiples of 100 the number falls between. ### Round Numbers Using a Place Value Homework & Practice 7.3 Round the number to the nearest ten Question 1. 29 _____ Answer: Nearest Ten of 29 is 30. Question 2. 564 _____ Answer: Nearest Ten of 564 is 560. Question 3. 843 ____ Answer: Nearest Ten of 843 is 840. Round the number to the nearest hundred Question 4. 281 ____ Answer: The nearest Hundred of 281 is 300. Question 5. 36 ____ Answer: The nearest Hundred of 36 is 0. Question 6. 975 ____ Answer: The nearest Hundred of 975 is 1000. Round the number to the nearest ten to the nearest hundred. Question 7. 152 Nearest ten: ______ Nearest hundred: ____ Answer: Nearest Ten of 152 is 150. Nearest Hundred of 152 is 200. Question 8. 308 Nearest ten: Nearest hundred: ____ Answer: The nearest ten of 308 is 310. The nearest hundred of 308 is 300. Question 9. 45 Nearest ten: ______ Nearest hundred: ____ Answer: Nearest Ten of 45 is 50. The nearest Hundred of 45 is 0. Question 10. What is the least number that rounds to 20 when rounded to the nearest ten? What is the greatest number? Least: ____ Greatest: ____ Answer: The least number that rounds to 20 when rounded to the Nearest Ten is 15. The greatest number that rounds to 20 when rounded to the Nearest Ten is 24. Question 11. DIG DEEPER! Number Sense A three-digit number has the digits 3, 5, and 6.It rounds to 700 when rounded to the nearest hundred. What is the number? Explain. Answer: Given: Three digit number digits are 3,5 and 6. Three digit number rounded to 700 is 653 because in given numbers Hundred place has to be 6 as it has to be rounded to 700. Tens place has to be equal to 5 or greater than 5, 5 taken for tens place. Ones place is left out digit that is 3. The number is 653. Question 12. YOU BE THE TEACHER Descartes says that a number rounded to the nearest ten can be greater than the same number rounded to the nearest hundred. Is Descartes correct? Explain. Answer: Descartes says that a number rounded to the Nearest Ten can be greater than the same number rounded to the Nearest Hundred is correct. For Example: Estimate the sum 1,472 + 398 + 772 + 164 by rounding each number to the nearest hundred. 1,472….1,500 398……. 400 772……..800 164……..200 Total amount rounded to hundred:2900 In the example above, the exact sum is 2,806. Note how close this is to the estimate, which is 94 greater. Estimate the sum 1,472 + 398 + 772 + 164 by first rounding each number to the nearest ten. 1,472….1,470 398…….. 400 772………770 164………160 Total amount rounded to tens place is 2,800. Note that the estimate is 2,800, which is only 6 less than the actual sum of 2,806. Question 13. Modeling Real Life On which months are there about 450 people at the basketball courts? Explain Answer: Months about 450 people at the basketball courts are July and August because in these months only courts count is about and above 450. DIG DEEPER! Round the time to the nearest ten minutes. Question 14. Answer: Nearest Ten Minutes of 5:48 is 5:50. Question 15. Answer: Nearest Ten Minutes of 2:35 is 2:40. Review & Refresh Find the product Question 16. Answer: 9 X 0=0. Question 17. Answer: 10 X 9= 90. Question 18. Answer: 9 X 3= 27. Question 19. Answer: 6 X 9= 54. ### Lesson 7.4 Estimate Sums Explore and Grow Round each addend. Then find the sum. Answer: 83 rounded=80 156 rounded=200 119 rounded=120 103 rounded= 100 Sum =120+80=200 Sum= 200+100= 300 Construct Arguments Compare your answers to your partner’s answers. Explain why they are the same or why they are different. Answer: The answers are different because the numbers are given to me and my partner are completely different. Think and Grow: Estimate Sums An estimate is a number that is close to an exact number. You can estimate a sum by rounding or by using compatible numbers. Compatible numbers are numbers that are easy to add mentally and are close to the actual numbers. Example Estimate 258 + 631. One Way: Use rounding. Round each addend to the nearest hundred. Then f ind the sum of the rounded numbers. Another Way: Use compatible numbers. Answer: ONE WAY: Rounding system 258 rounded nearest hundred: 300 631 rounded nearest hundred: 600 Total Rounded Nearest Hundred of 258 and 631=900 OTHER WAY: Use Compatible number Compatible number of 258=250 Compatible number of 631= 625 Total Sum of Compatible number of 258 and 631= 250+625= 875 Show and Grow Question 1. Round to the nearest ten to estimate the sum. Answer: Nearest Ten of 38= 40. Nearest Ten of 45= 50 Total sum of Nearest Ten of 45 and 38=40+50=90. Question 2. Round to the nearest hundred to estimate the sum. Answer: Nearest Hundred of 407= 400. Nearest Hundred of 189= 200 Total Sum of Nearest Hundred of 407 and 189= 400+200=600. Use compatible numbers to estimate the sum. Question 3. Answer: 71 Compatible Number= 75 22 Compatible Number= 20 Total Sum of Compatible Number of 71 and 22= 75+20=95. Question 4. Answer: 353 Compatible Number= 355 142 Compatible Number= 140 Total Sum of Compatible Number of 353 and 142= 355+140= 495. Apply and Grow: Practice Round to the nearest ten to estimate the sum. Question 5. Answer: Nearest Ten of 214= 210. Nearest Ten of 357= 360 Sum of Nearest Ten of 214 and 357= 210+360 = 570. Question 6. Answer: Nearest Ten of 465= 470. Nearest Ten of 23= 20 Sum of Nearest Ten of 465 and 23= 470+20 = 490. Question 7. Answer: Nearest Ten of 532= 530. Nearest Ten of 241= 240 Total Sum of Nearest Ten of 214 and 357= 530+240 = 570. Round to the nearest hundred to estimate the sum. Question 8. Answer: Nearest Hundred of 62 = 100. Nearest Hundred of 75= 100 Total Sum of Nearest Hundred of 62 and 75= 100+100=200. Question 9. Answer: Nearest Hundred of 304 = 300. Nearest Hundred of 381= 400 Total Sum of Nearest Hundred of 304 and 381= 300+400=700. Question 10. Answer: Nearest Hundred of 897 = 900. Nearest Hundred of 126= 100 Total Sum of Nearest Hundred of 897 and 126= 900+100=1000. Use compatible numbers to estimate the sum. Question 11. Answer: Compatible Number of 222= 225 Compatible Number of 678= 670 Total Sum of Compatible Number of 222 and 678= 225+670=895. Question 12. Answer: Compatible Number of 491= 495 Compatible Number of 407= 465 Total Sum of Compatible Number of 491 and 407= 495+465=960. Question 13. Answer: Compatible Number of 347= 350 Compatible Number of 52= 45 Total Sum of Compatible Number of 347 and 52= 395. Estimate the sum. Question 14. 326 + 472 __ + ___ = ____ Answer: Sum of 326 + 472 = 798. Question 15. 205 + 101 ____ + ____ = _____ Answer: Sum of 205 + 101 = 306. Question 16. 58 + 24 ____ + ____ = ____ Answer: Sum of 58 +24 = 82. Question 17. Structure Estimate the sum of 324 + 277 two different ways. Answer: ONE WAY: Rounding system Nearest Ten of 324= 320 Nearest Ten of 277= 280 Total Sum of Nearest Hundred of 324 and 277= 320+280= 600. OTHER WAY: Compatible Numbers Compatible Numbers of 324=330 Compatible Numbers of 277= 285 Total Sum of Compatible Numbers of 324 and 277=330+285=615. Think and Grow: Modeling Real Life An airplane flies from Cleveland to Saint Louis. Then it flies from Saint Louis to Chicago. About how many miles does the airplane fly in all? Understand the problem: Make a plan: Solve: The airplane flies about ______ miles in all. Answer: Distance covered by the airplane flies overall = 262 miles+49 miles+253 miles+547 miles= 1553 miles . Distance covered by Airplane from Cleveland to Saint Louis=491 miles Distance covered by Airplane from Saint Louis to Chicago= 262 miles Total distance covered by the Airplane from Cleveland to Saint Louis and Saint Louis to Chicago = 491 miles + 262 miles= 753 miles. Show and Grow Question 18. Use the map above. An airplane flies from Dallas to Saint Louis, and then flies from Saint Louis to Nashville. About how many miles does the airplane fly in all? Answer: Miles covered by the airplane from Dallas to Saint Louis= 547 miles Miles covered by the airplane from Saint Louis to Nashville= 253 miles Total Number of miles the airplane flew in all= 547 miles+253 miles= 800 miles. Question 19. There are 178 third-grade students, 239 fourth-grade students, and 309 fifth-grade students at a museum. About how many students are at the museum? Explain. Is there another way you can estimate to solve the problem? Explain. Answer: Number of third-grade students at a museum=178 Number of fourth-grade students at a museum=239 Number of fifth-grade students at a museum=309 Total Number of students at a museum=178+239+309=726. No, there is no other way to estimate the solution except addition. ### Estimate Sums Homework & Practice 7.4 Round to the nearest ten to estimate the sum. Question 1. Answer: Nearest Ten of 239= 240. Nearest Ten of 417= 420 Total Sum of Nearest Ten of 239 and 417= 240+420 = 660. Question 2. Answer: Nearest Ten of 351= 350. Nearest Ten of 164= 160 Total Sum of Nearest Ten of 351 and 164 = 350+160 = 510. Question 3. Answer: Nearest Ten of 55= 60. Nearest Ten of 43= 40 Total Sum of Nearest Ten of 55 and 43 = 60+40 = 100. Round to the nearest hundred to estimate the sum. Question 4. Answer: Nearest Hundred of 523= 500. Nearest Hundred of 376=400 Total Sum of Nearest Hundred of 523 and 376= 500 + 400 = 900. Question 5. Answer: Nearest Hundred of 648=600 Nearest Hundred of 21=0 Total Sum of Nearest Hundred of 648 and 21= 600+0 = 600. Question 6. Answer: Nearest Hundred of 762=800. Nearest Hundred of 235= 200 Total Sum of Nearest Hundred of 762 and 235 = 800+200 = 1000. Use compatible numbers to estimate the sum. Question 7. Answer: Compatible Number of 26= 30 Compatible Number of 51= 55 Total Sum of Compatible Number of 26 and 51 = 30+55 = 85. Question 8. Answer: Compatible Number of 454= 465 Compatible Number of 448= 455 Total Sum of Compatible Number of 454 and 448 = 465+455 = 910. Question 9. Answer: Compatible Number of 177= 185 Compatible Number of 522= 530 Total Sum of Compatible Number of 177 and 552 =185+530 = 715. Estimate the sum Question 10. 621 + 314 ____ + ____ = ____ Answer: Sum of 621 + 314 = 935. Question 11. 105 + 82 ____ + ____ = _____ Answer: Sum of 105 + 82 =187. Question 12. 228 + 276 ____ + ____ = _____ Answer: Sum of 228 + 276 = 504. Question 13. DIG DEEPER! Will Newton’s estimated sum be greater than or less than the actual sum? Explain. Answer: Actual Sum of 486 + 379 = 486 + 379 = 865 Estimated Sum of 486 + 379 =500 + 400 = 900 Comparison: 865 > 900 Hence, the Actual Sum is lesser than the Estimated Sum because the estimated value is the value roughly calculated whereas the actual sum is the correct and accurate value. Question 14. Logic Newton has$25. Descartes has $32. Do they have more than$50 in all? Use estimates to explain.

Amount Newtons having= $25 Estimated value of$25= $30 Amount Descartes having =$32
Estimated value of $32 =$35
Total  Estimated Sum Newtons and Descartes having= $30 +$35 = \$65.

Question 15.
Modeling Real Life
An airplane flies from San Francisco to Las Vegas and then files from Las Vegas to Los Angeles. About how many miles does the airplane fly in all?

Distance covered by Airplane from San Francisco to Las Vegas=418 miles.
Distance covered by Airplane from Las Vegas to Los Angeles= 236 miles.
Total  distance covered by the Airplane from San Francisco to Las Vegas and Las Vegas to Los Angeles= 418 miles + 236 miles = 654 miles.

Question 16.
Modeling Real Life
A beach hut owner sells 118 towels, 121 surfboards, and 162 bathing suits. About how many items does the owner sell? Explain.

Number of towels the owner sells= 118
Number of surfboards the owner sells= 121
Number of bathing suits the owner sells= 162
Total number of items the owner sells= 118 towels + 121 surfboards +162 bathing suits = 401.
Review & Refresh
Compare

Question 17.

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Question 18.

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Question 19.
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### Lesson 7.5 Estimate Differences

Explore & Sum
Estimate each difference.

Use Compatible numbers

Construct Arguments—–
Compare your answers to your partner’s answers. Explain why they are the same or why they are different.

Answer: The answers differ from my partners answer because the numbers given to me and him are differ  may be the process is same which we followed to solve.
Think and Grow: Estimate Differences
You can estimate difference by rounding or by using compatible numbers
Example
Estimate 673 – 429.
One Way: Use rounding. Round each number to the nearest ten. Then find the difference of the rounded numbers.

Another Way: Use compatible numbers.

One way: Rounding numbers
Nearest ten of 673= 670
Nearest ten of 429= 430
Difference of Nearest ten of 673 and 429= 670 – 430 = 240.
Another Way: Use compatible numbers.
Compatible number of 673 =675
Compatible number of 429=425
Difference of Compatible number of 673 and 429= 675 – 425 = 250.
Show and Grow

Question 1.
Round to the nearest ten to estimate the difference.

Nearest Ten of 72= 70.

Nearest Ten of 37= 40
Difference of Nearest Ten of 72 and 37= 70- 40 = 30.

Question 2.
Round to the Nearest Hundred to estimate the difference.

Nearest Hundred of 586= 600.

Nearest Hundred of 314= 300
Difference of Nearest Ten of 586 and 314= 590- 310 = 280.
Use compatible numbers to estimate the difference

Question 3.

Compatible number of 95=100
Compatible number of 26= 25
Difference of Compatible Number of 95 and 26= 100 – 25 = 75.

Question 4.

Compatible number of 768=775
Compatible number of 273= 270
Difference of Compatible Number of 768 and 273= 775 – 270 = 505.
Apply and Grow: Practice
Round to the nearest ten to estimate the difference.

Question 5.

Nearest Ten of 556=560.

Nearest Ten of 129= 130
Difference of Nearest Ten of 556 and 129 = 560 – 130 = 430.

Question 6.

Nearest Ten of 384=380.

Nearest Ten of 31= 30
Difference of Nearest Ten of 384 and 31 = 380 – 30 = 350.

Question 7.

Nearest Ten of 702=700.

Nearest Ten of 428= 430
Difference of Nearest Ten of 702 and 428= 700 – 430 = 270.
Round to the nearest hundred to estimate the difference.

Question 8.

Nearest Hundred of 763=800.

Nearest Hundred of 98 =100
Difference of  Nearest Hundred of 763 and 98= 800 – 100 =700.

Question 9.

Nearest Hundred of 901= 900

Nearest Hundred of 305 = 300
Difference of  Nearest Hundred of 901 and 305= 900 – 300 = 600.

Question 10.

Nearest Hundred of 875 = 900.

Nearest Hundred of 529 = 500
Difference of  Nearest Hundred of 875 and 529 = 900 – 500 = 400.
Use compatible numbers to estimate the difference

Question 11.

Compatible Number of 985= 990
Compatible Number of 148=  145
Difference of Compatible Number of 985 and 148= 990 – 145 = 845.

Question 12.

Compatible Number of 676= 680
Compatible Number of 226= 255
Difference of Compatible Number of 676 and 226 = 680 – 255 = 455.

Question 13.

Compatible Number of 549= 550
Compatible Number of 52=  45
Difference of Compatible Number of 549 and 52 = 550 – 45 = 505.
Estimate the difference

Question 14.
455 – 221
____ – ____ = _____

Difference of 455 – 221 = 234.

Question 15.
674 – 348
____ – ____ = ____

Difference of 674 – 348 =  326.

Question 16.
97 – 53
____ – _____ – _____

Difference of 97 – 53 = 44.

Question 17.
DIG DEEPER!
Write a subtraction problem using 2 three-digit numbers that have an estimated difference of 200.

Answer: A Fruit seller has 469 mangoes with him on Monday. On Tuesday he finds 269 mangoes got rotten. How many are left out with him on Tuesday?

Question 18.
Structure
Did Descartes round to the nearest ten or to the nearest hundred to estimate the difference?

Given: 407 – 302 = 100

Nearest Ten of 407= 410

Nearest Ten of 302= 300
Difference of Nearest Ten of 407 and 302= 410 – 300 = 110.

Nearest Hundred of 407=400

Nearest Hundred of 302= 300
Difference of Nearest Hundred of 407 and 302= 400 – 300 = 100
Therefore, Descartes rounds to the nearest hundred of 407 and 302.
Think and Grow: Modeling Real Life
The diagram shows the numbers of days it takes four planets to orbit the Sun. About how many more days does it take Mars to orbit the Sun than Venus?
Estimate:

It takes Mars about _____ more days than Venus.

Number of days Mars to orbit the sun= 687 days
Number of days Venus to orbit the sun= 225 days

Number of more days it takes Mars to orbit the Sun than Venus= 687 – 225 = 462 days.

Show and Grow

Question 19.
Use the diagram above to find about how many more days it takes Earth to orbit the Sun than Mercury.

Number of days Earth to orbit the sun = 365 days
Number of days Mercury to orbit the sun = 88 days
Number of more days it takes Earth to orbit the Sun than Mercury= 365 – 88 = 277 days.

Question 20.
Your school gym can seat 500 people on one side and 350 people on the other side. There are 459 people in their seats. About how many more people can be seated in the gym?

Number of people seating on one side in the gym = 500
Number of people seating on other side in the gym = 350
Total number of seats in the gym = 500 + 350 = 850
Number of people occupied in the seats in the gym = 459
Number of more people can be seated in the gym = total seats – seats occupied = 850 – 459 =  391 seats.

Question 21.
A bus is traveling 876 miles from Raleigh to New Orleans. The bus travels 264 miles in the morning and 327 miles in the afternoon. About how many more miles does the bus have left to travel? Explain.

The distance the bus traveled from Raleigh to New Orleans = 876 miles
The distance the bus traveled in the morning = 264 miles
The distance the bus traveled in the afternoon = 327 miles
Total distance covered by the bus in the morning and afternoon= 264 miles+ 327 miles = 591 miles
The number of more miles the bus has left to travel = 876 miles – 591 miles = 285 miles.

### Estimate Differences Homework & Practice 7.5

Round to the nearest ten to estimate the difference.

Question 1.

Nearest Ten of 847= 850

Nearest Ten of 468= 470
Difference of Nearest Ten of 847 and 468= 850 – 470= 380.

Question 2.

Nearest Ten of 153=  150

Nearest Ten of 129= 130
Difference of Nearest Ten of 153 and 129= 150 – 130 = 20.

Question 3.

Nearest Ten of 34= 30

Nearest Ten of 21= 20
Difference of Nearest Ten of 34 and 21 = 30 – 20= 10.
Round to the nearest hundred to estimate the difference.

Question 4.

Nearest Hundred of 598= 600

Nearest Hundred of 347= 350
Difference of Nearest Hundred of 598 and 347= 600  – 350 = 250.

Question 5.

Nearest Hundred of  811 =800

Nearest Hundred of 67 = 100
Difference of Nearest Hundred of 811 and 67 = 800 – 100 =700.

Question 6.

Nearest Hundred of 931 = 900

Nearest Hundred of 747 =700
Difference of Nearest Hundred of 931 and 747 = 900 – 700 = 200.
Use compatible numbers to estimate the difference

Question 7.

Compatible Number of 96 = 100
Compatible Number of 47 = 45
Difference of Compatible Number of 96 and 47= 100 – 45 = 65.

Question 8.

Compatible Number of 678 = 685
Compatible Number of 142 = 135
Difference of Compatible Number of 678 and 142 = 685 – 135 = 550.

Question 9.

Compatible Number of 746 = 755
Compatible Number of 51 = 45
Difference of Compatible Number of 746 and 51 = 755 – 45 = 715.
Estimate the difference.

Question 10.
258 – 205
___ – ____ = ____

Difference of 258 – 205 = 53.

Question 11.
781 – 62
____ – ____ = ____

Difference of 781 – 62 = 719.

Question 12.
914 – 522
____ – ____ = ____

Difference of 914 – 522 = 392.

Question 13.
YOU BE THE TEACHER
Your friend estimated the difference by rounding to the nearest hundred. Is your friend correct? Explain.

Given:

Nearest Hundred of 649 = 600
Nearest Hundred of 308 =  300
Difference of Nearest Hundred of 649 and 308 = 600 – 300 = 300
My friend’s value of the difference of Nearest Hundred of 649 and 308 is wrong because he has added the numbers instead of subtracting.

Question 14.
Structure
Estimate the difference of 581 – 213 in two different ways.

ONE WAY: Rounding System
Nearest Hundred of 581= 600
Nearest Hundred of 213= 200
The difference of Nearest Hundred of 581 and 213= 600 – 200 = 400.
OTHER WAY: Use Compatible Numbers
Compatible Number of 581= 575
Compatible Numbers of 213 = 220
Difference of Compatible Numbers of 581 and 213= 575 – 220 =  355.

Question 15.
Modeling Real Life
A drama club sold 259 tickets for a school play. So far, 103 people have arrived for the play. About how many more people are expected to arrive?

Number of tickets sold for school play= 259
Number of people arrived for the play = 103
Number of people expected to arrive still = 259 – 103 = 156.

Question 16.
Modeling Real Life
Construction workers are building an 800-foot tall building. They complete 76 feet one month and 195 feet the next month. About how many more feet do they have left to build?

The total length of the foot ball building = 800 feet
Number of feet workers completed in one month =76 feet
Number of feet workers completed in next month = 195 feet
Construction left out to build = Total -Completed work in one month – Completed work in next month
=800 – 76 – 195 = 529 feet.

Review & Refresh

Question 17.
Find the area of the rectangle

Given: Length of Rectangle= 10 m
Breath of Rectangle= 2 m
Area of Rectangle= Length x Breath = 10 m X 2 m = 20 square metres.

### Round and Estimate Numbers Performance Task

Question 1.
The table shows the number of photos a photographer takes each day.

a. About how many more photos does the photographer take on Saturday than Sunday?
b.Estimate the total number of photos taken all four days.
c.Is the actual number of photos more than or less than your estimate from above? Explain.
d.The photographer’s camera can store 700 photos. About how many more photos can the photographer take?

e. The photographer gives you all of the photos. You put some photos in an album. You have 453 photos left. How many photos are in your album?
f. Your album has 10 pages. You put an equal number of photos on each page. How many photos are on each page?

a) Photos taken on Saturday by the photographer = 221
Photos taken on Sunday by the photographer = 91

Difference of photos taken on Saturday than on Sunday by the photographer= 221 – 91 = 130.
b) Photos taken on Thursday by the photographer = 157
Photos taken on Friday by the photographer = 104
Photos taken on Saturday by the photographer = 221
Photos taken on Sunday by the photographer = 91

Total Number of photos taken by the photographer in all four days= 157+104+221+91 =  573.
c)Actual total number of photos the album holds =700
Total photos were taken by the photographer = 573
The actual total number of photos is greater than the total estimated photos taken by the photographer.
d)Actual number of photos taken =573
Total number of photos camera can hold = 700
Number of more photos can the photographer take= 700 – 573 = 127.
e) Total number of photos given to me by the photographer = 573
Number of photos left with me = 453
Number of photos are in your album = 573 – 453 = 120.
f) Number of pages the album has = 10 pages
Total number of photos album holds = 700
Number of photos on each page= 700 10 =70 pages.

### Round and Estimate Numbers Activity

Round to Find a Pearl
Directions:
1.Players take turns rolling a die.
2.On your turn, move your piece the number of spaces shown on the die. If the space is purple, then round the number to the nearest ten. If the space is green, then round the number to the nearest hundred.
3.Find the rounded number on a pearl and cover it with a counter.
4.Repeat this process until all of the pearls are covered.The player who covers the most pearls wins

### Round and Estimate Numbers Chapter Practice

7.1 Place Value
Circle the value of the underlined digit.

Question

Identify the value of each digit.

Question 3.

Question 4.

7.2 Round Numbers Using a Number Line
Round the number to the nearest ten and to the nearest hundred.

Question 5.
725
Nearest ten: ____
Nearest hundred: _____

The nearest Ten of 725 is 730.

The nearest Hundred of 725 is 700.

Question 6.
34 Nearest ten: ______
Nearest hundred: ______

Nearest Ten of 34 is 30.

Nearest Hundred of 34 is 0.
7.3 Round Numbers Using Place Value
Round the number to the nearest ten and to the nearest hundred.

Question 7.
247
Nearest ten: ____
Nearest hundred: _____

Nearest Ten of 247 is 250.

Nearest Hundred of 247 is 200.

Question 8.
571
Nearest ten: ____
Nearest hundred: _____

The nearest Ten of 571 is  570.

The nearest Hundred of 571 is 600.

Question 9.
86
Nearest ten: ____
Nearest hundred: _____

Nearest Ten of  86 is 90

The nearest Hundred of 86 is 100.

Question 4.
Number Sense
Descartes rounds 742 to 700. To what place does he round?

Nearest Ten of 742 is 740

The nearest Hundred of 742 is 700.
Descartes rounds 742 to its Nearest Hundred.
7.4 Estimate Sums
Estimate the sum

Question 11.
33 + 59
___ + ____ = ___

Sum of 33 + 59 = 92.

Question 12.
124 + 477
____ + ____ = ____

Sum of  124 + 477 = 601.

Question 13.
122 + 181
____ + ____ = ____

Sum of 122 + 181 = 303.
7.5 Estimate Differences
Estimate the difference

Question 14.
692 – 71
___ – ____ = _____

Difference of 692 – 71 = 621

Question 15.
478 – 152
____ – ____ = ____

Difference of 478 – 152 = 326.

Question 16.
537 – 409
____ – ____ = _____