## Envision Math Common Core 5th Grade Answers Key Topic 14 Graph Points on the Coordinate Plane enVision STEM Project: Earth’s Rotation
Do Research Use the Internet or other sources to find out more about Earth’s rotation. Investigate why it appears that the Sun is moving across the sky. Design a model to explain Earth’s day/night cycle. Compare Earth’s rotation to another planet’s rotation.
Write a Report: Journal Include what you found. Also in your report:
• Write a step-by-step procedure of how to use a ball and a flashlight to represent the day/night cycle.
• Explain what happens if the ball rotates slowly. What happens if the ball rotates quickly?
• Make up and solve problems for plotting points and using graphs to show relationships.

Review What You Know

A-Z Vocabulary
Choose the best term from the Word List. Write it on the blank.

• equation
• factor
• line plot
• numerical expression
• variable

Question 1.
A(n) ____ contains numbers and at least one operation.

A(n) numerical expression contains numbers and at least one operation.

Explanation:
In the above-given question,
given that,
A(n) numerical expression contains numbers and at least one operation.
for example:
8x + 4y.
where x and y are variables.
8 and 4 are constants.

Question 2.
A letter or symbol that represents an unknown amount is a(n) ____.

A letter or symbol that represents an unknown amount is a(n) variable.

Explanation:
In the above-given question,
given that,
A letter or symbol that represents an unknown amount is a(n) variable.
for example:
8 + n = 12.
a variable is a letter or symbol that represents a number(unknown quantity).

Question 3.
A number sentence that uses the = symbol is a(n) ____.

A number sentence that uses the = symbol is a(n) equation.

Explanation:
In the above-given question,
given that,
A number sentence that uses the = symbol is a(n) equation.
for example:
4 + 5 = 9.
8 – 2 = 6.

Question 4.
A display that shows Xs or dots above a number line is a(n) ___.

A display that shows Xs or dots above a number line is a(n) line plot.

Explanation:
In the above-given question,
given that,
A display that shows Xs or dots above a number line is a(n) line plot.
for example:
x < 3.

Evaluate Expressions
Evaluate each numerical expression.

Question 5.
3 × 4 × (10 – 7) ÷ 2

3 x 4 x (10 – 7) / 2 = 12.

Explanation:
In the above-given question,
given that,
the equation is 3 x 4 x (10 – 7) / 2.
3 x 4 x (3)/3.
3 x 4 x 1.
3 x 4 = 12.
3 x 4 x (10 – 7) / 2 = 12.

Question 6.
(8 + 2) 6 – 4

(8 + 2) 6 – 4 = 12.

Explanation:
In the above-given question,
given that,
the equation is (8 + 2) 6 – 4.
(6) 6 – 4.
(6) 2.
6 x 2 = 12.
(8 + 2) 6 – 4 = 12.

Question 7.
8 + 2 × 6 – 4

8 + 2 x 6 – 4 = 20.

Explanation:
In the above-given question,
given that,
the equation is 8 + 2 x 6 – 4.
10 x 6 – 4.
10 x 2 = 20.
8 + 2 x 6 – 4 = 20.

Question 8.
40 ÷ 5 + 5 × (3 – 1)

40 / 5 + 5 x (3 – 1) = 18.

Explanation:
In the above-given question,
given that,
the equation is 40 / 5 + 5 x (3 – 1).
40 / 5 + 5 x (2).
8 + 5 x 2.
8 + 10 = 18.
40 / 5 + 5 x (3 – 1) = 18.

Question 9.
15 ÷ 3 + 2 × 10

15 / 3 + 2 x 10 =

Explanation:
In the above-given question,
given that,
the equation is 15 / 3 + 2 x 10.
5 + 2 x 10.
5 + 20.
25.
15 / 3 + 2 x 10 = 25.

Question 10.
21 × (8 – 6) ÷ 14

21 x (8 – 6) / 14 = 3.

Explanation:
In the above-given question,
given that,
the equation is 21 x (8 – 6) / 14.
21 x ( 2) / 14.
21 x 1/7.
21 / 7 = 3.
21 x (8 – 6) / 14 = 3.

Write Expressions
Write a numerical expression for each word phrase.

Question 11.
Three less than the product of eight and six

Three less than the product of eight and six = 45.

Explanation:
In the above-given question,
given that,
three less than the product of eight and six.
product of 6 and 8 is 48.
6 x 8 = 48.
48 – 3 = 45.

Question 12.
Thirteen more than the quotient of twenty divided by four

Thirteen more than the quotient of twenty divided by four is 18.

Explanation:
In the above-given question,
given that,
thirteen more than the quotient of twenty divided by four is 18.
20 / 4 = 5.
5 + 13 = 18.
so thirteen more than the quotient of twenty divided by four is 18.

Question 13.
Four times the difference between seven and two

Four times the difference between seven and two is 20.

Explanation:
In the above-given question,
given that,
Four times the difference between seven and two is 20.
7 – 2 = 5.
4 x 5 = 20.
so four times the difference between seven and two is 20.

Compare Expressions

Question 14.
Use < or > to compare 13 × (54 + 28) and 13 × 54 + 28 without calculating. Explain your reasoning.

13 x (54 + 28) < 13 x 54 + 28.

Explanation:
In the above-given question,
given that,
the equation is 13 x (54 + 28).
13 x 82 = 1066.
13 x 54 + 28.
702 + 28 = 730.
so 13 x (54 + 28) < 13 x 54 + 28.

Pick a Project

PROJECT 14A
What does a city planner do?
Project: Plan a City PROJECT 14B
What are some of the oldest childhood games? PROJECT 14C
How can dogs help rescue people?
Project: Write a Story of a Missing Hiker PROJECT 14D
How can artists use grids in their work?
Project: Draw a Picture Using a Grid ### Lesson 14.1 The Coordinate System

Activity

Solve&Share
On the first grid, plot a point where two lines intersect. Name the location of the point. Plot and name another point. Work with a partner. Take turns describing the locations of the points on your first grid. Then plot the points your partner describes on your second grid. Compare your first grid with your partner’s second grid to see if they match. Use the grids below to solve this problem. You can use grid paper to graph ordered pairs. Show your work! Look Back! Construct Arguments Why does the order of the two numbers that name a point matter? Explain your thinking

Visual Learning Bridge

Essential Question
How Do You Name a Point on a Coordinate Grid?

A.
A map shows the locations of landmarks and has guides for finding them. In a similar way, a coordinate grid is used to graph and name the locations of points in a plane. You can use ordered pairs to locate points on a coordinate grid. B.
A coordinate grid has a horizontal x-axis and a vertical y-axis. The point at which the x-axis and y-axis intersect is called the origin. C.
A point on the grid is named using an ordered pair of numbers. The first number, the x-coordinate, names the distance from the origin along the x-axis. The second number, the y-coordinate, names the distance from the origin along the y-axis. Convince Me! Reasoning in the example above, name the ordered pair for Point B if it is 3 units to the right of Point A. Tell how you decided

The points are (3, 3).

Explanation:
In the above-given question,
given that,
the point B if it is 3 units to the right of point A.
the point is (1, 3).
on the x-axis, the point is 1.
on the y-axis, the point is 3.
so the point is (1,3).
if it is 3 units to the right of point A.
so the points are (3, 3).

Guided Practice

Do You Understand?

Question 1.
You are graphing Point E at (0,5). Do you move to the right zero units, or up zero units? Explain.

We will move up to zero units.

Explanation:
In the above-given question,
given that,
the point is (0, 5).
the point 0 on the x-axis.
the point 5 on the y-axis.
we have to move up zero units.
so we will move up to zero units.

Question 2.
A-Z Vocabulary What ordered pair names the origin of any coordinate grid?

The points (0, 0) names the origin of any coordinate grid.

Explanation:
In the above-given question,
given that,
the ordered pair names the origin of any coordinate grid.
the points are (0, 0), (1, 1), (2, 2), (3, 3) and so on.
the points (0, 0) names the origin of any coordinate grid.

Question 3.
Describe how to graph Point K at (5, 4).

Point 5 on the x-axis and 4 on the y-axis.

Explanation:
In the above-given question,
given that,
the point k at (5, 4) on the co-ordinate axis.
we have to move up zero units.
point 5 is on the x-axis.
point 4 is on the y-axis.
point 5 on the x-axis and 4 on the y-axis.

Do You Know How?

In 4 and 5, write the ordered pair for each point. Use the grid.

Question 4.
B The ordered pairs are (3, 2), (1, 4), and (5, 3).

Explanation:
In the above-given question,
given that,
the points are A, B, C, and D.
the points are (1, 4).
1 is on the x-axis.
4 is on the y-axis.
the point is (3, 2).
3 is on the x-axis.
2 is on the y-axis.
the point is (5, 3).
5 is on the x-axis.
3 is on the y-axis.
so the ordered pairs are (3, 2), (1, 4), and (5, 3).

Question 5.
A

In 6 and 7, name the point for each ordered pair on the grid above.

Question 6.
(5, 3)

Point 5 moves up to 3 units.

Explanation:
In the above-given question,
given that,
point 5 is on the x-axis.
point 3 is on the y-axis.
so the point is (5, 3).
point 5 moves up zero units.

Question 7.
(1, 4)

Point 1 moves up to 4 units.

Explanation:
In the above-given question,
given that,
point 1 is on the x-axis.
point 4 is on the y-axis.
so the point is (1, 4).
point 1 moves up to 4 units.

Independent Practice

In 8-13, write the ordered pair for each point. Use the grid. Question 8.
T

The ordered pair is (0, 5).

Explanation:
In the above-given question,
given that,
point 0 is on the origin.
point 5 is on the y-axis.
the ordered pair is (0, 5).
so the ordered pair is (0, 5).

Question 9.
X

The ordered pair is (4, 3).

Explanation:
In the above-given question,
given that,
point 4 is on the x-axis.
point 3 is on the y-axis.
the ordered pair is (4, 3).
so the ordered pair is (4, 3).

Question 10.
Y

The ordered pair is (1, 0).

Explanation:
In the above-given question,
given that,
point 1 is on the X-axis.
point 0 is on the y-axis.
the ordered pair is (1, 0).
so the ordered pair is (1, 0).

Question 11.
W

The ordered pair is (3, 3).

Explanation:
In the above-given question,
given that,
point 3 is on the x-axis.
point 3 is on the y-axis.
the ordered pair is (3, 3).
so the ordered pair is (3, 3).

Question 12.
Z

The ordered pair is (1, 4).

Explanation:
In the above-given question,
given that,
point 1 is on the x-axis.
point 4 is on the y-axis.
the ordered pair is (1, 4).
so the ordered pair is (1, 4).

Question 13.
S

The ordered pair is (5, 5).

Explanation:
In the above-given question,
given that,
point 5 is on the x-axis.
point 5 is on the y-axis.
the ordered pair is (5, 5).
so the ordered pair is (5, 5).

In 14-18, name the point for each ordered pair on the grid above.

Question 14.
(2, 2)

The point is L.

Explanation:
In the above-given question,
given that,
the point is (2,2).
2 is on the x-axis.
2 is on the y-axis.
so the point is 2.

Question 15.
(5, 4)

The point is Q.

Explanation:
In the above-given question,
given that,
the point is (5, 4).
5 is on the x-axis.
4 is on the y-axis.
so the point is Q.

Question 16.
(1, 5)

The point is N.

Explanation:
In the above-given question,
given that,
the point is (1, 5).
1 is on the x-axis.
5 is on the y-axis.
so the point is N.

Question 17.
(0, 3)

The point is M.

Explanation:
In the above-given question,
given that,
the point is (0, 3).
0 is on the x-axis.
3 is on the y-axis.
so the point is M.

Question 18.
(4, 0)

The point is P.

Explanation:
In the above-given question,
given that,
the point is (4, 0).
4 is on the x-axis.
0 is on the y-axis.
so the point is p.

Problem Solving

Question 19.
Higher Order Thinking Describe to a friend how to find and name the ordered pair for Point R on the grid. The point is (4, 5).

Explanation:
In the above-given question,
given that,
the point is R.
4 is on the x-axis.
5 is on the y-axis.
so the point is (4, 5).

In 20-24, complete the table. List the point and ordered pair for each vertex of the pentagon at the right.  The points are B, C, D, E, and F.

Explanation:
In the above-given question,
given that,
The point E is on the ordered pair (1, 1).
the point D is on the ordered pair (1, 2).
point C is on the ordered pair (1, 3).
point B is on the ordered pair (2, 4).
point F is on the ordered pair (3, 1).

Question 25.
Reasoning Why is the order important when naming or graphing the coordinates of a point?

The order is important when naming or graphing the coordinates of a point.

Explanation:
In the above-given question,
given that,
the order is important because A is on the (3, 3).
B is on the (2, 4).
C is on the (1, 3).
D is on the (1, 2).
E is on the (1, 1).
F is on the (3, 1).
G is on the (5, 1).

Question 26.
How are the x-axis and the y-axis related on a coordinate grid?

The x-axis and the y-axis are related.

Explanation:
In the above-given question,
given that,
the order is important because A is on the (3, 3).
B is on the (2, 4).
C is on the (1, 3).
D is on the (1, 2).
E is on the (1, 1).
F is on the (3, 1).
G is on the (5, 1).

Assessment Practice

Question 27.
Which of the following points is located at (4, 2)? A. Point A
B. Point M
C. Point B
D. Point P

Option M is correct.

Explanation:
In the above-given question,
given that,
the point is (4, 2).
4 is located on the x-axis.
2 is located on the y-axis.
so option M is correct.

### Lesson 14.2 Graph Data Using Ordered Pairs

Activity

Sole & Share
Graph and label the point for each ordered pair below on the grid. Then connect the points with line segments to form a shape. What shape did you draw?

Use Appropriate Tools You can graph points on a coordinate grid. Show your work! The shape formed is square.

Explanation:
In the above-given question,
given that,
the ordered pairs are (2, 1), (5, 1), (5, 4), and (2, 4).
the point (2, 1) is on the A.
the point (5, 1) is on the B.
the point (5, 4) is on the C.
the point (2, 4) is on the D.
so the shape formed is square. Look Back! What tool could you use to help connect points A, B, C, and D? Explain.

Visual Learning Bridge

Essential Question How Do You Graph a Point on a Coordinate Grid?

A.
The table below shows the growth of a plant over a period of several days. Graph ordered pairs to show the plant’s growth. Let x be the number of days and let y be the height of the plant in centimeters. The ordered pairs are (1, 4), (3, 8), (5, 10), (7, 11), and (9, 14).

B.
Step 1
Graph the first point (1, 4).
Start at (0, 0). Move 1 unit to the right along the x-axis. Then move 4 units up. C.
Step 2
Plot the rest of the ordered pairs from the table. Use a ruler to connect the points. Convince Me! Reasoning Based on the data, about how tall was the plant on day 4? Day 8?

Guided Practice

Do You Understand?

Question 1.
Natalie is graphing Point T at (1,8). Should she move to the right 8 units or up 8 units? Explain.

She moves 8 units up.

Explanation:
In the above-given question,
given that,
the point T at (1, 8).
point 1 is on the x-axis.
point 8 is on the y-axis.
so she moves 8 units up.

Question 2.
Describe how to graph the point (c, d).

Do You Know How?

In 3-6, graph each point on the grid and label it with the appropriate letter. Question 3.
E (1, 3)

The point is E.

Explanation:
In the above-given question,
given that,
point 1 is on the x-axis.
point 3 is on the y-axis.
the ordered pair is (1, 3).
so the point is E.

Question 4.
F (4, 4)

The point is F.

Explanation:
In the above-given question,
given that,
point 4 is on the x-axis.
point 4 is on the y-axis.
the ordered pair is (4, 4).
so the point is F.

Question 5.
G (5, 2)

The point is G.

Explanation:
In the above-given question,
given that,
point 5 is on the x-axis.
point 2 is on the y-axis.
the ordered pair is (5, 2).
so the point is G.

Question 6.
H (0, 2)

The point is H.

Explanation:
In the above-given question,
given that,
point 0 is on the x-axis.
point 2 is on the y-axis.
the ordered pair is (0, 2).
so the point is H. Independent Practice

In 7-18, graph and label each point on the grid at the right. Question 7.
J (2, 6)

The point is J.

Explanation:
In the above-given question,
given that,
point 2 is on the x-axis.
point 6 is on the y-axis.
the ordered pair is (2, 6).
so the point is J.

Question 8.
K (6, 2)

The point is K.

Explanation:
In the above-given question,
given that,
point 6 is on the x-axis.
point 2 is on the y-axis.
the ordered pair is (6, 2).
so the point is K.

Question 9.
L (4, 5)

The point is L.

Explanation:
In the above-given question,
given that,
point 4 is on the x-axis.
point 5 is on the y-axis.
the ordered pair is (4, 5).
so the point is L.

Question 10.
M (0, 8)

The point is M.

Explanation:
In the above-given question,
given that,
point 0 is on the x-axis.
point 8 is on the y-axis.
the ordered pair is (0, 8).
so the point is M.

Question 11.
N (3, 9)

The point is N.

Explanation:
In the above-given question,
given that,
point 3 is on the x-axis.
point 9 is on the y-axis.
the ordered pair is (3, 9).
so the point is N.

Question 12.
V (6, 6)

The point is V.

Explanation:
In the above-given question,
given that,
point 6 is on the x-axis.
point 6 is on the y-axis.
the ordered pair is (6, 6).
so the point is V.

Question 13.
P (1, 4)

The point is P.

Explanation:
In the above-given question,
given that,
point 1 is on the x-axis.
point 4 is on the y-axis.
the ordered pair is (1, 4).
so the point is P.

Question 14.
Q (5, 0)

The point is Q.

Explanation:
In the above-given question,
given that,
point 5 is on the x-axis.
point 0 is on the y-axis.
the ordered pair is (5, 0).
so the point is Q.

Question 15.
R (7, 3)

The point is R.

Explanation:
In the above-given question,
given that,
point 7 is on the x-axis.
point 3 is on the y-axis.
the ordered pair is (7, 3).
so the point is R.

Question 16.
S (7, 8)

The point is S.

Explanation:
In the above-given question,
given that,
point 7 is on the x-axis.
point 8 is on the y-axis.
the ordered pair is (7, 8).
so the point is S.

Question 17.
T (8, 1)

The point is T.

Explanation:
In the above-given question,
given that,
point 8 is on the x-axis.
point 1 is on the y-axis.
the ordered pair is (8, 1).
so the point is T.

Question 18.
U (3, 3)

The point is E.

Explanation:
In the above-given question,
given that,
point 1 is on the x-axis.
point 3 is on the y-axis.
the ordered pair is (1, 3).
so the point is E. Problem Solving

Question 19.
Reasoning How is graphing (0, 2) different from graphing (2,0)?

(0, 2) is on the y-axis, and (2, 0) is on the x-axis.

Explanation:
In the above-given question,
given that,
the ordered pairs are (0, 2) and (2, 0).
(0, 2) is 2 units up from the origin.
(2, 0) is 2 units right from the origin.

Question 20.
Number Sense Shane took a test that had a total of 21 items. He got about of the items correct. About how many items did he get correct?

Question 21.
Higher Order Thinking Point C is located at (10, 3) and Point D is located at (4,3). What is the horizontal distance between the two points? Explain.

The distance between the points is (6, 0).

Explanation:
In the above-given question,
given that,
point C is located at (10, 3).
point D is located at (4, 3).
10 – 4 = 6.
3 – 3 = 0.
so the distance between the points is (6, 0).

Question 22.
Laurel buys 3 balls of yarn. Each ball of yarn costs $4.75. She also buys 2 pairs of knitting needles. Each pair costs$5.75. She pays for her purchase with two 20-dollar bills. What is her change?

The change is $14.25. Explanation: In the above-given question, given that, Laurel buys 3 balls of yarn. Each ball of yarn costs$4.75.
She also buys 2 pairs of knitting needles.
Each pair costs $5.75. 3 x$4.75 = $14.25.$5.75 x 2 = $11.5.$14.25 + $11.5 =$25.75.
20 x 2 = 40 dollar bills.
40 – 25.75 = $14.25. Question 23. Graph the points below on the grid at the right. A (2, 4) B (1, 2) C (2, 0) D (3, 0) E (4, 2) F (3, 4) Answer: The points are (2, 4), (1, 2), (2, 0), (3, 0), (4, 2), and (3, 4). Explanation: In the above-given question, given that, The points are (2, 4), (1, 2), (2, 0), (3, 0), (4, 2), and (3, 4). point 2 is on the x-axis. point 4 is on the y-axis. point 1 is on the x-axis. point 2 is on the y-axis. point 2 is on the x-axis. point 0 is on the y-axis. point 3 is on the x-axis. point 4 is on the x-axis. point 2 is on the y-axis. point 3 is on the x-axis. point 4 is on the y-axis. Question 24. Alejandro wants to connect the points to form a shape. What would be the most appropriate tool for him to use? Use the tool to connect the points. Answer: The shape formed is the hexagon. Explanation: In the above-given question, given that, Alejandro wants to connect the points to form a shape. points are (2, 4), (1, 2), (2, 0), (3, 0), (4, 2), and (3, 4). point 2 is on the x-axis. point 4 is on the y-axis. point 1 is on the x-axis. point 2 is on the y-axis. point 2 is on the x-axis. point 0 is on the y-axis. point 3 is on the x-axis. point 4 is on the x-axis. point 2 is on the y-axis. point 3 is on the x-axis. point 4 is on the y-axis. so the shape formed is the hexagon. Assessment Practice Question 25. Talia draws a map of her neighborhood on a coordinate grid. Her map shows the school at S (1,6), her house at H (4,3), and the library at L (7,2). Graph and label each location on the grid at the right. Answer: Points are (1, 6), (4, 3), and (7, 2). Explanation: In the above-given question, given that, Talia draws a map of her neighborhood on a coordinate grid. Her map shows the school at S (1,6), her house at H (4,3), and the library at L (7,2). point 1 is on the x-axis. point 6 is on the y-axis. point 4 is on the x-axis. point 3 is on the y-axis. point 7 is on the x-axis. point 2 is on the y-axis. ### Lesson 14.3 Solve Problems Using Ordered Pairs Activity Solve&Share The table below uses number patterns to describe changes in the width and length of a rectangle. Let x be the width and y be the length. Then plot each of the four ordered pairs in the table on the coordinate grid. What do you think the length is if the width is 5? You can make a graph to help solve the problem. Show your work! Look Back! Look for Relationships What pattern do the points form on your graph? Visual Learning Bridge Essential Question How Can You Use Ordered Pairs to Solve Problems? A. Both Ann and Bill earn the amount shown each week. Ann starts with no money, but Bill starts with$5. How much will Bill have when Ann has $30? Represent this situation using a table and a graph. You know that when Ann has$0, Bill has $5. B. Make a table showing how much money Ann and Bill have after each week. Let x = Ann’s earnings and y = Bill’s earnings. C. Plot the ordered pairs from the table. Draw a line to show the pattern. Extend your line to the point where the x-coordinate is 30. The corresponding y-coordinate is 35. So, Bill has$35 when Ann has $30. Convince Me! Look for Relationships What is the relationship between Bill’s earnings and Ann’s earnings? Guided Practice Do You Understand? Question 1. In the example on page 574, find another point on the line. What does this point represent? Answer: Question 2. Algebra In the example on page 574, write an equation to show the relationship between Ann’s earnings and Bill’s earnings. Remember to let x = Ann’s earnings and y = Bill’s earnings. Answer: Let x = Ann’s earnings. y = Bill’s earnings. Explanation: In the above-given question, given that, x + 5. Ann has$30 and $35.$30 + 5 = $35. Do You Know How? Write the missing coordinates and tell what the point represents. Question 3. Answer: The missing coordinates are (5, 200). Explanation: In the above-given question, given that, the points are (20, 800), (15, 600), (10, 400). 20 – 5 = 15. 15 – 5 = 10. 10 – 5 = 5. 800- 200 = 600. 600 – 200 = 400. 400 – 200 = 200. so the missing coordinates are (5, 200). Independent Practice In 4 and 5, find the missing coordinates and tell what the point represents. Question 4. Answer: The missing coordinates are (900, 800). Explanation: In the above-given question, given that, the ordered pairs are (1500, 1200), (1200, 1000), (600, 600), and (300, 400). on x-axis subtract 300. 1500 – 300 = 1200. 1200 – 300 = 900. 900 – 300 = 600. 600 – 300 = 300. on y-axis subtract 200. 1200 – 200 = 1000. 1000 – 200 = 800. 800 – 200 = 600. 600 – 200 = 400. so the missing coordinates are (900, 800). Question 5. Answer: The missing coordinates are (200, 150). Explanation: In the above-given question, given that, the ordered pairs are (600, 550), (500, 450), (400, 350), (300, 250), and (100, 50). subtract 100 on x-axis. subtract 100 on y-axis. 600 – 100 = 500. 500 – 100 = 400. 400 – 100 = 300. 300 – 100 = 200. 200 – 100 = 100. so the missing coordinates are (200, 150). Question 6. For Exercise 5, find two other points on the line. Then graph and label them. Describe the relationship between deer sightings and elk sightings. Answer: Problem Solving In 7 and 8, use the table at the right. Question 7. Graph the points in the table on the grid at the right. Then draw a line through the points. Answer: Time(h) is on the x-axis. pages read is on the y-axis. Explanation: In the above-given question, given that, in 1 hour number of pages read is 20. in 2 hours number of pages read is 40. in 3 hours number of pages read is 60. in 4 hours number of pages read is 80. in 5 hours number of pages read is 100. Question 8. Look for Relationships If the pattern continues, how many pages will have been read after 6 hours? Extend your graph to solve. Answer: The number of pages that will have been read after 6 hours = 120. Explanation: In the above-given question, given that, in 1 hour number of pages read is 20. in 2 hours number of pages read is 40. in 3 hours number of pages read is 60. in 4 hours number of pages read is 80. in 5 hours number of pages read is 100. in 6 hours number of pages read is 120. Question 9. Higher Order Thinking Suppose you have a graph of speed that shows a lion can run four times as fast as a squirrel. Name an ordered pair that shows this relationship. What does this ordered pair represent? Answer: The ordered pair represents (1, 4). Explanation: In the above-given question, given that, the lion can run four times as fast as a squirrel. x + 4y. x represents the speed of a squirrel. y represents the speed of a lion. so a lion can run four times as fast as a squirrel. Question 10. Number Sense Candace drives a total of 48 miles each day to get to work and back home. She works 5 days a week. Her car gets 21 miles per gallon of gas. About how many gallons of gas does she need to drive to work and back home each week?! Answer: The number of gallons of gas does she need to drive to work = 48 gallons. Explanation: In the above-given question, given that, Candace drives a total of 48 miles each day to get to work and back home. She works 5 days a week. Her car gets 21 miles per gallon of gas. 48 x 5 = 240. 240 / 5 = 48. so the number of gallons of gas does she need to drive to work. Assessment Practice Question 11. What does the point (15, 4) represent on the graph at the right? A. The ant crawled 15 meters in 19 seconds. B. The ant crawled 15 meters in 4 seconds. C. The ant crawled 4 meters in 19 seconds. D. The ant crawled 4 meters in 15 seconds. Answer: Option B is correct. Explanation: In the above-given question, given that, point (15, 4) is in the coordinate plane. 15 is on the x-axis. 4 is on the y-axis. the ant crawled 15 meters in 4 seconds. so option B is correct. Question 12. What does the point (20, 5) represent on the graph? A. In 20 seconds, the ant crawled 5 centimeters. B. In 20 seconds, the ant crawled 5 meters. C. In 5 seconds, the ant crawled 20 meters. D. In 5 seconds, the ant crawled 15 meters. Answer: Option C is correct. Explanation: In the above-given question, given that, the point is (20, 5). 20 is on the x-axis. 5 is on the y-axis. in 5 seconds the ant crawled 20 meters. so option C is correct. ### Lesson 14.4 Reasoning Activity Problem Solving Solve & Share Six clowns apply for a circus job. The specific job requires the clown to have a clown shoe size less than 15 inches and to be shorter than 5 ft 8 in. tall. How many clowns meet the size requirements for the job? Complete the graph below to help you decide. Thinking Habits Be a good thinker! These questions can help you. • What do the numbers and symbols in the problem mean? • How are the numbers or quantities related? • How can I represent a word problem using pictures, numbers, or equations? Look Back! Reasoning How can you use reasoning about the completed graph to find the number of clowns that meet the requirements? Explain. Visual Learning Bridge Essential Question How Can You Use Reasoning to Solve Mathematical Problems? A. In 1705, a ship sank in the ocean at the point shown. Every year the ocean currents moved the ship 1 mile east and 2 miles north. Where was the ship located after 4 years? Where was the ship located after 10 years? Tell how you decided. What do I need to do to solve the problem? I need to find the ship’s location after 4 years and after 10 years. B. How can I use reasoning to solve this problem? I can • use what I know about graphing points. • graph ordered pairs. • look for relationships in the coordinates. • decide if my answer makes sense. Here’s my thinking.. C. I will use the graph to show the location each year for 4 years. Each point is 1 mile east and 2 miles north from the previous point. After 4 years the ship was at (8, 14). I see a pattern. The x-coordinate increases by 1, and the y-coordinate increases by 2: (4, 6), (5, 8), (6, 10), (7, 12), (8, 14) I can continue the pattern for another 6 years: (9,16), (10, 18), (11, 20), (12, 22), (13, 24), (14, 26) After 10 years, the ship was at (14, 26). Convince Me! Make Sense and Persevere How could you decide if your answers make sense? Guided Practice Tanya marked a grid in her garden. She planted a rose bush at (3, 1). She moved 2 feet east and 1 foot north and planted the second rose bush. She continued planting rose bushes so that each bush is 2 feet east and 1 foot north of the previous bush. Question 1. How can a coordinate grid help you reason about the problem? Answer: The point is (3, 1), (5, 2), and (7, 3). Explanation: In the above-given question, given that, the point is (3, 1). She moved 2 feet east and 1 foot north and planted the second rose bush. 3 + 2 = 5. 5 + 2 = 7. 1 + 1 = 2. 2 + 1 = 3. so the points are (3, 1), (5, 2), and (7, 3). Question 2. Draw and label the locations of the first four bushes on the grid. Do Tanya’s 0 2 bushes lie on a straight line? How do you know? Answer: The bushes lie in a straight line. Explanation: In the above-given question, given that, the point is (3, 1). She moved 2 feet east and 1 foot north and planted the second rose bush. 3 + 2 = 5. 5 + 2 = 7. 1 + 1 = 2. 2 + 1 = 3. so the points are (3, 1), (5, 2), and (7, 3). Question 3. What are the locations of the fifth and ninth rose bushes? Answer: The locations of the fifth and ninth rose bushes are in a straight line. Explanation: In the above-given question, given that, the point is (3, 1). She moved 2 feet east and 1 foot north and planted the second rose bush. 3 + 2 = 5. 5 + 2 = 7. 7 + 2 = 9. 1 + 1 = 2. 2 + 1 = 3. 3 + 1 = 4. so the points are (3, 1), (5, 2), and (7, 3), (9, 4). Independent Practice Reasoning A marching band uses a grid to determine the members’ positions. Juan starts at (2, 2). Every 15 seconds, he moves 4 yards east and 3 yards north. Question 4. How can you model this problem? Answer: After 15 seconds Juan moves (6, 5). Explanation: In the above-given question, given that, A marching band uses a grid to determine the members’ positions. Juan starts at (2, 2). Every 15 seconds, he moves 4 yards east and 3 yards north. 2 + 4 = 6. 2 + 3 = 5. so after 15 seconds Juan moves (6, 5). Question 5. Draw and label the locations of Juan’s first four positions. Do the points form a pattern? How can you tell? Answer: Juan’s first four positions are (6, 5), (10, 8), (14, 11), and (18, 14). Explanation: In the above-given question, given that, A marching band uses a grid to determine the members’ positions. Juan starts at (2, 2). Every 15 seconds, he moves 4 yards east and 3 yards north. 2 + 4 = 6, 6 + 4 = 10, 10 + 4 = 14, and 14 + 4 = 18. 2 + 3 = 5, 5 + 3 = 8, 8 + 3 = 11, and 11 + 3 = 14. so Juan’s first four positions are (6, 5), (10, 8), (14, 11), and (18, 14). Question 6. What will Juan’s location be after 60 seconds? 90 seconds? How does the coordinate grid help you reason about the locations? Answer: Juan,s location be after 60 and 90 seconds are (14, 11), and (18, 14). Explanation: In the above-given question, given that, A marching band uses a grid to determine the members’ positions. Juan starts at (2, 2). Every 15 seconds, he moves 4 yards east and 3 yards north. 2 + 4 = 6, 6 + 4 = 10, 10 + 4 = 14, and 14 + 4 = 18. 2 + 3 = 5, 5 + 3 = 8, 8 + 3 = 11, and 11 + 3 = 14. so Juan,s location be after 60 and 90 seconds are (14, 11), and (18, 14). Problem Solving Performance Task Rozo Robot A toy company is testing Rozo Robot. Rozo is 18 inches tall and weighs 2 pounds. The employees of the company marked a grid on the floor and set Rozo at (2,5). They programmed Rozo to walk 3 yards east and 4 yards north each minute. What will Rozo’s location be after 7 minutes? Question 7. Make Sense and Persevere Do you need all of the information given in the problem to solve the problem? Describe any information that is not needed. Answer: Question 8. Model with Math Label the graph and plot Rozo’s starting position. Then plot and label Rozo’s position at the end of each of the first 4 minutes. Answer: Question 9. Use Appropriate Tools What tool would you choose for drawing a line segment between points on a coordinate grid? Explain your thinking. Answer: You can use the coordinate grid to reason about relationships between the points Question 10. Look for Relationships Describe the relationships between the coordinates of the points that represent Rozo’s locations. Answer: Question 11. Reasoning What will Rozo’s location be after 7 minutes? Explain how you determined your answer. Answer: ### Topic 14 Fluency Practice Activity Point & Tally Find a partner. Get paper and a pencil. Each partner chooses light blue or dark blue. At the same time, Partner 1 and Partner 2 each point to one of their black numbers. Both partners find the product of the two numbers. The partner who chose the color where the product appears gets a tally mark. Work until one partner has seven tally marks.  Topic 14 Vocabulary Review Glossary Understand Vocabulary Choose the best term from the Word List. Write it on the blank. Word List • coordinate grid • ordered pair • origin • x-axis • x-coordinate • y-axis • y-coordinate Question 1. The point where the axes of a coordinate grid intersect is the _____ Answer: The point where the axes of a coordinate grid intersect is the origin. Explanation: In the above-given question, given that, the point where the axes of a coordinate grid intersect is the origin. for example: (x, y) = (3, 2). Question 2. A(n) ____ names an exact location on a coordinate grid. Answer: A(n) coordinate grid names an exact location on a coordinate grid. Explanation: In the above-given question, given that, A(n) coordinate grid names an exact location on a coordinate grid. for example: (2, 3) is on the coordinate plane. 2 is on the x-axis. 3 is on the y-axis. Question 3. The first number of an ordered pair describes the distance from the origin along the ____ Answer: The first number of an ordered pair describes the distance from the origin along with the ordered pair. Explanation: In the above-given question, given that, the first number of an ordered pair describes the distance from the origin along with the ordered pair. for example: (4, 5) 4 units on the x-axis. 5 units on the y-axis. Question 4. The second number of an ordered pair is the ______ Answer: The second number of an ordered pair is the y-coordinate. Explanation: In the above-given question, given that, the second number of an ordered pair is the y-coordinate. for example: In an ordered pair, the first number is always the x-coordinate. the second number is the y-coordinate. Question 5. A ____ is formed by two number lines that intersect at a right angle. Answer: A coordinate plane is formed by two number lines that intersect at a right angle. Explanation: In the above-given question, given that, A coordinate plane is formed by two number lines that intersect at a right angle. for example: x-axis = horizontal number line. y-axis = vertical number line. origin = where the number lines intersect. the coordinates of the origin are (0, 0). Draw a line from each lettered point in Column A to the ordered pair it represents.   Use Vocabulary in Writing Question 12. Why is the order of the coordinates important in an ordered pair? Use terms from the Word List in your explanation. Answer: The order of the coordinates is important because it forms a shape, a straight line. Explanation: In the above-given question, given that, points are A(5, 2), B(1, 7), C(2, 3), D(0, 7), E(7, 1), and F(0, 6). the points formed a shape. so the order of the coordinates is important in an ordered pair. ### Topic 14 Reteaching Set A pages 565-568 What ordered pair names Point A? Start at the origin. The x-coordinate is the horizontal distance along the x-axis. The y-coordinate is the vertical distance along the y-axis. Point A is at (7, 3). Remember to first find the x-coordinate. Then find the y-coordinate. Write the coordinates in (x, y) order. Use the grid to answer the questions. Question 1. Which point is located at (9, 5)? Answer: Point is located at (9, 5) is R. Explanation: In the above-given question, given that, point is (9, 5). 9 is on the x-axis. 5 is on the y-axis. so the point is located at (9, 5) is R. Question 2. Which point is located at (2, 3)? Answer: Point is located at (2, 3) is K. Explanation: In the above-given question, given that, the point is (2, 3). 2 is on the x-axis. 3 is on the y-axis. so the point is located at (2, 3) is K. Question 3. What ordered pair names Point T ? Answer: Point is located at (3, 4) is T. Explanation: In the above-given question, given that, the point is (3, 4). 3 is on the x-axis. 4 is on the y-axis. so the point is located at (3, 4) is T. Question 4. What is the ordered pair for the origin? Answer: Point is located at (0, 7). Explanation: In the above-given question, given that, the point is (0,7). 0 is on the x-axis. 7 is on the y-axis. so the point is located at (0, 7) is the origin. Set B pages 569-572, 573-576 In the table, the x-coordinate is in the left column and the y-coordinate is in the right column. Use the table to plot the ordered pairs. Then draw a line to connect the points. Remember that you can use a tool, such as a ruler, to draw a line to connect the points on the graph. Question 1. Use the table below to plot the ordered pairs. Then complete the graph by connecting the points. Answer: The points are (2, 1), (4, 2), (6, 3), and (8, 4). Explanation: In the above-given question, given that, the points on the x-axis are 2, 4, 6, and 8. the points on the y-axis are 1, 2, 3, and 4. so the ordered pairs are (2, 1), (4, 2), (6, 3), and (8, 4). Question 2. Write two ordered pairs with x-coordinates greater than 10 that are on the line. Answer: The two ordered pairs are (10, 5), and (12, 6). Explanation: In the above-given question, given that, the points on the x-axis are 2, 4, 6, and 8. the points on the y-axis are 1, 2, 3, and 4. 2 + 2 = 4. 4 + 2 = 6. 6 + 2 = 8. 1 + 1 = 2. 2 + 1 = 3. 3 + 1 = 4. 4 + 1 = 5. so the two ordered pairs are (10, 5), and (12, 6). Set C pages 577-580 Think about these questions to help you use reasoning to solve problems. Thinking Habits • What do the numbers and symbols in the problem mean? • How are the numbers or quantities related? • How can I represent a word problem using pictures, numbers, or equations? Remember that you can use a graph or a table to reason about and solve word problems. A company uses the graph to show how many packages each truck driver delivers. How many packages will one truck driver deliver in a 7-hour day? Question 1. What information can help you solve the problem? Answer: The number of packages each truck driver delivers in hours. Explanation: In the above-given question, given that, the number of packages each truck driver delivers in hours. in 1 hour the number of packages is 15. in 2 hours the number of packages is 30. in 3 hours the number of packages is 45. in 4 hours the number of packages is 60. Question 2. How can you find the number of packages a driver delivers in 3 hours? Answer: The number of packages a driver delivers in 3 hours is 45. Explanation: In the above-given question, given that, the number of packages each truck driver delivers in hours. in 1 hour the number of packages is 15. in 2 hours the number of packages is 30. in 3 hours the number of packages is 45. in 4 hours the number of packages is 60. so the number of packages a driver delivers in 3 hours is 45. Question 3. How many packages will one truck driver deliver in a 7-hour day? Answer: The number of packages will one truck deliver in a 7-hour day is 105. Explanation: In the above-given question, given that, the number of packages each truck driver delivers in hours. in 1 hour the number of packages is 15. in 2 hours the number of packages is 30. in 3 hours the number of packages is 45. in 4 hours the number of packages is 60. in 5 hours the number of packages is 75. in 6 hours the number of packages is 90. in 7 hours the number of packages is 105. Question 4. How can you find how many hours it will take for one truck driver to deliver 120 packages? Answer: The number of hours is 8. Explanation: In the above-given question, given that, the number of packages each truck driver delivers in hours. in 1 hour the number of packages is 15. in 2 hours the number of packages is 30. in 3 hours the number of packages is 45. in 4 hours the number of packages is 60. in 5 hours the number of packages is 75. in 6 hours the number of packages is 90. in 7 hours the number of packages is 105. ### Topic 14 Assessment Practice Use the coordinate grid below to answer 1-4. Question 1. Which is the ordered pair for Point Y? A. (4, 5) B. (4, 9) C. (7, 9) D. (9, 4) Answer: Option B is correct. Explanation: In the above-given question, given that, the point is (4, 9). 4 is on the x-axis. 9 is on the y-axis. so option B is correct. Question 2. Which point is located at (5, 2) on the coordinate grid? A. M B. N C. Q D. P Answer: Option B is correct. Explanation: In the above-given question, given that, the point is (5, 2). 5 is on the x-axis. 2 is on the y-axis. so option B is correct. Question 3. What is the ordered pair for Point Z? Answer: The ordered pair for point Z is (9, 1). Explanation: In the above-given question, given that, the point is (9, 1). 9 is on the x-axis. 1 is on the y-axis. so the ordered pair for point Z is (9, 1). Question 4. What is the ordered pair for Point P? Answer: The ordered pair for point P is (4, 5). Explanation: In the above-given question, given that, the point is (4, 5). 4 is on the x-axis. 5 is on the y-axis. so the ordered pair for point P is (4, 5). Question 5. Each year, Ginny recorded the height of a tree growing in her front yard. The graph below shows her data. What does the point (1, ?) represent? Answer: The point (1, 5) represents the height in feet. Explanation: In the above-given question, given that, Ginny recorded the height of a tree growing in her front yard. the points on the x-axis are 0, 1, 2, 3, and 4. the points on the y-axis are 4, 5, 6, 7, and 8. add the 1 on the x and y-axis. so the point (1, 5) represents the height in feet. Question 6. Explain how to graph the point (6, 4) on a coordinate plane. Answer: Point 6 is on the x-axis and 4 is on the y-axis. Explanation: In the above-given question, given that, the point is (6, 4). point 6 is on the x-axis and 4 is on the y-axis. Question 7. Varsha draws a map of her neighborhood on a coordinate plane. Her map shows the park at P (3, 1), her house at H (5, 6), and the soccer field at S (2,4). Graph and label each location below. Answer: The point is P(3, 1) is the park. the point H(5, 6) is her house. the point S(2, 4) is the soccer field. Explanation: In the above-given question, given that, Varsha draws a map of her neighborhood on a coordinate plane. Her map shows the park at P (3, 1), her house at H (5, 6), and the soccer field at S (2,4). the point is p(3, 1) is the park. the point H(5, 6) is her house. the point S(2, 4) is the soccer field. Question 8. Yesterday Billy earned$30 trimming hedges for Mrs. Gant. Today he will earn $10 an hour for weeding her garden. If he weeds her garden for 8 hours, how much in all will he earn working for Mrs. Gant? A.$40
B. $80 C.$ 110
D. $120 Answer: Option B is correct. Explanation: In the above-given question, given that, Billy earned$30 trimming hedges for Mrs. Gant.
Today he will earn $10 an hour for weeding her garden. If he weeds her garden for 8 hours, 8 x$10 = \$80.
so option B is correct.

Question 9.
How is graphing (0, 12) different from graphing (12, 0)?

(0, 12) is different from (12, 0).

Explanation:
In the above-given question,
given that,
the ordered pairs are (0, 12) and (12, 0).
(0, 12) is on the y-coordinate.
(12, 0) is on the x-coordinate.
so (0, 12) is different from (12, 0).

Question 10.
What ordered pair represents the point where the x-axis and y-axis intersect? What is the name of this point?

The ordered pair (0, 0) represents the point where the x-axis and y-axis intersect.

Explanation:
In the above-given question,
given that,
the ordered pair (0, 0) represents the origin.
the x-axis and y-axis intersect are called the origin.
so the ordered pair (0, 0) represents the point where the x-axis and y-axis intersect.

Question 11.
Three vertices of a rectangle are located at (1, 4), (1, 2), and (5, 2).
A. Graph and label each of the three vertices below. B. What are the coordinates of the fourth vertex of the rectangle?

The coordinates of the fourth vertex of the rectangle are (5, 4).

Explanation:
In the above-given question,
given that,
three vertices of a rectangle are located at (1, 4), (1, 2), and (5, 2).
the other side is (5, 4).
for the rectangle, opposite sides are equal in length.
so the coordinates of the fourth vertex of the rectangle are (5, 4). Digging for Dinosaur Bones
Omar’s mother is a paleontologist. She digs up and studies dinosaur bones. Omar is helping at the dig site.

Question 1.
The Dinosaur Bone Dig 1 grid shows the location of the tent and the triceratops skull Omar’s mother found.
Part A
What ordered pair names the location of the triceratops skull? Explain how you know. Part B
omar found a leg bone at (4, 12). Graph this point on the coordinate grid and label it L. Explain how you located the point using the terms origin, x-coordinate, x-axis, y-coordinate, and y-axis.
Part C
Next, Omar dug 3 meters east and 1 meter south from the leg bone. Graph a point where Omar dug and label it A. What ordered pair names the point?

Part A: (6, 2).
Part B: (4, 12).
Part C: (7, 13).

Explanation:
In the above-given question,
given that,
Omar found a leg bone at (4, 12).
Omar dug 3 meters east and 1 meter south from the leg bone.
4 + 3 = 7.
12 + 1 = 13.
so part C is (7, 13).

Question 2.
Omar’s mother started at the triceratops skull. She kept moving east 1 meter and north 2 meters to dig for more dinosaur bones. Complete the table and the graph to find how far north she was when she was 11 meters east of the tent.

When she was 11 meters east of the tent, the far = 6.

Explanation:
In the above-given question,
given that,
Omar’s mother started at the triceratops skull.
She kept moving east 1 meter and north 2 meters to dig for more dinosaur bones.
(4, 12) is the ordered pair given?
4 + 1 = 5.
12 + 2 = 14.
(5, 14) is the ordered pair.
11 – 5 = 6.
so when was 11 meters east of the tent, the far is 6 meters.
Part A
Complete the table of ordered pairs. Part B
Graph the points from the table in Part A on the coordinate grid in the Dinosaur Bone Dig 2 grid. Draw a line through the points. Extend the line past 11 meters east.
Part C
How far north was Omar’s mother when she was 11 meters east of the tent? Explain how to use the graph to solve and why your answer makes sense. 