Engage NY Eureka Math 5th Grade Module 6 Lesson 1 Answer Key

Eureka Math Grade 5 Module 6 Lesson 1 Problem Set Answer Key

Question 1.
Each shape was placed at a point on the number line s. Give the coordinate of each point below.

Explanation :
The given number line is divided into 3 equals parts from 0-1,1-2 and so on.
Fraction of each part is $$\frac{1}{3}$$.
So, the coordinates of each point located is written in above figure .

Question 2.
Plot the points on the number lines.
a.

Plot A so that its distance from the origin is 2.

Explanation :
The given Number line is divided into 3 parts from 0 -3 that means each unit is 1 .
Point A is marked at 2 and is shown in above figure .

b.

Plot R so that its distance from the origin is $$\frac{5}{2}$$.

Explanation :
The Each part of the above number line is $$\frac{1}{2}$$.
R is plotted at $$\frac{5}{2}$$. and is shown in above figure .

c.

Plot L so that its distance from the origin is 20.

Explanation :
The Each part of the above number line is 5 .
The representation of number line is in decreasing order of 5 . so L is plotted below 35
L is plotted at 20 and is shown in above figure .

d.

Plot a point T so that its distance from the origin is $$\frac{2}{3}$$ more than that of S.

Explanation :
The given Number line is divided into 6 Equal parts from 4 – 5 that means each unit is $$\frac{1}{6}$$.
Point S is marked at  4$$\frac{1}{6}$$ and is shown in above figure .
point T so that its distance from the origin is $$\frac{2}{3}$$ more than that of S.
Point T = 4$$\frac{1}{6}$$ + $$\frac{2}{3}$$ = $$\frac{25}{6}$$ + $$\frac{4}{6}$$
= $$\frac{29}{6}$$ = 4 $$\frac{5}{6}$$
Point T = 4 $$\frac{5}{6}$$  . is marked and is shown in above figure .

Question 3.
Number line g is labeled from 0 to 6. Use number line g below to answer the questions.

a. Plot point A at $$\frac{3}{4}$$.
b. Label a point that lies at 4$$\frac{1}{2}$$ as B.
c. Label a point, C, whose distance from zero is 5 more than that of A.
The coordinate of C is _______.
d. Plot a point, D, whose distance from zero is 1$$\frac{1}{2}$$ less than that of B.
The coordinate of D is ________.
e. The distance of E from zero is 1$$\frac{3}{4}$$ more than that of D. Plot point E.
f. What is the coordinate of the point that lies halfway between A and D? _______ Label this point F.

Point A = $$\frac{3}{4}$$
Point C = 5 + $$\frac{3}{4}$$=5 $$\frac{3}{4}$$
Point B = 4$$\frac{1}{2}$$
Point D = 1$$\frac{1}{2}$$ less than that of B = 4$$\frac{1}{2}$$  – 1$$\frac{1}{2}$$ = 3 .
Point D = 3
Point E = 1$$\frac{3}{4}$$ more than that of D = 3 + 1$$\frac{3}{4}$$ = 4$$\frac{3}{4}$$.
The Coordinate of the point that lies halfway between A and D = Point F = 1.875

Question 4.
Mrs. Fan asked her fifth-grade class to create a number line. Lenox created the number line below:

Parks said Lenox’s number line is wrong because numbers should always increase from left to right. Who is correct? Explain your thinking.
Lenox is right .
Explanation :
Any Orientation is acceptable .

Question 5.
A pirate marked the palm tree on his treasure map and buried his treasure 30 feet away. Do you think he will be able to easily find his treasure when he returns? Why or why not? What might he do to make it easier to find?

No,
Explanation :
Because point or location will help to find the treasure easily .

Eureka Math Grade 5 Module 6 Lesson 1 Exit Ticket Answer Key

Question 1.
Use number line l to answer the questions.

a. Plot point C so that its distance from the origin is 1.
b. Plot point E $$\frac{4}{5}$$ closer to the origin than C. What is its coordinate? _________
c. Plot a point at the midpoint of C and E. Label it H.
a .Point C is plotted .
b .Point E = $$\frac{4}{5}$$closer to the origin than C. = 1 – $$\frac{4}{5}$$ = $$\frac{1}{5}$$ .
c. Point H = the midpoint of C and E = 1 + $$\frac{1}{5}$$ = $$\frac{6}{5}$$/2 =$$\frac{6}{10}$$ = $$\frac{2}{3}$$ .

Question 1.
Answer the following questions using number line q below.
a. What is the coordinate, or the distance from the origin, of the ? ___________
b. What is the coordinate of the ? _________
c. What is the coordinate of the ? __________
d. What is the coordinate at the midpoint of the and the ? __________

a the coordinate, or the distance from the origin, of the is 3
b the coordinate of the is  8
c the coordinate of the is 14
d the coordinate at the midpoint of the and the is (8 + 14)/2 = 11
Explanation :
The number line is divided into 3 parts from 0-3,3-6 and so on . . . .
So Each unit is 1 .

Question 2.
Use the number lines to answer the questions.

a Plot T so that its distance from the origin is 10.

b Plot M so that its distance is $$\frac{11}{4}$$ from the origin. What is the distance from P to M?

c Plot a point that is 0.15 closer to the origin than Z.

d Plot U so that its distance from the origin is $$\frac{3}{6}$$ less than that of W.

Explanation :
The each part of the above number line is 1 unit .
T is plotted at 11 and is shown in above figure .

Explanation :
The each part of the above number line is $$\frac{1}{4}$$ unit .
Point P = 1$$\frac{1}{4}$$ = $$\frac{5}{4}$$
Point M= $$\frac{11}{4}$$
Distance between P and M =$$\frac{11}{4}$$ – $$\frac{5}{4}$$ = $$\frac{6}{4}$$

Explanation :
Point Z = 0.95
Point Y = point that is 0.15 closer to the origin than Z. = 0.95- 0.15 = 0.8
Point Y is plotted .

Explanation :
Point W = 9 $$\frac{4}{6}$$
Plot U so that its distance from the origin is $$\frac{3}{6}$$ less than that of W
Point U = 9$$\frac{4}{6}$$ – $$\frac{3}{6}$$ = 9 $$\frac{1}{6}$$.
Point U is plotted .

Question 3.
Number line k shows 12 units. Use number line k below to answer the questions.

a. Plot a point at 1. Label it A.
b. Label a point that lies at 3$$\frac{1}{2}$$ as B.
c. Label a point, C, whose distance from zero is 8 units farther than that of B.
The coordinate of C is __________.
d. Plot a point, D, whose distance from zero is $$\frac{6}{2}$$ less than that of B.
The coordinate of D is __________.
e. What is the coordinate of the point that lies $$\frac{17}{2}$$ farther from the origin than D? Label this point E.
f. What is the coordinate of the point that lies halfway between F and D? Label this point G.
All the points are plotted and shown in the below figure .

Explanation :
a Point A = 1
b Point B = 3$$\frac{1}{2}$$
c Point C = 8 units farther than that of B = 8 + 3$$\frac{1}{2}$$ = 11 $$\frac{1}{2}$$
The coordinate of C is 11 $$\frac{1}{2}$$
d Point D = $$\frac{6}{2}$$ less than that of B = 3$$\frac{1}{2}$$ – $$\frac{6}{2}$$
= $$\frac{7}{2}$$ – $$\frac{6}{2}$$  = $$\frac{1}{2}$$
The coordinate of D is $$\frac{1}{2}$$
e Point E = $$\frac{17}{2}$$ farther from the origin than D = $$\frac{1}{2}$$  + $$\frac{17}{2}$$  = $$\frac{18}{2}$$ = 9
f  Point F = 9 $$\frac{1}{2}$$
Point G = halfway between F and D =( 9 $$\frac{1}{2}$$ + $$\frac{1}{2}$$ )/2 = 10/2 = 5

Question 4.
Mr. Baker’s fifth-grade class buried a time capsule in the field behind the school. They drew a map and marked the location of the capsule with an X so that his class can dig it up in ten years. What could Mr. Baker’s class have done to make the capsule easier to find?