Go through the enVision Math Common Core Grade 5 Answer Key Topic 14 Graph Points on the Coordinate Plane regularly and improve your accuracy in solving questions.

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.

Answer:
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) ____.

Answer:
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) ____.

Answer:
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) ___.

Answer:
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

Answer:
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

Answer:
(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

Answer:
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)

Answer:
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

Answer:
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

Answer:
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

Answer:
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

Answer:
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

Answer:
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.

Answer:
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: Make Your Own Game

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

Answer:
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.

Answer:
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?

Answer:
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).

Answer:
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

Answer:
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
Answer:

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

Question 6.
(5, 3)

Answer:
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)

Answer:
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

Answer:
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

Answer:
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

Answer:
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

Answer:
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

Answer:
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

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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.

Answer:
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.

Answer:
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?

Answer:
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?

Answer:
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

Answer:
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!

Answer:
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.

Answer:
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).

Answer:

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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)

Answer:
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)?

Answer:
(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?

Answer:

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.

Answer:
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?

Answer:
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)?

Answer:
(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?

Answer:
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?

Answer:
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).

Topic 14 Performance Task

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?

Answer:
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.

Answer:
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.

Answer:
The ordered pairs are (6, 2), (7, 3), ( 8, 4), and (9, 5).

Explanation:
In the above-given question,
given that,
East of the tent in meters is given.
they are 6, 7, 8, and 9 meters are given.
the first ordered pair is (6, 2) is given.
so the ordered pairs are (7, 3), (8, 4), and (9, 5).
when she was 11 meters east of the tent is (11, 7).

Go through the enVision Math Common Core Grade 3 Answer Key Topic 10 Multiply by Multiples of 10 regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 10 Multiply by Multiples of 10

enVision STEM Project: Animal and Plant Characteristics
Do Research Use the Internet or other sources to find information about how the characteristics of some plants and animals help them survive. Think about how characteristics can be different among members of the same species.
Journal: Write a Report Include what you found. Also in your report:

• Tell about an insect that uses camouflage.
• Describe an example of how a plant’s thorns help it survive.
• Make up and solve multiplication problems about the animals or plants you research. Use multiples of 10.

Review What You Know

Vocabulary

Choose the best term from the box. Write it on the blank.

• multiplication
• factor
• equation
• Zero Property of Multiplication

Question 1.
A number sentence where the value on the left and right of the equal sign (=) is the same is called a(n) ___
Answer:
A number sentence where the value on the left and right of the equal sign (=) is the same is called a(n) = Equation .

Question 2.
The ___ states that any number multiplied by zero has a product of zero.
Answer:
The Zero Property of Multiplication states that any number multiplied by zero has a product of zero.

Question 3.
___ is an operation that gives the total number that results when you join equal groups.
Answer:
Multiplication is an operation that gives the total number that results when you join equal groups.

Multiplication Table

Find the value that makes the equations true. Use the multiplication table to help.
.
21 ÷ 7 = ___
7×__= 21
Answer:
21 ÷ 7 = 3
7× 3= 21

Explanation :
Step 1: Choose the first number from the numbers listed in the left-most column and the second number from the top-most row.
Step 2: Starting from the 3 move towards the right and starting from the 7 move towards down.  The square where the two numbers meet gives the product 21 .

Question 5.
45 ÷ 5 = ___
5 × __ = 45
Answer:
45 ÷ 5 = 9
5 × 9 = 45

Explanation :
Step 1: Choose the first number from the numbers listed in the left-most column and the second number from the top-most row.
Step 2: Starting from the 9 move towards the right and starting from the 5 move towards down.  The square where the two numbers meet gives the product 45 .

Question 6.
48 ÷ 6 = ___
6 × __ = 48
Answer:
48 ÷ 6 = 8
6 × 8 = 48

Explanation :
Step 1: Choose the first number from the numbers listed in the left-most column and the second number from the top-most row.
Step 2: Starting from the 8 move towards the right and starting from the 7 move towards down.  The square where the two numbers meet gives the product 56 .

Question 7.
56 ÷ 8 = ___
8 × __= 56
Answer:
56 ÷ 8 = 7
8 × 7 = 56

Explanation :
Step 1: Choose the first number from the numbers listed in the left-most column and the second number from the top-most row.
Step 2: Starting from the 3 move towards the right and starting from the 7 move towards down.  The square where the two numbers meet gives the product 21 .

Multiplication Properties

Find each product.

Question 8.
3 × 3 × 2 =___
Answer:
3 × 3 × 2 = 9 × 2 = 18

Question 9.
5 × 1 × 3 = ___
Answer:
5 × 1 × 3 = 5 × 3 = 15

Question 10.
4 × 2 × 4 = ___
Answer:
4 × 2 × 4 = 8 × 4 = 24

Question 11.
2 × 2 × 4 = ___
Answer:
2 × 2 × 4 =4 × 4 = 16

Question 12.
4 × 0 × 2 = ___
Answer:
4 × 0 × 2 = 0 × 2 =0

Question 13.
2 × 5 × 3 = ___
Answer:
2 × 5 × 3 = 10 × 3 =30

Multiplication on the Number Line

Question 14.
Which equation does the number line show?

A. 1 × 10 = 10
B. 3 × 10 × 1 = 30
C. 4 × 5 = 20
D. 5 × 10 = 50
Answer :
Option D. 5 × 10 = 50
Explanation:
Each jump represents + 10 .
Number of jumps made = 5
so, 5 × 10 = 50 .
from 0 to 50 the equation is represented .

Pick a Project

PROJECT 10A
What do you need to do to plan a trip?
Project: Research the Distance Between Two Cities

PROJECT 10B
How do stores make sure they have enough of an item to sell?
Project: Create Your Own Store

PROJECT 10C
How do trees help our environment?
Project: Design a Park and Sing a Song

PROJECT 10D
How many items can you fit in a box?
Project: Make a Product Game

Lesson 10.1 Use Patterns to Multiply

Activity

Solve & Share

Companies package their goods in a variety of ways. One company packages a case of water as 2 rows of 10 bottles. How many bottles are in each of the cases shown in the table below? Explain your thinking.

You can use appropriate tools. Place-value blocks or a number line can help you apply the math you know.

Look Back! How can place-value patterns help you when multiplying by 20?
Answer :
Number of bottles in 1 case = 2 rows of 10 bottles = 2 × 10 = 20 bottles .

Explanation :
Number of bottles in 1 case =  1 jump of 20 is 20. 1 × 20 = 20
Number of bottles in 2 case =  2 jumps of 20 are 40. 2 × 20 = 40
Number of bottles in 3 case =  3 jumps of 20 are 60. 3 × 20 = 60
Number of bottles in 4 case =  4 jumps of 20 are 80. 4 × 20 = 80

Visual Learning Bridge

Glossary

Essential Question
How Can You Use Patterns to Multiply?

A.
A half-century is a period of 50 years. Find the number of years in 5 half-centuries.

You can use place-value blocks or an open number line to multiply.

B.
One Way
Find 5 × 50. Use place-value blocks.

1 × 50 is 1 group of 5 tens = 5 tens or 50
2 × 50 is 2 groups of 5 tens = 10 tens or 100
3 × 50 is 3 groups of 5 tens = 15 tens or 150
4 × 50 is 4 groups of 5 tens = 20 tens or 200
5 × 50 is 5 groups of 5 tens = 25 tens or 250
You can skip count to find the number of years in 5 half-centuries.

There are 250 years in 5 half-centuries.

C.
Another Way
Find 5 × 50. Use an open number line.

1 jump of 50 is 50. 1 × 50 = 50
2 jumps of 50 are 100. 2 × 50 = 100
3 jumps of 50 are 150. 3 × 50 = 150
4 jumps of 50 are 200. 4 × 50 = 200
5 jumps of 50 are 250. 5 × 50 = 250
There are place-value patterns when multiplying by multiples of 10.

There are 250 years in 5 half-centuries.

Convince Me! Use Structure Suppose the multiple of 10 in the table above was 40 years instead of 50. Explain how you can use place-value patterns to find each product.
Answer :
Find 5 × 50. Use place-value blocks.

1 × 40 is 1 group of 4 tens = 4 tens or 40
2 × 40 is 2 groups of 4 tens = 80 tens or 80
3 × 40 is 3 groups of 4 tens = 12 tens or 120
4 × 40 is 4 groups of 4 tens = 16 tens or 160
5 × 40 is 5 groups of 4 tens = 20 tens or 200
There are 200 years in 5 half-centuries.

Guided Practice

Do You Understand?

Question 1.
Explain how to use place-value patterns to multiply 9 × 50.
Answer:

1 jump of 50 is 50. 1 × 50 = 50
2 jumps of 50 are 100. 2 × 50 = 100
3 jumps of 50 are 150. 3 × 50 = 150
4 jumps of 50 are 200. 4 × 50 = 200
5 jumps of 50 are 250. 5 × 50 = 250
6 jumps of 50 are 250. 6 × 50 = 300
7 jumps of 50 are 350. 7 × 50 = 350
8 jumps of 50 are 400. 8 × 50 = 400
9 jumps of 50 are 450. 9 × 50 = 450
There are place-value patterns when multiplying by multiples of 10.

Question 2.
How are the products in Box B on the previous page like skip counting by 5?
Answer:

Do You Know How?

Question 3.
Draw or use place-value blocks to show 3 × 60. Then find the product.
Answer:

1 × 60 is 1 group of 6 tens = 6 tens or 60
2 × 60 is 2 groups of 6 tens = 12 tens or 120
3 × 60 is 3 groups of 6 tens = 18 tens or 180
This are place value blocks of 3 × 60 = 180 .

Question 4.
Use the open number line to multiply 4 × 60.

Answer:

1 jump of 60 is 60. 1 × 60 = 60
2 jumps of 60 are 120. 2 × 60 = 120
3 jumps of 60 are 180. 3 × 60 = 180
4 jumps of 60 are 240. 4 × 60 = 240

Independent Practice

Leveled Practice In 5-10, use an open number line or draw place-value blocks to find each product.

Question 5.
3 × 70

Answer:

1 jump of 70 is 70. 1 × 70 = 70
2 jumps of 70 are 140. 2 × 70 = 140
3 jumps of 70 are 210. 3 × 70 = 210
4 jumps of 70 are 280. 4 × 70 = 280

Question 6.
8 × 20

Answer:

1 × 20 is 1 group of 2 tens = 2 tens or 20
2 × 20 is 2 groups of 2 tens = 4 tens or 40
3 × 20 is 3 groups of 2 tens = 6 tens or 60
4 × 20 is 4 groups of 2 tens = 8 tens or 80
5 × 20 is 5 groups of 2 tens =  10 tens or 100
6 × 20 is 6 groups of 2 tens = 12 tens or 120
7 × 20 is 7 groups of 2 tens = 14 tens or 140
8 × 20 is 8 groups of 2 tens =  16 tens or 160
This are place value blocks of 8 × 20 = 160 .

Question 7.
9 × 30
Answer:

1 jump of 30 is 30. 1 × 30 = 30
2 jumps of 30 are 90. 2 × 30 = 90
3 jumps of 30 are 120. 3 × 30 = 120
4 jumps of 30 are 120. 4 × 30 = 120
5 jumps of 30 are 150. 5 × 30 = 150
6 jumps of 30 are 180. 6 × 30 = 180
7 jumps of 30 are 210. 7 × 30 = 210
8 jumps of 30 are 240. 8 × 30 = 240
9 jumps of 30 are 270. 9 × 30 = 270
There are place-value patterns when multiplying by multiples of 10.

Question 8.
5 × 60
Answer:

1 jump of 60 is 60. 1 × 60 = 60
2 jumps of 60 are 120. 2 × 60 = 120
3 jumps of 60 are 180. 3 × 60 = 180
4 jumps of 60 are 240. 4 × 60 = 240
5 jumps of 60 are 300. 5 × 60 = 300

Question 9.
6 × 60
Answer:

1 jump of 60 is 60. 1 × 60 = 60
2 jumps of 60 are 120. 2 × 60 = 120
3 jumps of 60 are 180. 3 × 60 = 180
4 jumps of 60 are 240. 4 × 60 = 240
5 jumps of 60 are 300. 5 × 60 = 300
6 jumps of 60 are 360. 6 × 60 = 360

Question 10.
2 × 30
Answer:

1 jump of 30 is 30. 1 × 30 = 30
2 jumps of 30 are 90. 2 × 30 = 60
There are place-value patterns when multiplying by multiples of 10.

Problem Solving

Question 11.
The Aztecs had a solar calendar. How many days are in 7 of the longer months in all? Show how to use place value to solve.

Answer:

Question 12.
Higher Order Thinking On one open number line, show 4 × 30. On the other open number line, show 3 × 40. How are the problems alike? How are they different?

Answer:

1 jump of 30 is 30. 1 × 30 = 30
2 jumps of 30 are 90. 2 × 30 = 60
3 jump of 30 is 30. 3 × 30 = 90
4 jumps of 30 are 120. 4 × 30 = 120 .

1 jump of 40 is 40. 1 × 40 = 40
2 jumps of 40 are 80. 2 × 40 = 80
3 jumps of 40 are 120. 3 × 40 = 120
jump of both number lines are different but the product is same .

Question 13.
Reasoning Martina has $504. She spends $199 on new computer software. Use mental math to find how much money Martina has left.
Answer:
Total Money with Martina = $504 .
Cost of New computer software = $199 .
Money left with Martina = $504 – $199 = 500 + 4 – (200 – 1) = 300 + 5 = 305$ .

Question 14.
Use place-value blocks to find 1 × 40, 2 × 40,3 × 40, and 4 × 40. What is the same in each of the products you listed?
Answer:

1 × 40 is 1 group of 4 tens = 4 tens or 40
2 × 40 is 2 groups of 4 tens = 80 tens or 80
3 × 40 is 3 groups of 4 tens = 12 tens or 120
4 × 40 is 4 groups of 4 tens = 16 tens or 160
All products end with 0 and all are even numbers .

Question 15.
A package of crepe paper streamers has 2 rolls. Yen bought 3 packages. How many inches of crepe paper did Yen get?

Answer:
Number of rolls in each package = 2
Number of packages = 3
Number of inches of crepe paper in 3 = 3 × 2 = 6 rolls .

Assessment Practice

Question 16.
Select all the expressions that have a product of 300.
3 × 10
5 × 60
5 × 600
6 × 50
6 × 500
Answer:

Explanation :
3 × 10 = 30
5 × 60 = 300
5 × 600 = 3000
6 × 50 = 300
6 × 500 = 3000

Question 17.
Select all the expressions that have a product of 240.
3 × 80
4 × 60
6 × 40
8 × 30
9 × 30
Answer:

Explanation :
3 × 80 = 240
4 × 60 = 240
6 × 40 = 240
8 × 30 = 240
9 × 30 = 270

Lesson 10.2 Use Mental Math to Multiply

Activity

Solve & Share

Find the products of 4 × 50, 3 × 40, and 9 × 20. Describe the patterns you find.

You can look for relationships. Think about how place-value patterns can help you solve the problems.

Look Back! How can you use place value to describe the patterns in the products?
Answer :

Visual Learning Bridge

Essential Question
How Can Place Value Help You Use Mental Math to Multiply by a Multiple of 10?

A.
A regular box of crayons has 30 crayons. A jumbo box holds 60 crayons. There are 5 boxes of regular crayons on one shelf and 5 boxes of jumbo crayons on another shelf. How many crayons are on each shelf?

You can use basic multiplication facts to multiply by multiples of 10.

B.
Find 5 × 30.

Think about tens. Multiply 5 by the number of tens.
5 × 30 = 5 × 3 tens
5 × 30 = 15 tens
5 × 30 = 150
There are 150 crayons on one shelf.

C.
Find 5 × 60.

Sometimes the basic multiplication fact makes the product look different.
5 × 60 = 5 × 6 tens
5 × 60 = 30 tens
5 × 60 = 300
There are 300 crayons on the other shelf.

Convince Me! Make Sense and Persevere Suppose there are 50 crayons in each of the 5 boxes. Use mental math to find 5 × 50. How many crayons are in 5 boxes?
Answer :
Number of crayons in each box = 50
Number of boxes = 5
Number of crayons in 5 boxes = 5 × 50
5 × 50 = 5 × 5 tens
5 × 50 = 25 tens
5 × 50 = 250 crayons.
Therefore, Number of crayons in 5 boxes = 250 crayons .

Guided Practice

Do You Understand?

Question 1.
How can you find the product of 9 × 80? explain.
Answer:

Question 2.
Jon says, “4 × 6 is 4 groups of 6 ones. 4 times 6 equals 24.”
Complete the sentences to describe 4 × 60 in a similar way.
4 × 60 is 4 groups of 6 ___
4 times 60 equals ___
Answer:
4 × 60 is 4 groups of 6 = 4 × 6 = 24 .
4 times 60 equals = 4 × 60 = 240 .

Do You Know How?

In 3-8, complete each equation.

Question 3.
6 × 6 = ___
6 × 60 = ___
Answer:
6 × 6 = 36
6 × 60 =36 tens  = 360 .

Question 4.
3 × 2 = ___
3 × 20 = ___
Answer:
3 × 2 = 6
3 × 20 = 60 = 6 tens

Question 5.
5 × 4 = ___
5 × 40 = ___
Answer:
5 × 4 = 20
5 × 40 = 20 tens = 200 .

Question 6.
8 × 2 = ___
80 × 2 = ___
Answer:
8 × 2 = 16
80 × 2 = 16 tens = 160 .

Question 7.
4 × 9 = ___
40 × 9 = ___
Answer:
4 × 9 = 36
40 × 9 = 36 tens = 360 .

Question 8.
7 × 8 = ___
70 × 8 = ___
Answer:
7 × 8 = 56
70 × 8 =56 tens = 560 .

Independent Practice

Leveled Practice In 9-19, complete each equation.

Question 9.
6 × 70 = (6 × __ ) tens
6 × 70 = __ tens
6 × 70 = __
Answer:
6 × 70 = (6 × 7 ) tens
6 × 70 = 42 tens
6 × 70 = 420

Question 10.
9 × 50 = (9 × __) tens
9 × 50 = __ tens
9 × 50 = ___
Answer:
9 × 50 = (9 × 5 ) tens
9 × 50 = 45 tens
9 × 50 = 450

Question 11.
2 × 6 = ___
2 × 60 = __
Answer:
2 × 6 = 12
2 × 60 = 12 tens
2 × 60 = 120

Question 12.
5 × 8 = ___
5 × 80 = __
Answer:
5 × 8 = 40
5 × 80 = 40 tens
5 × 80 = 400

Question 13.
9 × 4 = ___
9 × 40 = ___
Answer:
9 × 4 = 36
9 × 40 = 36 tens
9 × 40 = 360

Question 14.
2 × 30 = ___
Answer:
2 × 3 = 6
2 × 30 = 6 tens
2 × 30 = 60

Question 15.
60 × 9 = ___
Answer:
6 × 9 = 54
60 × 9 = 54 tens
60 × 9 = 540

Question 16.
___ = 8 × 20
Answer:
8 × 2 = 16
8 × 20 = 16 tens
8 × 20 = 160

Question 17.
80 × 5 = ___
Answer:
8 × 5 = 40
80 × 5 = 40 tens
80 × 5 = 400

Question 18.
___ = 90 × 2
Answer:
9 × 2 = 18
90 × 2 = 18 tens
90 × 2 = 180

Question 19.
30 × 4 = ___
Answer:
3 × 4 = 12
30 × 4 = 12 tens
30 × 4 = 120 .

Problem Solving

Question 20.
The horse conch can reach a length of 24 inches. Use multiplication to write 2 different equations that represent the conch’s length.

Answer:
Length of the horse conch = 24 inches .
The two different equations that represent length of horse conch =
24 =  6 × 4
24 = 3 × 8

Question 21.
Model with Math Juanita buys 7 sheets of postage stamps at the post office. Each sheet has 20 stamps. How many stamps does she buy in all? Explain how you solved the problem. Tell why you chose that method.
Answer:
Number of sheets of postage stamps = 7
Number of postage stamps for each sheet = 20 .
Number of postage stamps for 7 sheets = 7 × 20
7 × 2 = 14
7 × 20 = 4 tens
7 × 20 = 140 .
Therefore, Number of postage stamps for 7 sheets = 140 stamps .
This method is chosen because where 7 × 2 = 14 is the simply calculation steps are used to calculate the products .

Question 22.
Algebra What value makes the equation below true?
9 × ? = 630
Answer:
9 × ? = 630
9 × ? = 63 Tens
9 × 7 = 63
9 × 70 = 630

Question 23.
Janet bought 137 green beads. Now she has 349 beads. How many beads did Janet have before?
Answer:
Number of green beads = 137 .
Number of beads now = 349 .
Number of beads Janet have before = 349 – 137 = 212 beads .
Therefore, Number of beads Janet have before = 212 beads

Question 24.
Higher Order Thinking Ali and his family are going to the amusement park. If there are 2 adults and 5 children, how much will the tickets cost?

Answer:
Ticket cost for adult = $30 .
Number of Adults = 2
Tickets cost for adults = 2 × $30 = $60 .
Ticket cost for child = $20 .
Number of children = 5
Tickets cost for children’s = 5 × $20 = $100 .
Total Tickets cost = $60 + $ 100 = $160 .

Assessment Practice

Question 25.
Mr. Ridley owns a clothing store. The table at the right shows the number of racks and the number of pieces of clothing on each rack. Match each equation with its product to find the number of pieces of each type of clothing that are on the racks.

Answer:

2 × 60 = 120 .
3 × 40 = 120 .
4 × 20 = 80 .
2 × 40 = 80 .

Lesson 10.3 Use Properties to Multiply

Activity

Solve & Share

Three students found 5 × 30 in different ways. Which student is correct? Explain.

Properties can help you critique reasoning.

Look Back! What property of multiplication did Earl use in his reasoning?
Answer :
Property used is Associative property
Associative property :
For all real numbers a, b and c .
(a⋅b)⋅c=a⋅(b⋅c)

$\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right)$

When you multiply any three real numbers, the grouping (or association) of the numbers does not change the result.

Visual Learning Bridge

Essential Question
How Can You Use Properties to Multiply by Multiples of 10?

A.
How can you find the product of 4 × 20?

Remember the 10s facts pattern. Think about the product of a number and 10. The product has a zero in the ones place. The other factor is written to the left of the zero.

You know how to use an open number line to model multiplication.
You can use properties to explain a rule for finding a product when one factor is a multiple of 10.

B.
One Way
You can use the Associative Property of Multiplication to group the factors.

Think of 20 as 2 × 10
4 × 20 = 4 × (2 × 10)
4 × 20 = (4 × 2) × 10
4 × 20 = 8 × 10
4 × 20 = 80

C.
Another Way
You can use the Distributive Property to decompose a factor.
4 × 20 = (2 + 2) × 20
4 × 20 = (2 × 20) + (2 × 20)
4 × 20 = 40 + 40
4 × 20 = 80

Convince Me! Be Precise Use properties of multiplication to explain why 3 × 60 = 18 × 10.
Answer :
3 × 60 =
You can use the Associative Property of Multiplication to group the factors.
Think of 60 as 6 × 10
3 × 60 = 3 × (6 × 10)
3 × 60 = (3 × 6) × 10
3 × 60 = 18 × 10
3 × 60 = 180
3 × 60 = 18 × 10 = 180 .

Guided Practice

Do You Understand?

Question 1.
Why can you say that 3 × 20 = (2 × 20) + 20?
Answer:
Yes, 3 × 20 = (2 × 20) + 20 because
3 × 20 = 20 + 20 + 20 = (2 × 20 )+ 20 .

Question 2.
Why can you say that 3 × 20 = (3 × 2) × 10?
Answer:
3 × 20 =
You can use the Distributive Property to decompose a factor.
20 = 2 × 10
so , 3 × 20 = (3 × 2) × 10 = 6 × 10 = 60 .

Do You Know How?

In 3 and 4, find each product using properties of multiplication.

Question 3.
9 × 60 = 9 × (__ × 10)
9 × 60 = (9 × __) × 10
9 × 60 = ___ × 10 = ___
Answer:
You can use the Associative Property of Multiplication to group the factors.
9 × 60 = 9 × ( 6 × 10)
9 × 60 = (9 × 6) × 10
9 × 60 = 54 × 10 = 540

Question 4.
4 × 90 = (___ + 2) × 90
4 × 90 = (__ × 90) + ( ___ × 90)
4 × 90 = ___ + __ = ___
Answer:
You can use the Distributive Property to decompose a factor.
4 × 90 = (2 + 2) × 90
4 × 90 = (2 × 90) + ( 2 × 90)
4 × 90 = 180 + 180 = 360 .

Independent Practice

Leveled Practice In 5-12, show how to find each product using properties of multiplication.

Question 5.
7 × 60 = 7 × (___ × 10)
7 × 60 = (7 × __ ) × 10
7 × 60 = __ × 10 = ___
Answer:
You can use the Associative Property of Multiplication to group the factors
7 × 60 = 7 × ( 6 × 10)
7 × 60 = (7 × 6 ) × 10
7 × 60 = 42 × 10 = 420

Question 6.
5 × 40 = __ × (__ × 10)
5 × 40 = (__ × __) × 10
5 × 40 = ___ × ___ = __
Answer:
You can use the Associative Property of Multiplication to group the factors
5 × 40 = 5 × ( 4 × 10)
5 × 40 = (5 × 4) × 10
5 × 40 = 20 × 10 = 200

Question 7.
8 × 30
Answer:
8 × 30 = 8 × ( 3 × 10)
8 × 30 = (8 × 3) × 10
8 × 30 = 24 × 10 = 240

Question 8.
4 × 70
Answer:
You can use the Distributive Property to decompose a factor.
4 × 70 = (2 + 2) × 70
4 × 70 = (2 × 70) + ( 2 × 70)
4 × 70 = 140 + 140 = 280 .

Question 9.
5 × 90
Answer:
You can use the Associative Property of Multiplication to group the factors
5 × 90 = 5 × ( 9 × 10)
5 × 90 = (5 × 9) × 10
5 × 90 = 45 × 10 = 450

Question 10.
8 × 80
Answer:
You can use the Distributive Property to decompose a factor.
8 × 80 = (4 + 4) × 80
8 × 80 = (4 × 80) + ( 4 × 80)
8 × 80 = 320 + 320 = 640 .

Question 11.
6 × 40
Answer:
You can use the Associative Property of Multiplication to group the factors
6 × 40 = 6 × ( 4 × 10)
6 × 40 = (6 × 4) × 10
6 × 40 = 24 × 10 = 240 .

Question 12.
9 × 80
Answer:
You can use the Associative Property of Multiplication to group the factors
9 × 80 = 9 × ( 8 × 10)
9 × 80 = (9 × 8) × 10
9 × 80 = 72 × 10 = 720 .

Problem Solving

Question 13.
Look at the picture graph at the right. How many pounds of newspaper did Grade 3 collect?

Answer:
Each rectangle represents 30 pounds .
Number of pounds of newspaper in Grade 3 = 4 rectangles = 4 × 30 = 120 pounds .

Question 14.
How many pounds of newspaper did Grade 3 and Grade 4 collect together? Explain your plan for solving.
Answer:
Each rectangle represents 30 pounds .
Number of pounds of newspaper in Grade 3 = 4 rectangles = 4 × 30 = 120 pounds .
Number of pounds of newspaper in Grade 4 = 3 rectangles = 3 × 30 = 90 pounds .
Total pounds of newspaper did Grade 3 and Grade 4 collect together = 120 + 90 = 210 pounds .

Question 15.
Higher Order Thinking Grade 5 collected 150 pounds of newspaper. How many more symbols would be in the row for Grade 5 than for Grade 2?
Answer:
Number of pounds of newspapers Grade 5 collected = 150 pounds .
Each rectangle represents 30 pounds .
Number of rectangles symbol in grade 5 = 150 pounds ÷ 30 = 5 rectangles .
Number of rectangles in grade 2 = 2 rectangles.
Number of more symbols would be in the row for Grade 5 than for Grade 2 = 5 – 2 = 3 more symbols .

Question 16.
Generalize Without finding the products, how can you tell whether 4 × 60 or 7 × 40 is greater?
Answer:
4 × 60 or 7 × 40 is greater 7 × 40 .
4 × 60 = 4 × 6 × 10 .
7 × 40 = 4 × 7 × 10 .
we notice 4 × 10 is common so, greater than number greater the product. we notice 7 is greater than 6 so , 7 × 40 = 280 is greater than 4 × 60

Question 17.
Explain how to use mental math to add 521 + 104.
Answer:
521 + 104 = 625 .
add ones values numbers 1 + 4 = 5 .
add tens value numbers = 2 + 0 = 2
Add hundred value numbers = 5 + 1 = 6
so, the sum = 625 .

Question 18.
Tikie said that it is easy to count by 50s. Explain how she could use counting by 50s to find 5 × 60.
You can use properties and equations to help construct an argument!

Answer:
You can use the Associative Property of Multiplication to group the factors
5 × 60 = 5 × ( 6 × 10)
5 × 60 = (5 × 6) × 10
5 × 60 = 30 × 10 = 300 .

Assessment Practice

Question 19.
Which products are equal to 180? Select all that apply.
1 × 80
6× (3 × 10)
6× 30
3 × (6 × 10)
3 × 60
Answer:

Explanation :
1 × 80 =80
6× (3 × 10) = 180
6× 30 = 180
3 × (6 × 10) = 180
3 × 60 = 180

Question 20.
Which products are equal to 200? Select all that apply.
2 × 10
5 × (4 × 10)
5 × 40
2 × (1 × 10)
4 × 50
Answer:

Explanation :
2 × 10 = 20
5 × (4 × 10) = 200
5 × 40 = 200
2 × (1 × 10) = 20
4 × 50 = 200

Lesson 10.4 Look For and Use Structure

Problem Solving

Activity

Solve & Share

Stefan says that he could use this multiplication table to help multiply 3 × 40 to get 120. Explain Stefan’s strategy.

Thinking Habits
Be a good thinker! These questions can help you.
• What patterns can I see and describe?
• How can I use the patterns to solve the problem?
• Can I see expressions and objects in different ways?

Answer :
3 × 40 = 120 .

Explanation :
Reading a multiplication chart
Step 1: Choose the first number 3 from the numbers listed in the left-most column and the second number 40 from the top-most row.
Step 2: Starting from the first number 3 move towards the right and starting from the second number 40 move towards down.  The square where the two numbers meet gives the product 120 !

The multiplication tables of 1, 2, 5, and 10 are easier to remember as they follow a pattern. The product of any number with 1 is the number itself whereas the product of any number with 2 is double the number. The ones digits of the multiplication table of 5 alternates between 0 and 5 and it is easy to remember the table of 10 as well because the digit at the ones place is always zero. These parts of the multiplication chart which are easy to remember are called lower times table.

One important property of multiplication is that the order in which you multiply any two numbers does not affect the product.
So, in a multiplication chart, for any product, you can find the identical number with the numbers reversed in the statement.

Look Back! Use Structure Could Stefan also use the multiplication table to solve 4 × 40 in the same way? explain how you decided.
Answer :
Yes, it is explained in the same way .
4 × 40 = 160 .

Explanation :
Reading a multiplication chart
Step 1: Choose the first number 4 from the numbers listed in the left-most column and the second number 40 from the top-most row.
Step 2: Starting from the first number 4 move towards the right and starting from the second number 40 move towards down.  The square where the two numbers meet gives the product 160 !

Visual Learning Bridge

Essential Question
How Can I Use Structure to Multiply with Multiples of 10?

A.
Find the missing products in the multiplication table.

You can look for relationships in the multiplication table.

B.
How can I make use of structure to solve this problem?
I can
• look for patterns to help solve a problem.
• describe the patterns that i find.
• identify how numbers are organized.

C.
Here’s my thinking

As I move down the columns, the numbers increase by the value of the column.
As I move across the rows, the numbers increase by the value in the column where 10 is a factor.
I used patterns I know for multiplying by multiples of 10.

Convince Me! Use Structure The ones digit never changes in the products in the multiplication table above. Explain why.

Guided Practice
Use Structure Sean is making muffins. He is choosing to make either 7 or 8 batches. He is also choosing whether to use 40, 50, 60, or 70 raisins for each batch. Sean starts this table to show the total number of raisins he will need for each choice.

You can use the structure of the products and factors to find a pattern.

Question 1.
Find the missing products in the table to show how many raisins Sean will use for each batch. Think about patterns or properties you know.

Answer:

Explanation :
As I move down the columns, the numbers increase by the value of the column that is 40, 50, 60 and 70 respectively .
As I move across the rows, the numbers increase by the value in the column where 10 is a factor.

Question 2.
Sean uses 480 raisins in total. How many batches does he make? How many raisins does he use for each batch?
Answer:

Explanation :
Total Raisins used = 480
The column represents the number of batches that is 8 .
The Row represents the number of raisins in each batch = 60 raisins.
8 × 60 = 480 .

Independent Practice

Use Structure
Jolene is making a display with equal rows of stickers. She is choosing whether to use 20, 30, 40, or 50 stickers in each row. She is also choosing whether to have 2, 3, or 4 rows. Jolene starts this table to show the total number of stickers she will need for each choice.

Question 3.
Find the missing products in the table to show how many stickers Jolene will need for each choice. Think about patterns or properties you know.

Answer:

Explanation :
As I move down the columns, the numbers increase by the value of the column that is 20, 30, 40 and 50 respectively .
As I move across the rows, the numbers increase by the value in the column where 10 is a factor.

Question 4.
Jolene uses 150 stickers in total. How many rows does she have in her display? How many stickers does she put in each row?
Answer:

Explanation :
Number of stickers used = 150 .
Number of rows used represents the row value that is 3 .
Number of stickers in each row represents the column value that is 50 .
3 × 50 = 150 stickers .

Problem Solving

Performance Task

Music Lessons
Four students each took music lessons for different instruments this month. They want to know who spent the most money on music lessons.

Question 5.
Make Sense and Persevere What do you need to do to solve the problem?
Answer:
To calculate the  problem we need .
Price paid for 1 lesson  and Number of lessons .
Total cost = Price paid for 1 lesson × Number of lessons .
June = 60 × 4 = 240 dollars
Li = 20 × 8 = 160 dollars .
Mick = 10 × 9 = 90 dollars .
Rita = 40 × 7 = 280 dollars

Question 6.
Use Structure How can you find the total amount for each student? Think about properties or patterns you know.
Answer:

Think about and look for relationships to help solve problems.

Answer  :

Explanation :
To calculate the  problem we need .
Price paid for 1 lesson  and Number of lessons .
Total cost = Price paid for 1 lesson × Number of lessons .
June = 60 × 4 = 240 dollars
Li = 20 × 8 = 160 dollars .
Mick = 10 × 9 = 90 dollars .
Rita = 40 × 7 = 280 dollars

Question 7.
Model with Math Use math you know to complete the table. Circle the name of the student who spent the greatest amount.
Answer:

Explanation :
Total cost = Price paid for 1 lesson × Number of lessons .
June = 60 × 4 = 240 dollars
Li = 20 × 8 = 160 dollars .
Mick = 10 × 9 = 90 dollars .
Rita = 40 × 7 = 280 dollars
Among all Rita spends more money than all .
280 > 240 >160 > 90 .

Question 8.
Construct Arguments Did the student who spent the most per lesson also spend the greatest amount in total? explain why or why not.
Answer:
No, the student who spent the most per lesson did not spend the greatest amount in total because the student attends only 4 classes .
The Student spend the greatest amount in total attends 7 classes for 40 dollars for each class spends 280 dollars in total .
That means it depends on number of classes and cost of each class

Topic 10 Fluency Practice Activity

Shade a path from START to FINISH. Follow the sums or differences that are correct. You can only move up, down, right, or left.

Answer :

Topic 10 Vocabulary Review

Glossary

Understand Vocabulary

Word List
• Associative Property of Multiplication
• Distributive Property
• equal groups
• factor
• open number line
• product
• skip count

Question 1.
Skip count by 20s. Cross out any numbers that you do NOT say
when skip counting by 20s.
20 30 40 50 90
Answer:

Question 2.
Cross out any equations below in which 10 is NOT a factor.
3 × 10 = 30 10 = 5 × 2 50 = 10 × 5 10 × 0 = 0
Answer:

Explanation :
10 is the sum of factors 5 and 2 . so it doesn’t have 10 factor .

Question 3.
Cross out any equations below that do NOT show the Associative Property of Multiplication.
(4 × 6) × 7 = 4 (6 × 7) 4 × 3 = 3 × 4 0 = 2 × 0
Answer:

Explanation :
Associative property :
For all real numbers a, b and c .
(a⋅b)⋅c=a⋅(b⋅c)

$\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right)$

When you multiply any three real numbers, the grouping (or association) of the numbers does not change the result.

Question 4.
Cross out any equations below in which 8 is NOT the product.
8 = 2 × 4 8 × 8 = 64 2 × (4 × 1) = 8 2 × 8 = 16
Answer:

Write T for true or F for false.

____
Question 5.
An example of the Distributive Property is 6 × 0 = 0.
Answer:
False .
Explanation :
1.Simplify the numbers. In this example, 101 = 100 + 1, so . . . . . .
2.Split the problem into two easier problems. Take the number outside the parentheses, and multiply it by each number inside the parentheses, one at a time.
3.Add the products.

Question 6.
Equal groups have the same amount in each group.
Answer:
True.

Question 7.
An open number line is a plain line that can be used to help you multiply.
Answer:
True .
Explanation :
Multiplying on the number line works no matter what number you count off by.
For example, the number line in the following figure counts off by 5s. This time, the only numbers marked are the multiples of 5, so you can use this number line to multiply any number by 5.

Use Vocabulary in Writing

Question 8.
Use at least 2 terms from the Word List to explain how to solve 3 × 30.
Answer:
Distributive property
open number line .

Topic 10 Reteaching

Set A
pages 381-384

Find 5 × 70.
Show 5 jumps of 70 on the number line.

1 jump of 70 is 70. 1 × 70 = 70
2 jumps of 70 are 140. 2 × 70 = 140
3 jumps of 70 are 210. 3 × 70 = 210
4 jumps of 70 are 280. 4 × 70 = 280
5 jumps of 70 are 350. 5 × 70 = 350
There are place-value patterns when multiplying by 10.

Remember that you can skip count to show multiplication.

In 1-3, use an open number line to solve.

Question 1.
4 × 80

Answer:

Explanation:
1 jump of 80 is 80. 1 × 80 = 80
2 jumps of 80 are 160. 2 × 80 = 160
3 jumps of 80 are 240. 3 × 80 = 240
4 jumps of 80 are 320. 4 × 80 = 320
There are place-value patterns when multiplying by 10.

Question 2.
7 × 20

Answer:

Explanation :
1 jump of 20 is 20. 1 × 20 = 20
2 jumps of 20 are 40. 2 × 20 = 40
3 jumps of 20 are 60. 3 × 20 = 60
4 jumps of 20 are 80. 4 × 20 = 80
5 jumps of 20 are 100. 5 × 20 = 100
6 jumps of 20 are 120. 5 × 20 = 120
7 jumps of 20 are 140. 5 × 20 = 140
There are place-value patterns when multiplying by 10.

Question 3.
3 × 50

Answer:

Explanation :
1 jump of 50 is 50. 1 × 50 = 50
2 jumps of 50 are 100. 2 × 50 = 100
3 jumps of 50 are 150. 3 × 50 = 150
here are place-value patterns when multiplying by 10.

Set B
pages 385-388
You can use basic multiplication facts to multiply by multiples of 10.
Find 6 × 30
Multiply the number of tens by 6.
6 × 30 = 6 × 3 tens
6 × 30 = 18 tens
6 × 30 = 180

Place-value patterns can help you learn a shortcut!

Remember to think about basic facts.

In 1-10, find each product.

Question 1.
3 × 30
Answer:
You can use basic multiplication facts to multiply by multiples of 10.
3 × 30
Multiply the number of tens by 3.
3 × 30 = 3 × 3 tens
3 × 30 = 9 tens
3 × 30 = 90

Question 2.
50 × 9
Answer:
You can use basic multiplication facts to multiply by multiples of 10.
9 × 50
Multiply the number of tens by 9.
9 × 50 = 9 × 5 tens
9 × 50 = 45 tens
9 × 50 = 450

Question 3.
6 × 60
Answer:
You can use basic multiplication facts to multiply by multiples of 10.
6 × 60
Multiply the number of tens by 6.
6 × 60 = 6 × 6 tens
6 × 60 = 36 tens
6 × 60 = 360

Question 4.
5 × 80
Answer:
You can use basic multiplication facts to multiply by multiples of 10.
5 × 80
Multiply the number of tens by 5.
5 × 80 = 5 × 8 tens
5 × 80 = 40 tens
5 × 80 = 400

Question 5.
8 × 40
Answer:
You can use basic multiplication facts to multiply by multiples of 10.
8 × 40
Multiply the number of tens by 8.
8 × 40 = 8 × 4 tens
8 × 40 = 32 tens
8 × 40 = 320

Question 6.
80 × 7
Answer:
You can use basic multiplication facts to multiply by multiples of 10.
7 × 80
Multiply the number of tens by 7.
7 × 80 = 7 × 8 tens
7 × 80 = 56 tens
7 × 80 = 560

Question 7.
70 × 4
Answer:
You can use basic multiplication facts to multiply by multiples of 10.
4 × 70
Multiply the number of tens by 4.
4 × 70 = 4 × 7 tens
4 × 70 = 28 tens
4 × 70 = 280

Question 8.
8 × 30
Answer:
You can use basic multiplication facts to multiply by multiples of 10.
8 × 30
Multiply the number of tens by 8.
8 × 30 = 8 × 3 tens
8 × 30 = 24 tens
8 × 30 = 240

Question 9.
7 × 70
Answer:
You can use basic multiplication facts to multiply by multiples of 10.
7 × 70
Multiply the number of tens by 7.
7 × 70 = 7 × 7 tens
7 × 70 = 49 tens
7 × 70 = 490

Question 10.
60 × 5
Answer:
You can use basic multiplication facts to multiply by multiples of 10.
5 × 60
Multiply the number of tens by 5.
5 × 60 = 5 × 6 tens
5 × 60 = 30 tens
5 × 60 = 300

Set C
pages 389-392

Find 7 × 80.
Think of 80 as 8 × 10. Then use the Associative Property of Multiplication.
7 × 80 = 7 × (8 × 10)
7 × 80 = (7 × 8) × 10)
7 × 80 = 56 × 10
7 × 80 = 560
You can use properties of operations, such as the Associative Property and the Distributive Property, to help multiply.

Remember that the Associative Property of Multiplication lets you regroup factors. In 1 and 2, find the product using properties.

Question 1.
5 × 80 = 5 × (__× 10)
5 × 80 = (5 × __ ) × 10
5 × 80 = __ × 10 = __
Answer:
Write 80 as 8 × 10. Then use the Associative Property of Multiplication.
5 × 80 = 5 × ( 8 × 10)
5 × 80 = (5 × 8 ) × 10
5 × 80 = 40 × 10 = 400

Question 2.
7 × 40 = ___ × (__× 10)
7 × 40 = (__ × __) × 10
7 × 40 = ___ × 10 = ___
Answer :
Write 40 as 4 × 10. Then use the Associative Property of Multiplication.
7 × 40 = 7 × ( 4 × 10)
7 × 40 = ( 7 × 4 ) × 10
7 × 40 = 28 × 10 = 280

Set D
pages 393-396
Think about these questions to help you make use of structure.
Thinking Habits
• What patterns can I see and describe?
• How can I use the patterns to solve the problem?
• Can I see expressions and objects in different ways?

Remember to use patterns or properties to multiply by multiples of 10.
Christy is making a savings plan. She wants to know how much she will save if she saves $40 for 6, 7, 8, or 9 weeks.

Question 1.
How can you use patterns to help solve this problem?
Answer:
As I move down the columns, the numbers increase by the value of the column.
As I move across the rows, the numbers increase by the value in the column where 10 is a factor.
I used patterns I know for multiplying by multiples of 10.

Question 2.
Find the total amount Christy would save after 6, 7, 8, or 9 weeks. Think about patterns or properties you know.
Answer:

As I move down the columns, the numbers increase by the value of the column.
As I move across the rows, the numbers increase by the value in the column where 10 is a factor.
I used patterns I know for multiplying by multiples of 10.

Topic 10 Assessment Practice

Question 1.
Julia gives each of her 4 friends a sheet of stickers. Each sheet has 20 stickers. How many stickers do her friends have in all?
Answer:
Number of friends = 4
Number of stickers = 20 .
Number of stickers with each friend = 20 ÷ 4 = 5 stickers .

Question 2.
Select all of the expressions equal to 8 × 60.
48 × 10
6 × 80
(8 × 6) × 10
8 × (8 × 10)
60 × 80
Answer:

Explanation :
48 × 10 = 480
6 × 80 = 480
(8 × 6) × 10 = 480
8 × (8 × 10) = 640
60 × 80 = 4800

Question 3.
Mrs. Rode bought 80 packs of juice boxes for her school’s party. The juice boxes came in packs of 8. How many juice boxes did Mrs. Rode buy? explain how to solve.
Answer:
Number of juice boxes = 80 packs.
Number of packs = 8 .
Total Number of juices = 8 × 80
Write 80 as 8 × 10. Then use the Associative Property of Multiplication.
8 × 80 = 8 × ( 8 × 10)
8 × 80 = (8 × 8 ) × 10
8 × 80 = 64 × 10 = 640 Juices .

Question 4.
The third-grade teachers at Jenny’s school need 5 boxes of yellow folders and 4 boxes of red folders. Each box has 40 folders. How many folders do the teachers need?
A. 160
B. 320
C. 200
D. 360
Answer:
Option D – 360 folders
Explanation :
Number of Yellow folders = 5 boxes .
Number of Red folders = 4 boxes .
Number of folders in each box = 40 folders .
Total Folders Teacher needs = ( 5 × 40 ) + ( 4 × 40 ) = ( 5 + 4 ) 40 = 9 × 40 = 360 folders

Question 5..
Write each expression in the correct answer space to show expressions equal to 6 × 30 and 3 × 80.

(3 × 8) 10
3 × (6 × 10)
24 × 10
8 × (3 × 10)
6 × (3 × 10)
18 × 10
3 × (8 × 10)
(6 × 3) × 10
Answer:

Question 6.
Match each expression on the left to an equal expression.

Answer:

Question 7.
What is 4 × 30?
A. 22
B. 34
C. 120
D. 160
Answer:
Option C – 120
Explanation :
4 × 30
Write 80 as 8 × 10. Then use the Associative Property of Multiplication.
4 × 30 = 4 × ( 3 × 10)
4 × 30 = (4 × 3 ) × 10
4 × 30 = 12 × 10 = 120

Question 8.
Tyler does 40 pushups each day. How many pushups does he do in 5 days?
Answer:
Number of pushups done in each day = 40
Number of days = 5
Number of pushups done in 5 days = 5 × 40 = 200 pushups.

Question 9.
The family membership to a children’s museum is $90 for a year. On Friday 5 families bought memberships. How much did the museum receive for the new memberships?
Answer:
Cost of Family membership = $90 for a year
Cost of 5 Families membership = 5 × 90 = 450 $ .
Therefore, the museum receive for the new memberships is 450 $ .

Question 10.
Select all of the expressions that are equal to 7 × 50.
7 × (5 × 10)
35 × 10
7 × 5
75 × 10
(7 × 5) × 10
Answer:

Explanation :
7 × (5 × 10) = 350
35 × 10 =350
7 × 5 = 35
75 × 10 =750
(7 × 5) × 10 = 350

Question 11.
Tyrone drives 30 miles every day. How many miles does Tyrone drive in 7 days?
A. Use a number line to solve the problem.
B. Describe another way to solve the problem.
Answer:
Number of miles Tyrone every day = 30 miles .
Number of days Tyrone drives = 7 days.
Number of miles Tyrone drive for 7 days = 7 × 30 = 210 miles .
A .

B.
Write 30 as 3 × 10. Then use the Associative Property of Multiplication.
7 × 30 = 7 × ( 3 × 10)
7 × 30 = (7 × 3 ) × 10
7 × 30 = 21 × 10 = 210 miles.

Topic 10 Performance Task

Pet Adoption
Carson and Adriana volunteer at a local animal rescue center. The adoption fee is different based on the animal and its age.
Carson made an Adoption Fee graph to show the fees for adult dogs, puppies, adult cats, and kittens. Adriana recorded the number of each animal adopted during the summer in the Animals Adopted table.
Use the Adoption Fee graph and the Animals Adopted table to answer Questions 1-3.

Question 1.
Carson wants to find the total adoption fees the rescue center received for adopted adult dogs. Show how Carson can use a number line to do this.

Answer:
Total Adoption fees the rescue center received for adopted adult dogs = $ 60 .
The cost is divided in increase of $20 .
It is represented on a number line is shown below .

Question 2.
Adriana says that she can use (4 × 8) × 10 to find the total adoption fees for adopted puppies. Is she correct? explain why or why not. Then find the total.

Answer:
Yes she is right .
Explanation :
Adoption fee for puppy = $80 .
Number of puppies adopted = 4
Total Fee for adopting puppies = 4 × 80 = 320$ .
Write 80 as 8 × 10. Then use the Associative Property of Multiplication.
4 × 80 = 4 × ( 8 × 10)
4 × 80 = (4 × 8 ) × 10
4 × 80 = 32 × 10 = 320$ .

Question 3.
Find the adoption fees the rescue center received for kittens. Think about patterns or properties you know. Show your work.
Answer:
Adoption fee for kittens = $60 .
Number of kittens adopted = 3
Total Fee for adopting kittens = 3 × 60 = 180$ .
Write 60 as 6 × 10. Then use the Associative Property of Multiplication.
3 × 60 = 3 × ( 6 × 10)
3 × 60 = (3 × 6 ) × 10
3 × 60 = 18 × 10 = 180$ .
Therefore, the adoption fees the rescue center received for kittens = 180$

The animal rescue center sells toy packages for pets.
The Toy Packages graph shows the amount earned for different types of packages. The Toy Packages Sold table shows how many packages were sold in the summer.
Use the Toy Packages graph and the Toy Packages Sold table to answer Questions 4 and 5.

Question 4.
How much money did the animal rescue center earn from toys for large dogs? Show your work.

Answer:
Cost of toy packages of large dogs = $50
Number of packages sold = 5
Money earned for selling 5 large dogs packages = 5 × 50
Write 50 as 5 × 10. Then use the Associative Property of Multiplication.
5 × 50 = 5 × ( 5 × 10)
5 × 50 = (5 × 5 ) × 10
5 × 50 = 25 × 10 = 250$ .
Therefore, Money earned for selling 5 large dogs packages = $250 .

Question 5.
Carson says that the center earned more money selling toys for small dogs than from selling toys for large dogs. Is he correct? explain why or why not.
Use the Toy Packages graph to answer Question 6.
Answer:
No he is wrong , More money is received by selling Large dog packages than small dog packages .
Explanation :
Cost of toy packages of large dogs = $50
Number of packages sold = 5
Money earned for selling 5 large dogs packages = 5 × 50 = $250 .
Cost of toy packages of small dogs = $30
Number of packages sold = 7
Money earned for selling 7 small dogs packages = 7 × 30 = $210 .
$250 >$210

Question 6.
Adriana forgot to record the number of packages of cat toys that were sold. She knows that the center earned a total of $140 from the toys for cats. How many packages of cat toys did they sell?
Answer:
Total Money earned from toys of cats = $140 .
Cost of toy packages of cats  = $20 .
Number of toy cats packages sold = 140 ÷ 20 = 7 packages .
Therefore, packages of cat toys sold = 7 packages .

Go through the enVision Math Common Core Grade 5 Answer Key Topic 16 Geometric Measurement: Classify Two-Dimensional Figures regularly and improve your accuracy in solving questions.

enVision Math Common Core 5th Grade Answers Key Topic 16 Geometric Measurement: Classify Two-Dimensional Figures

enVision STEM Project: Ecosystems
Do Research Use the Internet or other sources to learn more about ecosystems. Look for examples of changes that living organisms might cause. List three different ecosystems and describe any changes that humans might have made to each one.
Journal: Write a Report Include what you found. Also in your report:
• Compare two ecosystems. List 10 living things and 5 non-living things you might find in each one.
• Think about changes that can occur in an ecosystem. Are the changes positive or negative? Why?
• Use two-dimensional shapes to make a map or diagram of an ecosystem.

Review What You Know

A-Z Vocabulary

Choose the best term from the box. Write it on the blank.

• degree
• polygon
• line segment
• quadrilateral
• parallel
• vertex
• perimeter

Question 1.
A ___ is a polygon with four sides.

Answer:
A quadrilateral is a polygon with four sides.

Explanation:
In the above-given question,
given that,
A quadrilateral is a polygon with four sides.
for example:
square is a quadrilateral.
square has four sides of equal length.
square has four internal right angles.
so a quadrilateral is a polygon with four sides.

Question 2.
The point where two sides of a polygon intersect is a ___

Answer:
The point where two sides of a polygon intersect is a vertex.

Explanation:
In the above-given question,
given that,
the point where two sides of a polygon intersect is a vertex.
for example:
triangle is a polygon.
a polygon with three sides is a triangle.
we name a triangle by its three vertices.
so the point where two sides of a polygon intersect is a vertex.

Question 3.
The distance between ____ sides of a polygon is always the same.

Answer:
The distance between parallel sides of a polygon is always the same.

Explanation:
In the above-given question,
given that,
the distance between the number of sides of a polygon is always the same.
for example:
the rectangle is a polygon.
the rectangle has opposite sides that are equal.
so the distance between parallel sides of a polygon is always the same.

Question 4.
The ____ is a unit of measure for angles.

Answer:
A degree is a unit of measure for angles.

Explanation:
In the above-given question,
given that,
a degree is a unit of measure for angles.
for example:
a circle is divided into 360 equal degrees.
so that a right angle is 90 degrees.
so the degree is a unit of measure for angles.

Decimals
Find each answer.

Question 5.
2.75 + 9.08

Answer:
2.75 + 9.08 = 11.83.

Explanation:
In the above-given question,
given that,
addition of two numbers.
the numbers are 2.75 and 9.08.
2.75 + 9.08.
11.83.

Question 6.
17.6 – 3.08

Answer:
17.6 – 3.08 = 14.52.

Explanation:
In the above-given question,
given that,
subtraction of two numbers.
the numbers are 17.6 and 3.08.
17.6 – 3.08.
14.52.

Question 7.
83.2 × 0.1

Answer:
83.2 x 0.1 = 8.32.

Explanation:
In the above-given question,
given that,
multiplication of two numbers.
the numbers are 83.2 and 0.1.
83.2 x 0.1.
8.32.

Question 8.
24.27 × 10³

Answer:
24.27 x 1000 = 24270.

Explanation:
In the above-given question,
given that,
multiplication of two numbers.
the numbers are 24.27 and 10 x 10 x 10.
10 x 10 x 10 = 1000.
24.27 x 1000 = 24270.

Fractions
Find each answer.

Question 9.
3\(\frac{2}{3}\) + 6\(\frac{9}{10}\)

Answer:
3(2/3) + 6(9/10) = 7.2.

Explanation:
In the above-given question,
given that,
addition of two numbers.
the numbers are 3(2/3) and 6(9/10).
2/3 = 0.6.
9/10 = 0.9.
3(0.6) + 6(0.9).
1.8 + 5.4 = 7.2.
3(2/3) + 6(9/10) = 7.2.

Question 10.
8\(\frac{1}{2}\) – 4\(\frac{4}{5}\)

Answer:
8(1/2) – 4(4/5) = 0.8.

Explanation:
In the above-given question,
given that,
subtraction of two numbers.
the numbers are 8(1/2) and 4(4/5).
1/2 = 0.5.
4/5 = 0.8.
8(0.5) – 4(0.8).
4 – 3.2 = 0.8.
8(1/2) – 4(4/5) = 0.8.

Question 11.
8 ÷ \(\frac{1}{2}\)

Answer:
8 ÷ \(\frac{1}{2}\) = 16.

Explanation:
In the above-given question,
given that,
division of two numbers.
the numbers are 8 and 1/2.
8 / 0.5.
16.
8 ÷ \(\frac{1}{2}\) = 16.

Question 12.
\(\frac{1}{3}\) ÷ 6

Answer:
\(\frac{1}{3}\) ÷ 6 = 0.05.

Explanation:
In the above-given question,
given that,
division of two numbers.
the numbers are 6 and 1/3.
1/3 = 0.3.
0.3 / 6 = 0.05.
\(\frac{1}{3}\) ÷ 6 = 0.05.

Write an Equation

Question 13.
Louisa drew a polygon with six sides of equal length. If the perimeter of Louisa’s polygon is 95.4 centimeters, how long is each side? Use an equation to solve.

Answer:
The length of each side = 15.9 cm.

Explanation:
In the above-given question,
given that,
If the perimeter of Louisa’s polygon is 95.4 centimeters.
a polygon with 6 sides is called a hexagon.
perimeter of hexagon = 6a.
where a = side.
p = 6 a.
95.4 = 6 a.
a = 95.4 / 6.
a = 15.9 cm.
so the length of each side = 15.9 cm.

Question 14.
The area of a rectangle is 112 square inches. If the length of the rectangle is 16 inches, what is the width of the rectangle? Use an equation to solve.

Answer:
The width of the rectangle is = 7 in.

Explanation:
In the above-given question,
given that,
The area of a rectangle is 112 square inches.
If the length of the rectangle is 16 inches.
area of the rectangle = l x w.
where l = length and w = width.
112 = 16 x w.
112 /16 = w.
w = 7.
so the width of the rectangle = 7 in.

Pick a Project

PROJECT 16A
Where can you find a pyramid?
Project: Build a Pyramid

PROJECT 16B
How do blueprints use different shapes?
Project: Draw a Blueprint

PROJECT 16C
What shapes make up a map?
Project: Hunt for Shapes in a Map

PROJECT 16D
What does the Florida flag look like?
Project: Design a Flag

Answer:
The Florida flag looks like a cross mark.

Explanation:
In the above-given question,
given that,
in the flag, has the cross mark.
the cross mark is inside the flag.
so the Florida flag looks like a cross mark.
cross mark indicates it is not correct.

Lesson 16.1 Classify Triangles

Solve & Share
One triangle is shown below. Draw five more triangles with different properties. Next to each triangle, list its properties such as 2 equal sides, 1 right angle, 3 acute angles, and so on. Work with a partner to solve this problem.

In a triangle, angles will be either acute, right, or obtuse.

Look Back! Reasoning What are some different ways you can put triangles into categories? Explain.

Answer:
They are acute, obtuse, equilateral, right triangles.

Explanation:
In the above-given question,
given that,
the equilateral triangle has all the sides equal length.
an acute triangle is a trigon with three sides and three angles each less than 90 degrees.
an obtuse triangle will have one and only one obtuse angle.
the other two angles are acute angles.
a right triangle is a triangle in which one angle is a right angle.
an isosceles triangle has at least two sides of the same length.
so the triangles are acute, obtuse, equilateral, right triangles.

Visual Learning Bridge

Essential Question How Can You Classify Triangles?

A.
Triangles can be classified by the lengths of their sides.

Equilateral triangle All sides are the same length.

Isosceles triangle At least two sides are the same length.

Scalene triangle No sides are the same length

Can you tell if the sides of a triangle are the same length without measuring them?

The total measure of all the angles in a triangle is 180°.

B.
Triangles can also be classified by the measures of their angles.

Right triangle One angle is a right angle.

Acute triangle All three angles are acute angles.

Obtuse triangle One angle is an obtuse angle.

Convince Me! Construct Arguments Can you draw an equilateral right triangle? Explain using precise mathematical language.

To justify a mathematical argument, you must use precise mathematical language and ideas to explain your thinking

Answer:
Yes, we can draw an equilateral right triangle.

Explanation:
In the above-given question,
given that,
we can draw an equilateral triangle with 90 degrees.
right angle means it has 90 degrees.
an equilateral triangle has all the sides are equal.
so we can draw an equilateral right triangle.

Guided Practices

Do You Understand?

Question 1.
Can a right triangle have an obtuse angle? Why or why not?

Answer:
No, the right triangle has an obtuse angle.

Explanation:
In the above-given question,
given that,
the right triangle cannot be an obtuse angle.
since a right-angled triangle has one right angle, the other two angles are acute.
therefore, an obtuse-angled triangle can never have a right angle.
the side opposite the obtuse angle in a triangle is the longest.
so the right triangle is not an obtuse angle.

Question 2.
Can an equilateral triangle have only two sides of equal length? Why or why not?

Answer:
No, an equilateral triangle has only two sides of equal length.

Explanation:
In the above-given question,
given that,
an equilateral triangle has all three sides are equal.
if only two sides are equal in length, then it is an isosceles triangle.
so the equilateral triangle does not have only two sides of equal length.

Do You Know How?

In 3 and 4, classify each triangle by its sides and then by its angles.

Question 3.

Answer:
The triangle is an equilateral triangle.

Explanation:
In the above-given question,
given that,
the three angles are equal.
the three sides are equal sides.
an equilateral triangle has all the sides are equal.
so the triangle is an equilateral triangle.

Question 4.

Answer:
The triangle is an isosceles triangle.

Explanation:
In the above-given question,
given that,
the two sides have an equal length.
they are 7 inches.
the other side is 9.9 in.
an isosceles triangle has only two sides are equal.
so the above triangle is an isosceles triangle.

Independent Practice

In 5-10, classify each triangle by its sides and then by its angles.

Question 5.

Answer:
The above triangle is an acute-angle triangle.

Explanation:
In the above-given question,
given that,
the two sides and the two sides have the same length.
they are 75 degrees and 6 in.
the other side has a different side length.
acute angle triangle has two equal lengths.
so the above triangle is an acute-angled triangle.

Question 6.

Answer:
The triangle is a scalene triangle.

Explanation:
In the above-given question,
given that,
the triangle has three sides.
the three sides have three different lengths.
a scalene triangle has different lengths.
so the above-given triangle is a scalene triangle.

Think about what you need to compare to classify the triangle correctly.

Question 7.

Answer:
The triangle is an equilateral triangle.

Explanation:
In the above-given question,
given that,
the triangle has the 3 equal sides and three equal angles.
60 + 60 + 60 = 180.
an equilateral triangle has all three sides equal in length.
so the above triangle is an equilateral triangle.

Question 8.

Answer:
The triangle is an obtuse-angled triangle.

Explanation:
In the above-given question,
given that,
the triangle has 2 equal sides.
obtuse-angled triangle has only two equal side lengths.
so the triangle is an obtuse-angled triangle.

Question 9.

Answer:
The triangle is a scalene triangle.

Explanation:
In the above-given question,
given that,
the triangle has three different side lengths.
the side lengths are 6m, 10m, and 8m.
a scalene triangle has three different side lengths.
so the triangle is a scalene triangle.

Question 10.

Answer:
The triangle is an isosceles triangle.

Explanation:
In the above-given question,
given that,
the triangle has two different side lengths.
they are 12 cm and 6.5 cm.
an isosceles triangle has the two sides equal.
so the triangle is an isosceles triangle.

Problem Solving

Question 11.
The Louvre Pyramid serves as an entrance to the Louvre Museum in Paris. The base of the pyramid is 35 meters long and the sides are 32 meters long. Classify the triangle on the front of the Louvre Pyramid by the lengths of its sides and the measures of its angles.

Answer:
The Louvre triangle is in the shape of an isosceles triangle.

Explanation:
In the above-given question,
given that,
The Louvre Pyramid serves as an entrance to the Louvre Museum in Paris.
The base of the pyramid is 35 meters long and the sides are 32 meters long.
an isosceles triangle has two equal side lengths.
the other side is a difference in length.
so the Louvre triangle is in the shape of an isosceles triangle.

Question 12.
A pizza is divided into twelve equal slices. Glenn and Ben each ate \(\frac{1}{6}\) of the pizza on Monday. The next day Ben ate \(\frac{1}{2}\) of the pizza that was left over. How many slices of the original pizza remain? Explain your reasoning.

Answer:
The number of slices of the original pizza remains = 2 pieces.

Explanation:
In the above-given question,
given that,
A pizza is divided into twelve equal slices.
Glenn and Ben each ate \(\frac{1}{6}\) of the pizza on Monday.
The next day Ben ate \(\frac{1}{2}\) of the pizza that was leftover.
1/6 + 1/2.
1/6 = 0.16.
1/2 = 0.5.
0.16 + 0.5 = 0.66.
so the number of slices of the original pizza remains = 2 pieces.

Question 13.
During a sale at the bookstore, books sold for $3 and magazines sold for $2.50. Jan spent $16 and bought a total of 6 books and magazines. How many of each did she buy?

Answer:
The number of each did she buy = $17.

Explanation:
In the above-given question,
given that,
During a sale at the bookstore, books sold for $3, and magazines sold for $2.50.
Jan spent $16 and bought a total of 6 books and magazines.
6 x 3 = $18.
6 x $2.50 = $15.
$18 + $15 = 33.
$33 – $16 = $17.
so the number of each did she buy = $17.

Question 14.
Higher Order Thinking The measures of two angles of a triangle are 23° and 67°. Is the triangle acute, right, or obtuse? Use geometric terms in your explanation.

Answer:
The triangle is an acute-angled triangle.

Explanation:
In the above-given question,
given that,
The measures of two angles of a triangle are 23° and 67°.
the triangles have two different angles.
they are 23° and 67°.
so the triangle is an acute-angled triangle.

Question 15.
Make Sense and Persevere An animal shelter houses dogs, cats, and rabbits. There are 126 animals at the shelter. Of the animals, \(\frac{1}{3}\) are cats. Three fourths of the remaining animals are dogs. How many of the animals are rabbits? Show your work.

Answer:
The number of animals is rabbits = 21.

Explanation:
In the above-given question,
given that,
An animal shelter houses dogs, cats, and rabbits.
There are 126 animals at the shelter.
Of the animals, \(\frac{1}{3}\) are cats.
Three-fourths of the remaining animals are dogs.
1/3 = 0.3.
3/4 = 0.75.
0.3 + 0.75 = 1.05.
so the number of animals is rabbits = 21.

Assessment Practice

Question 16.
Two sides of a triangle measure 5 inches and 6 inches. Jason says the triangle must be scalene. Is Jason correct? Explain.

Answer:
No, Jason is not correct.

Explanation:
In the above-given question,
given that,
Two sides of a triangle measure 5 inches and 6 inches.
a scalene triangle has all three sides have different lengths.
an isosceles triangle has the two sides are equal.
so Jason is not correct.

Lesson 16.2 Classify Quadrilaterals

Solve & Share
Draw any length line segment that will fit in the space below. The line segment can go in any direction, but it must be straight. Draw another line segment of any length that is parallel to the first one. Connect the ends of each line segment with line segments to make a closed four-sided figure. What does your shape look like? Can you classify it? Discuss your ideas with a partner.

Answer:
The shape looks like is a rectangle.

Explanation:
In the above-given question,
given that,
the line segment has 5 cm in length.
the other line segment has the same 2 cm in length.
so the lines joined is formed a rectangle.
the rectangle has two opposite sides that are equal.
the rectangle has the area = length x width.
so the shape looks like a rectangle.

You can use reasoning to find the differences and similarities between shapes when classifying quadrilaterals. Show your work!

Look Back! Reasoning How can you draw a quadrilateral different from the one above? Describe what you can change and why it changes the quadrilateral.

Answer:
The quadrilateral formed is square.

Explanation:
In the above-given question,
given that,
the line segment is increased by 3 cm.
5 – 2 = 3.
so it has 4 equal side lengths.
area of the square = 4 s.
where S = sides.
so the quadrilateral formed is square.

Visual Learning Bridge

Essential Question What Are Some Properties of Quadrilaterals?
A.
Categories of quadrilaterals are classified by their properties.
• How many pairs of opposite sides are parallel?
• Which sides have equal lengths?
• How many right angles are there?

Think about the questions below when you are classifying quadrilaterals.

B.
A trapezoid has one pair of parallel sides.

A parallelogram has two pairs of opposite sides parallel and equal in length.

C.
A rectangle has four right angles.

A rhombus has all sides the same length.

D.
A square has all sides the same length.

A square has four right angles.

Convince Me! Generalize How is a parallelogram different from a rhombus? How are they similar?

Guided Practice

Do You Understand?

Question 1.
A-Z Vocabulary How are a square and a rhombus alike?

Answer:
Yes, a square and a rhombus have four equal sides.

Explanation:
In the above-given question,
given that,
the square has four sides of the same length.
square has four right angles.
rhombus has all sides the same length.
so the square and a rhombus have four equal sides.

Question 2.
Vocabulary How is a trapezoid different from a parallelogram?

Answer:
Yes, both of them are different.

Explanation:
In the above-given question,
given that,
a trapezoid has one pair of parallel sides.
a parallelogram has two pairs of opposite sides and is equal in length.
so both of them are different.

Do You Know How?

In 3-6, use as many names as possible to identify each polygon. Tell which name is most specific.

Use the questions at the top of page 626 to help you classify the quadrilaterals.

Question 3.

Answer:
The quadrilateral is a square.

Explanation:
In the above-given question,
given that,
the quadrilateral has 4 equal sides.
four right angles.
so the square has 4 equal sides.
so the quadrilateral is a square.

Question 4.

Answer:
The quadrilateral is a rectangle.

Explanation:
In the above-given question,
given that,
the quadrilateral has opposite equal sides.
four right angles.
so the rectangle has opposite equal sides.
so the quadrilateral is a rectangle.

Question 5.

Answer:
The quadrilateral is a rhombus.

Explanation:
In the above-given question,
given that,
the quadrilateral has 4 equal sides.
so the rhombus has 4 equal sides.
so the quadrilateral is a rhombus.

Question 6.

Answer:
The quadrilateral is a parallelogram.

Explanation:
In the above-given question,
given that,
the quadrilateral has opposite sides are equal.
four right angles.
so the rectangle has opposite equal sides.
so the quadrilateral is a parallelogram.

Independent Practice

Question 7.
Identify the polygon using as many names as possible.

Answer:
The polygon is a square and rhombus.

Explanation:
In the above-given question,
given that,
the polygon has 4 equal sides.
the polygon has 4 equal angles.
so the polygon is a square and rhombus.

Question 8.
Identify the polygon using as many names as possible.

Answer:
The polygon is a quadrilateral and trapezoid.

Explanation:
In the above-given question,
given that,
the polygon has 4 different sides.
the polygon has one right angle.
so the polygon is a quadrilateral and trapezoid.

Question 9.
Why is a square also a rectangle?

Answer:
Yes, a square is also a rectangle.

Explanation:
In the above-given question,
given that,
the square has 4 equal right angles.
the rectangle has 4 equal right angles.
so square and rectangle are the same.
so the square is also a rectangle.

Question 10.
Which special quadrilateral is both a rectangle and a rhombus? Explain how you know.

Answer:
The special quadrilateral is a square.

Explanation:
In the above-given question,
given that,
the square is a rectangle.
square has 4 equal right angles.
rectangle also has 4 equal right angles.
rhombus also has 4 equal right angles.
so the special quadrilateral is a square.

Problem Solving

Question 11.
Each time Sophie makes a cut to a polygon, she can make a new type of polygon. What kind of polygon is left if Sophie cuts off the top of the isosceles triangle shown?

Answer:
The polygon formed is a trapezoid.

Explanation:
In the above-given question,
given that,
Each time Sophie makes a cut to a polygon, she can make a new type of polygon.
the polygon is an isosceles triangle.
after Sophie makes a cut to a polygon.
so the polygon formed is a trapezoid.

Question 12.
Number Sense Donald’s car gets about 30 miles per gallon. About how many miles can Donald drive on 9.2 gallons of gas? At $3.15 a gallon, about how much would that amount of gas cost?

Answer:
The amount of gas cost = $869.4 miles.

Explanation:
In the above-given question,
given that,
Donald’s car gets about 30 miles per gallon.
9.2 x 30 = 276 miles.
276 x $3.15 = $869.4 miles.
so the amount of gas cost = $869.4 miles.

Question 13.
Is it possible to draw a quadrilateral that is not a rectangle but has at least one right angle? Explain.

Answer:
Yes, it is possible to draw a quadrilateral that is not a rectangle.

Explanation:
In the above-given question,
given that,
the square is also a quadrilateral.
square has 4 equal right angles.
square has 4 equal side lengths.
so it is possible to draw a quadrilateral that is not a rectangle.

Question 14.
The area of a quadrilateral is 8.4 square feet. Find two decimals that give a product close to 8.4.

Answer:
The two decimals are 2.1 and 4.0.

Explanation:
In the above-given question,
given that,
the area of a quadrilateral is 8.4 square feet.
area = l x w.
where l = 2.1 and w = 4.0.
area = 2.1 x 4.0.
area = 8.4.
so the two decimals are 2.1 and 4.0.

Question 15.
Be Precise Suppose you cut a square into two identical triangles. What type of triangles will you make?

Answer:
The triangle I make is the isosceles triangle.

Explanation:
In the above-given question,
given that,
Suppose you cut a square into two identical triangles.
an isosceles triangle has the two sides equal.
the triangle formed is the isosceles triangle.
so the triangle I can make is an isosceles triangle.

Question 16.
Higher Order Thinking A parallelogram has four sides that are the same length. Is it a square? Explain how you know.

What do you know about the sides of a parallelogram?

Assessment Practice

Question 17.
Which quadrilateral could have side lengths 1 m, 5 m, 1 m, 5 m?
A. square
B. rectangle
C. trapezoid
D. rhombus

Answer:
Option B is the correct answer.

Explanation:
In the above-given question,
given that,
the quadrilateral could have side lengths 1 m, 5 m, 1 m, and 5 m.
the rectangle has the opposite sides equal.
so option B is the correct answer.

Question 18.
Which of the following statements is NOT true?
A. A rectangle is also a parallelogram.
B. A trapezoid is also a quadrilateral.
C. A rhombus is also a rectangle.
D. A square is also a rectangle.

Answer:
Option C is the correct answer.

Explanation:
In the above-given question,
given that,
a rectangle is also a parallelogram.
a trapezoid is also a quadrilateral.
a square is also a rectangle.
a rhombus is not a rectangle.
rhombus has all four equal sides.
so option C is the correct answer.

Lesson 16.3 Continue to Classify Quadrilaterals

Solve & Share
Look at the quadrilaterals below. In the table, write the letters for all the figures that are trapezoids. Then do the same with each of the other quadrilaterals. Work with a partner to solve this problem.

You can classify quadrilaterals that have more than one property. Show your work!

List the letter of each figure in each group.

Answer:
The number of trapezoids is Q, R, S, U, and O.
parallelograms are L, M, and N.
the rectangle is G.
the rhombus is V.

Explanation:
In the above-given question,
given that,
the number of trapezoids is Q, R, S, U, and O.
parallelograms are L, M, and N.
the rectangle is G.
the rhombus is V.

Look Back! Construct Arguments which quadrilateral had the most figures listed? Explain why this group had the most.

Visual Learning Bridge

Essential Question
How Are Special Quadrilaterals Related to Each Other?

A.
This Venn diagram shows how special quadrilaterals are related to each other.

How can you use the Venn diagram to describe other ways to classify a square? What does the diagram show about how a trapezoid relates to other special quadrilaterals?

B.
Each circle in the Venn diagram shows a category of quadrilateral.
Items in overlapping sections of the Venn diagram belong to more than one group.
“Square” is in more than one circle in the Venn diagram.

A square is also a rectangle, rhombus, parallelogram, and quadrilateral.

C.
In the diagram, the circle for trapezoids does not intersect with any other circles. This shows that a trapezoid is also a quadrilateral, but never a parallelogram, rectangle, rhombus, or square.

Convince Me! Construct Arguments When can a rectangle be a rhombus? Can a rhombus be a rectangle? Explain using examples.

Guided Practice

Do You Understand?

Question 1.
Explain how the Venn diagram on page 630 shows that every rectangle is a parallelogram.

Answer:
Yes, every rectangle is a parallelogram.

Explanation:
In the above-given question,
given that,
square is a rectangle, parallelogram, rhombus, and quadrilateral.
square is also a rectangle.
square has 4 equal right angles.
a rectangle has 4 equal right angles.
so every rectangle is a parallelogram.

Question 2.
How are a rectangle and a rhombus alike?

Answer:
The rectangle and rhombus are alike when they have 4 equal right angles.

Explanation:
In the above-given question,
given that,
square is a rectangle, parallelogram, rhombus, and quadrilateral.
square is also a rectangle.
square has 4 equal right angles.
a rectangle has 4 equal right angles.
so every rectangle is a parallelogram.
rhombus also have 4 equal right angles.
so the rectangle and rhombus are alike.

Do You Know How?

In 3-6, tell whether each statement is true or false. If false, explain.

Question 3.
All rectangles are squares.

Answer:
Yes, all rectangles are squares.

Explanation:
In the above-given question,
given that,
the square is a rectangle.
square has 4 equal right angles.
rectangles have 4 equal right angles.
so all rectangles are squares.

Question 4.
Every rhombus is a parallelogram.

Answer:
Yes, the rhombus is a parallelogram.

Explanation:
In the above-given question,
given that,
a rhombus has 4 equal sides lengths.
rhombus has 4 equal right angles.
a parallelogram has opposite sides equal.
so the rhombus is a parallelogram.

Question 5.
Parallelograms are special rectangles.

Answer:
Parallelograms are special rectangles.

Explanation:
In the above-given question,
given that,
rectangles have two opposite side lengths.
the parallelogram has two opposite side lengths.
so parallelograms are special rectangles.

Question 6.
A trapezoid can be a square.

Answer:
No, the trapezoid cannot be a square.

Explanation:
In the above-given question,
given that,
the square has 4 sides.
trapezoid also has 4 sides.
square has all sides equal.
a trapezoid has all sides not equal.
so trapezoid is not a square.

Independent Practice

In 7-10, write whether each statement is true or false. If false, explain why.

Question 7.
All rhombuses are rectangles.

Answer:
False.

Explanation:
In the above-given question,
given that,
a rhombus has 4 equal side lengths.
rectangles have 2 opposite side lengths.
so the statement is not correct.

Question 8.
Every trapezoid is a quadrilateral.

Answer:
Yes, the trapezoid is a quadrilateral.

Explanation:
In the above-given question,
given that,
the trapezoid is also a quadrilateral but never a parallelogram, rectangle, rhombus, or square.
so the trapezoid is a quadrilateral.

Question 9.
Rhombuses are special parallelograms.

Answer:
Yes, the rhombus is a special parallelogram.

Explanation:
In the above-given question,
given that,
a rhombus has 4 equal sides.
parallelograms have 4 sides.
so rhombus is a special parallelogram.

Question 10.
All rectangles are quadrilaterals.

Answer:
The statement is not correct.

Explanation:
In the above-given question,
given that,
rectangles have two opposite side lengths.
the quadrilateral has two opposite side lengths.
so the statement is not correct.

Question 11.
What properties does the shape have? Why is it not a parallelogram?

Answer:
The shape formed is a rhombus.

Explanation:
In the above-given question,
given that,
the shape formed is a rhombus.
rhombus has 4 equal side lengths.
rhombus has 4 equal right angles.
so the shape formed is a rhombus.

Question 12.
Why is a square also a rhombus?

Answer:
Yes, a square is also a rhombus.

Explanation:
In the above-given question,
given that,
a square has 4 equal sides.
square has 4 equal right angles.
rhombus has 4 equal sides.
rhombus has 4 equal right angles.
so the square is also a rhombus.

Problem Solving

Question 13.
Construct Arguments Draw a quadrilateral with one pair of parallel sides and two right angles. Explain why this figure is a trapezoid.

Answer:
Yes, it is a trapezoid.

Explanation:
In the above-given question,
given that,
a trapezoid has one pair of parallel sides and two right angles.
a quadrilateral with one pair of parallel sides and two right angles.
so the figure formed is a trapezoid.

Question 14.
A reflecting pool is shaped like a rhombus with a side length of 6 meters. What is the perimeter of the pool? Explain how you found your answer.
Think about the properties of a rhombus to help you solve.

Answer:
The perimeter of the pool is

Explanation:
In the above-given question,
given that,
A reflecting pool is shaped like a rhombus with a side length of 6 meters.
the perimeter of rhombus = 6 a.
where a = sides.
perimeter = 6 x 6.
perimeter = 36 sq m.
so the perimeter of the pool is 36 sq m.

Question 15.
A bakery sold 31 bagels in the first hour of business and 42 bagels in the second hour. If the bakery had 246 bagels to start with, how many bagels were left after the second hour?
img 42.7

Answer:
The number of bagels was left after the second hour = 3.36 bagels.

Explanation:
In the above-given question,
given that,
A bakery sold 31 bagels in the first hour of business and 42 bagels in the second hour.
If the bakery had 246 bagels to start with.
42 + 31 = 73.
246/73 = 3.36.
so the number of bagels were left after the second hour = 3.36 bagels.

Question 16.
Higher Order Thinking Ann says the figure below is a square. Pablo says that it is a parallelogram. Felix says that it is a rectangle. Can they all be right? Explain.

Answer:
Ann was correct.

Explanation:
In the above-given question,
given that,
the figure has 4 equal sides.
the figures have 4 equal angles.
the above figure is a square.
so Ann was correct.

Assessment Practice

Question 17.
Below is the Venn diagram of quadrilaterals.

Part A
Are rhombuses also rectangles? Explain.
Part B
What are all of the names that describe a rhombus?

Answer:
Squares and rectangles describe a rhombus.

Explanation:
In the above-given question,
given that,
rhombuses, squares, and rectangles are over-linked with each other.
square has 4 equal side lengths.
square has 4 equal right angles.
rectangles have 2 opposite equal sides.
rhombus has 4 equal side lengths.
so squares and rectangles describe a rhombus.

Lesson 16.4 Construct Arguments

Activity

Problem Solving

Solve & Share
Alfie thinks that if he cuts a parallelogram along a diagonal, he will get two triangles that have the same shape and size. Is he correct? Solve this problem any way you choose. Construct a math argument to justify your answer.

Answer:
The two triangles are Scalene triangles.

Explanation:
In the above-given question,
given that,
Alfie thinks that if he cuts a parallelogram along a diagonal.
he will get two triangles that have the same shape and size.
the triangles formed are scalene triangles.
a scalene triangle has 3 different side lengths.

Thinking Habits
Be a good thinker! These questions can help you.
• How can I use numbers, objects, drawings, or actions to justify my argument?
• Am I using numbers and symbols correctly?
• Is my explanation clear and complete?
• Can I use a counterexample in my argument?

Look Back! Construct Arguments Suppose you cut along a diagonal of a rhombus, a rectangle, or a square. Would you get two triangles that have the same shape and size? Construct an argument to justify your answer.

Visual Learning Bridge

Essential Question How Can You Construct Arguments?

A.
Anika says, “If I draw a diagonal in a parallelogram, I will always form two right triangles.” Is she correct? Construct a math argument to justify your answer.

You can construct an argument using what you know about triangles and quadrilaterals.

What do I need to do to solve the problem?
I need to examine several cases, including special parallelograms. Then I need to state my conclusion and write a good argument to justify it.

Here’s my thinking..

B.
How can I construct an argument?
I can
• use math to explain my reasoning
• use the correct words and symbols.
• give a complete explanation.
• use a counterexample in my argument.

C.
Anika is incorrect. The triangles are right triangles only when the parallelogram is a rectangle or square. Rectangles and squares have four right angles. So, each triangle formed by drawing a diagonal will have a right angle and be a right triangle. But if the parallelogram does not have right angles, each triangle will not have a right angle.

Convince Me! Construct Arguments How can counterexamples be helpful in constructing an argument?

Guided Practice

Jamal says, “Two equilateral triangles that are the same size can be joined to make a rhombus.”

Question 1.
What is the definition of an equilateral triangle? What is the definition of a rhombus?

Answer:
Yes, two equilateral triangles that are the same size can be joined to make a rhombus.

Explanation:
In the above-given question,
given that,
an equilateral triangle has all three sides has an equal length.
rhombus has all 4 sides are equal.
rhombus has all 4 equal right angles.
so the two equilateral triangles that are the same size can be joined to make a rhombus.

Question 2.
How could knowing these definitions help in constructing your argument?
Answer:

Question 3.
Is Jamal correct? Construct an argument to justify your answer.

Answer:
Yes, Jamal was correct.

Explanation:
In the above-given question,
given that,
an equilateral triangle has all three sides has an equal length.
rhombus has all 4 sides are equal.
rhombus has all 4 equal right angles.
so the two equilateral triangles that are the same size can be joined to make a rhombus.

Independent Practice

Construct Arguments
Lauren says, “If I draw a diagonal in a trapezoid, neither of the triangles formed will have a right angle.”

Stuck? Answering this question might help. Have I interpreted all word meanings correctly?

A diagram can help you construct arguments.

Question 4.
What is the definition of a trapezoid?

Answer:
The trapezoid is a quadrilateral with one pair of parallel sides.

Explanation:
In the above-given question,
given that,
the trapezoid is a quadrilateral with one pair of parallel sides.
area of trapezoid = 1/2(a + b) h.
where a and b are the bases.
h is the height.

Question 5.
Draw examples of a diagonal in a trapezoid.

Answer:
The shape formed is a triangle.

Explanation:
In the above-given question,
given that,
if the trapezoid is divided into two equal halves.
we can get the two triangles.
so the shape formed is a triangle.

Question 6.
How can you use a drawing to construct an argument?
Answer:

Question 7.
Is Lauren correct? Construct a math argument to justify your answer.
Answer:

Problem Solving

Performance Task
Flag Making
Mr. Herrera’s class is studying quadrilaterals. The class worked in groups, and each group made a “quadrilateral flag.”

Question 8.
Construct Arguments Which flags show parallelograms? Construct a math argument to justify your answer.

Answer:
Flag 1 shows a parallelogram.

Explanation:
In the above-given question,
given that,
Mr. Herrera’s class is studying quadrilaterals.
The class worked in groups, and each group made a “quadrilateral flag.
in 1st flag there are parallelograms.
so flag 1 shows a parallelogram.

Question 9.
Reasoning Explain how you would classify the quadrilaterals on the green flag and the blue flag.

Answer:

The definitions of the different quadrilaterals will help you construct arguments.

Question 10.
Critique Reasoning Marcia’s group made the red flag. Bev’s group made the orange flag. Both girls say their flag shows all rectangles. Critique the reasoning of both girls and explain who is correct.

Answer:

Question 11.
Make Sense and Persevere Does it make sense for this quadrilateral to be on any of the flags?

Answer:

Topic 16 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 16 Vocabulary Review

Understand Vocabulary

Word List
• acute triangle
• equilateral triangle
• isosceles triangle
• obtuse triangle
• parallelogram
• rectangle
• rhombus
• right triangle
• scalene triangle
• square
• trapezoid

Choose the best term from the Word List. Write it on the blank.

Question 1.
A 3-sided polygon with at least two sides the same length is a(n) _____

Answer:
A 3-sided polygon with at least two sides of the same length is a(n) is an equilateral triangle.

Explanation:
In the above-given question,
given that,
a 3-sided polygon with at least two sides of the same length is a(n) is an equilateral triangle.
for example:
an equilateral triangle has three sides that are all the same length and three angles that all measure 60 degrees.

Question 2.
A polygon with one pair of parallel sides is a(n) ____

Answer:
A polygon with one pair of parallel sides is a(n) is a trapezium.

Explanation:
In the above-given question,
given that,
a polygon with one pair of parallel sides is a(n) is a trapezium.
for example:
if the polygon has one pair of parallel sides is a trapezoid.

Question 3.
A(n) ____ has four right angles and all four sides the same length.

Answer:
A(n) rhombus has four right angles and all four sides the same length.

Explanation:
In the above-given question,
given that,
a(n) rhombus has four right angles and all four sides the same length.
for example:
a rhombus is a parallelogram with 4 sides of equal length.
area of rhombus = 6 a.
where a = sides.

Question 4.
All three sides of a(n) ____ are different lengths.

Answer:
All three sides of a(n) are scalene triangle are different lengths.

Explanation:
In the above-given question,
given that,
All three sides of a(n) are scalene triangle are different lengths.
for example:
a scalene triangle is a triangle in which all three sides have different lengths.

Question 5.
The measure of each of the three angles in a(n) ____ is less than 90°

Answer:
The measure of each of the three angles in a(n) acute angle triangle is less than 90°.

Explanation:
In the above-given question,
given that,
the measure of each of the three angles in a(n) acute angle triangle is less than 90°.
for example:
an acute angle triangle has three angles that each measure less than 90 degrees.

Question 6.
A rectangle is a special type of ____

Answer:
A rectangle is a special type of parallelogram.

Explanation:
In the above-given question,
given that,
a rectangle is a special type of parallelogram.
for example:
a rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular.

For each of these terms, draw an example and a non-example.

Answer:
An obtuse triangle is an isosceles triangle.
Rhombus with no right angle is a quadrilateral.
An isosceles right triangle is two equal sides.

Explanation:
In the above-given question,
given that,
An obtuse triangle is an isosceles triangle.
Rhombus with no right angle is a quadrilateral.
An isosceles right triangle is two equal sides.

Use Vocabulary in Writing

Question 10.
Alana claims that not all 4-sided polygons with 2 pairs of equal sides are parallelograms. Is Alana correct? Use terms from the Word List in your answer.

Answer:
No, she is not correct.

Explanation:
In the above-given question,
given that,
Alana claims that not all 4-sided polygons with 2 pairs of equal sides are parallelograms.
2 pairs of equal sides are not parallelograms.
so she was not correct.

Topic 16 Reteaching

Set A
pages 621-624
Classify the triangle by the measures of its angles and the lengths of its sides.
Since one of the angles is right, this is a right triangle. Since two of the sides are the same length, this is an isosceles triangle.

It is a right, isosceles triangle.

Remember that right, obtuse, and acute describe the angles of a triangle. Equilateral, scalene, and isosceles describe the sides of a triangle.

Classify each triangle by the measures of its angles and the lengths of its sides.

Question 1.

Answer:
The triangle is an equilateral triangle.

Explanation:
In the above-given question,
given that,
the triangles have 3 equal sides and three equal angles.
so the triangle is an equilateral triangle.

Question 2.

Answer:
The triangle is a scalene triangle.

Explanation:
In the above-given question,
given that,
the triangle has 3 different sides.
they are 3 in, 5 in, and 4 in.
the three side lengths are different.
so the triangle is a scalene triangle.

Question 3.

Answer:
The triangle is an isosceles triangle.

Explanation:
In the above-given question,
given that,
the triangle has 2 sides of equal length.
they are 8cm and 8 cm.
so the triangle is an isosceles triangle.

Question 4.

Answer:
The triangle is a scalene triangle.

Explanation:
In the above-given question,
given that,
the triangle has 3 different sides.
they are 16.4 cm, 16 cm, and 10 cm.
so the triangle is a scalene triangle.

Set B
pages 625-628

Quadrilaterals are classified by their properties.
A trapezoid has one pair of parallel sides.

A parallelogram has two pairs of equal parallel sides.

A rectangle is a parallelogram with 4 right angles.

A rhombus is a parallelogram with 4 equal sides.

A square is a parallelogram with 4 right angles and 4 equal sides.

Remember that some quadrilaterals can be identified by more than one name.

Identify each quadrilateral. Describe each quadrilateral by as many names as possible.

Question 1.

Answer:
The quadrilateral is a rectangle.

Explanation:
In the above-given question,
given that,
the polygon has 4 right angles.
the polygon with 4 right angles is a rectangle.
so the quadrilateral is a rectangle.

Question 2.

Answer:
The quadrilateral is a rhombus.

Explanation:
In the above-given question,
given that,
the polygon has 4 equal sides.
rhombus is a parallelogram with 4 equal sides.
so the quadrilateral is a rhombus.

Question 3.

Answer:
The polygon is a trapezoid.

Explanation:
In the above-given question,
given that,
the quadrilateral has 4 sides.
a trapezoid has one pair of parallel sides.
so the polygon is a trapezoid.

Question 4.

Answer:
The polygon is a square.

Explanation:
In the above-given question,
given that,
the quadrilateral has 4 equal sides and 4 equal angles.
a square is a parallelogram with 4 right angles and 4 equal sides.
so the polygon is a square.

Set C
pages 629-632
This Venn diagram shows how special quadrilaterals are related to each other.

Remember that each circle of the Venn diagram shows a subgroup of quadrilaterals.

Tell whether each statement is true or false.

Question 1.
All squares are rectangles.

Answer:
True.

Explanation:
In the above-given question,
given that,
all squares are rectangles.
square is a rectangle.
area of the square = 4s.

Question 2.
Every parallelogram is a rectangle.

Answer:
False.

Explanation:
In the above-given question,
given that,
a rectangle is a parallelogram.
but every parallelogram is a rectangle.
so the statement is false.

Question 3.
Rhombuses are special parallelograms.

Answer:
True.

Explanation:
In the above-given question,
given that,
rhombuses are special parallelograms.
rhombus is a special parallelogram.
area of the rhombus = 4 a.

Question 4.
All trapezoids are quadrilaterals.

Answer:
False.

Explanation:
In the above-given question,
given that,
a trapezoid is not a quadrilateral.
so the above statement is false.

Set D
pages 633-636
Think about these questions to help you construct arguments.

Thinking Habits
• How can I use numbers, objects, drawings, or actions to justify my argument?
• Am I using numbers and symbols correctly?
• Is my explanation clear and complete?
• Can I use a counterexample in my argument?

Remember that using definitions of geometric figures can help you construct arguments. Malcolm says, “The sum of the angle measures in any rectangle is 180°.”

Question 1.
What is the definition of a rectangle?

Answer:
A rectangle is a parallelogram with 4 right angles.

Explanation:
In the above-given question,
given that,
a rectangle is a parallelogram with 4 right angles.
area of the rectangles = length x width.

Question 2.
Draw a picture of a rectangle and label its angles.

Answer:
A rectangle is a parallelogram with 4 right angles.

Explanation:
In the above-given question,
given that,
a rectangle is a parallelogram with 4 right angles.
area of the rectangles = length x width.

Question 3.
Is Malcolm correct? Construct a math argument to justify your answer.
Answer:

Topic 16 Assessment Practice

Question 1.
Which of the following correctly describes the triangles? Select all that apply.

Both triangles have a right angle.
Only one triangle is a right triangle.
Only one triangle has an acute angle.
Both triangles have an obtuse angle.
Both triangles have at least two acute angles.

Answer:
Only one triangle is a right triangle.
only one triangle has an acute angle.

Explanation:
In the above-given question,
given that,
there are two triangles.
they have only one triangle is a right triangle.
only one triangle has an acute angle.

Question 2.
Which statement is true?
A. Trapezoids are parallelograms.
B. A square is always a rectangle.
C. A rectangle is always a square.
D. A rhombus is a trapezoid.

Answer:
Option B is correct.

Explanation:
In the above-given question,
given that,
a square is always a rectangle.
square has 4 equal right angles.
the rectangle has 4 equal right angles.

Question 3.
Select all the shapes that are parallelograms.

Answer:
Option 4 is correct.

Explanation:
In the above-given question,
given that,
the shapes are hexagon, rectangle, trapezoid, and parallelogram.
so option 4 is correct.

Question 4.
The necklace charm shown has one pair of m parallel sides. What type of quadrilateral is the charm? Explain.

Answer:
The charm is in the shape of a trapezoid.

Explanation:
In the above-given question,
given that,
The necklace charm shown has one pair of m parallel sides.
a trapezoid has one pair of parallel sides.
the above charm has one pair of parallel sides.
so the charm is in the shape of a trapezoid.

Question 5.
Identify the figure below using as many names as possible.

Answer:
The figure is a rhombus.

Explanation:
In the above-given question,
given that,
the square has 4 equal sides and 4 equal angles.
rhombus has 4 equal sides.
so the figure is a rhombus.

Question 6.
Claim 1: A square is a rectangle because it has 4 right angles.
Claim 2: A square is a rhombus because it has 4 equal sides.
Which claim is correct? Explain.

Answer:
Yes, both of them are correct.

Explanation:
In the above-given question,
given that,
a square is a rectangle because it has 4 right angles.
a square is a rhombus because it has 4 equal sides.
so both of them are correct.

Assessment Practice

Question 7.
Look at the rhombus and square below.

A. How are the two figures the same?
B. How are the two figures different?

Answer:
They are the same when they have 4 equal sides.
They are different when they have 4 equal right angles.

Explanation:
In the above-given question,
given that,
a square is a rectangle because it has 4 right angles.
a square is a rhombus because it has 4 equal sides.
they are the same when they have 4 equal sides.
they are different when they have 4 equal right angles.

Question 8.
Identify the figure below using as many names as possible.

Answer:
The polygon is a trapezoid.

Explanation:
In the above-given question,
given that,
the figure has 4 different sides.
so the polygon is a trapezoid.

Question 9.
Identify the figure below using as many names as possible.

Answer:
The polygon is a parallelogram.

Explanation:
In the above-given question,
given that,
the figure has opposite sides equal lengths.
parallelogram also has the opposite sides equal lengths.
so the polygon is a parallelogram.

Question 10.
What shape has two pairs of opposite sides that are parallel and has all sides of equal length but does NOT have four right angles?
A. Square
B. Rectangle
C. Rhombus
D. Trapezoid

Answer:
Option C is correct.

Explanation:
In the above-given question,
given that,
rhombus has two pairs of opposite sides that are parallel.
all sides of equal length but do not have 4 right angles.
so option C is correct.

Question 11.
Use the Venn diagram. Are rhombuses always, sometimes, or never also parallelograms? Explain.

Answer:
Rhombuses are always a parallelogram.

Explanation:
In the above-given question,
given that,
rhombuses are parallelograms.
rhombus is a parallelogram with 4 equal sides.
area of the rhombus = 4 a.
where a = side.
so rhombuses are always a parallelogram.

Question 12.
Describe triangle HJK in terms of its sides and angles.

Answer:
The triangle is an isosceles triangle.

Explanation:
In the above-given question,
given that,
triangle HJK is an isosceles triangle.
an isosceles triangle has 2 sides equal.
so the triangle HJK is an isosceles triangle.

Topic 16 Performance Task

Geometry in Art
Artists often use triangles and quadrilaterals in their pictures.

Question 1.
Use the Poster to answer the following questions.
Part A
Classify Triangle 1 in the Poster by its angles and by its sides.

Answer:
The triangle is a scalene triangle.

Explanation:
In the above-given question,
given that,
triangle 1 is a scalene triangle.
a scalene triangle has three different sides.

Part B
What are all of the names you can use to describe Shape 2 in the Poster?

Answer:
Shape 2 is a parallelogram.

Explanation:
In the above-given question,
given that,
shape 2 is a parallelogram.
a parallelogram has two pairs of equal parallel sides.
shape 2 is a parallelogram.

Part C
Triangles 3 and 4 are identical. They are joined in the Poster to form a square. Construct a math argument to show why Triangles 3 and 4 are isosceles right triangles.
Part D
If Triangle 3 is joined with another triangle that is the same size and shape, do the two triangles always form a square? Construct a math argument to explain your reasoning.
Part E
What are the measures of the angles of Triangle 3? Note that two angles in an isosceles triangle always have the same measure. Explain.

Answer:
Triangle 3 is a rhombus.

Explanation:
In the above-given question,
given that,
triangle 3 is a rhombus.
in the rhombus, there are 2 equilateral triangles.
triangles 3 and 4 are equilateral triangles.
so triangle 3 is a rhombus.

Question 2.
Classify the triangles and quadrilaterals in the Houses drawing to answer the following questions.
Part A
Are all the triangles shown in the design isosceles? Are they all equilateral? Construct a math argument, using properties, to explain why or why not.

Answer:
Yes, the triangles are equilateral and isosceles triangle.

Explanation:
In the above-given question,
given that,
there are equilateral and isosceles triangles.
an equilateral triangle has all the 3 sides are equal.
an isosceles triangle has only two sides that are equal.
so the triangles are both equilateral and isosceles triangle.

Part B
All of the quadrilaterals in the Houses drawing are rectangles. Does that mean all of the quadrilaterals are parallelograms? Does that mean all are squares? Construct a math argument, using properties, to explain your reasoning.

Answer:
Yes, all of the quadrilaterals in the house drawing are rectangles.

Explanation:
In the above-given question,
given that,
all of the quadrilaterals in the house drawing are rectangles.
all the quadrilaterals are parallelograms.
all squares are rectangles.
so all of the quadrilaterals in the house drawing are rectangles.