# Into Math Grade 7 Module 1 Lesson 6 Answer Key Practice Proportional Reasoning with Scale Drawings

We included HMH Into Math Grade 7 Answer Key PDF Module 1 Lesson 6 Practice Proportional Reasoning with Scale Drawings to make students experts in learning maths.

## HMH Into Math Grade 7 Module 1 Lesson 6 Answer Key Practice Proportional Reasoning with Scale Drawings

I Can make scale drawings and use them to find actual dimensions.

Step It Out
The scale on a scale drawing can be shown in the same unit or in different units.

Connect to Vocabulary
A scale is a ratio between two sets of measurements. A scale drawing is a proportional two dimensional drawing of an object.

1. Mario’s school is building a basketball court from the scale drawing.

A. The table shows some lengths from the drawing and the corresponding lengths on the actual court. How can you tell this is a scale drawing?
________________________
________________________
Answer: By converting the actual length from feet to inches we can find the scale drawing.

B. What is the scale of the drawing in inches to feet? ________________________
1 feet = 12 inches
Actual length = 12 feet
Convert from feet to inches
12 × 12 = 144 inch
The scale is 0.6 : 144
Divide by 0.6 to find the scale length
0.6:144 = 1:240
So, the scale of the drawing in inches to feet is 1:240

C. Write an equation for the proportional relationship between the actual length in feet x and the drawing length in inches y. ____________
x = 12y

D. Use your equation from Part C to find the actual length represented by a scale drawing length of 1.5 inches, and to find the scale drawing length that represents an actual length of 70 feet.
____ = $$\frac{1}{20}$$x, so x = ___
1.5 inches represents an actual length of ___ feet.
y = $$\frac{1}{20}$$ _______ = _______
70 feet represents a drawing length of _______ inches.
1.5 = $$\frac{1}{20}$$x
x = 30
y = $$\frac{1}{20}$$ 30

2. What is the relationship between area in the scale drawing and area on the actual basketball court?

A. Show how to find the area of the court in the scale drawing.
_____________________
Length = 4.2 in
Width = 2.5 in
Area of the court = l × w
A = 4.2 × 2.5
A =  10.50 sq. inches

B. Show how to find the length and width of the actual court.
_____________________
Scale = 1:20 ft
Length = 4.2 × 20 = 84 ft
Width = 2.5 × 20 = 50 ft

C. What is the area of the actual basketball court? Show your work.
_____________________
Length = 84 ft
Width = 50 ft
Area = 84 × 50 = 4200 sq. ft

D. Is the ratio of actual area to drawing area the same as the ratio of actual lengths to drawing lengths? Explain.
_____________________
_____________________
_____________________
Answer: No, the ratio of actual area to drawing area is the same as the ratio of actual lengths to drawing lengths.

Turn and Talk Is there a relationship between the scale for area and the scale for length? If so, describe the relationship.

3. Mario’s school is also planning to make a rectangular garden 60 feet wide by 70 feet long. On the grid provided, make a scale drawing of the rectangular garden using the scale given.

A. Write an equation for the actual length y based on a drawing length x.
_____________________
_____________________
The ratio is 3 units:20 ft
Let actual length be y
drawing length be x
3y = 20x
y = 20/3x
y = 6.66x

B. Use the equation you wrote in Part A to find the scale drawing lengths. Then make the scale drawing.
_____________________
_____________________

Turn and Talk How could you write an equation for the drawing length y based on an actual length x?

4. Mario’s school is also planning a smaller rectangular area as a sitting spot. A scale drawing of the sitting spot is shown. Redraw the sitting spot on the grid at a scale of

A. Write and simplify the ratio of the new scale to the original scale.

B. Each side of the new drawing will be (longer / shorter) than the corresponding side of the original drawing.
C. Draw the rectangle for the new scale.

Turn and Talk What is another way you could have found the dimensions of your new scale drawing?

Check Understanding

Question 1.
The dimensions of an Olympic swimming pool are shown. A scale drawing of the swimming pool has dimensions of 50 centimeters by 100 centimeters and a diagonal that is about 112 centimeters long.
A. What is the scale of the drawing in centimeters to meters?_____
100cm/50m = 2cm/m

B. What is the actual length of the diagonal of the pool? __________

Answer: The diagonal is 112 cm
112 ÷ 2 = 56 m
The diagonal is 56m

Question 2.
A different scale drawing of the same Olympic pool uses a scale of $$\frac{5 \mathrm{~cm}}{1 \mathrm{~m}}$$. What are the dimensions of the drawing? _______________
If the scale is $$\frac{5 \mathrm{~cm}}{1 \mathrm{~m}}$$, the dimensions of the drawing is 125 cm by 250 centimeters.
125/250 = 1/2

Question 3.
Use Structure Veronica’s town is building a tennis court using the scale drawing below. Find the scale between the drawing and the actual court. Then use the scale to show how a given length on the drawing represents a length on the tennis court, and how a given length on the tennis court is represented in the drawing.

A. The table shows some lengths in the drawing and the corresponding lengths on the actual court. Explain how you can tell from the table that the drawing is a scale drawing.

_____________________
_____________________

B. What is the ratio between the actual length and the drawing length as a unit rate?
_____________________
Every 1 inch in the picture represents 5 ft of the actual length
The ratio between the actual length and the drawing length as a unit rate is 5:1.

C. Write an equation for the proportional relationship between the drawing lengths and the court lengths, where x is length in the drawing in inches and y is length on the court in feet.
_____________________
where,
x is the length in the drawing in inches and
y is the length on the court in feet.

D. Use your equation from Part C to find the actual length represented by a scale drawing length of 3.5 inches.
_____________________
If drawing length = 3.5 inch
then actual length = 3.5 × 5 = 17.5 feet

E. Use your equation from Part C to find the scale drawing length that represents an actual length of 40 feet.
_____________________
The ratio of the actual length and the drawing length as a unit rate is 5:1.
40/5 = 8
So, the drawing length = 8 in.

Question 4.
What is the relationship between area in the scale drawing and area on the actual tennis court?

A. Show how to find the area of the scale drawing of the tennis court.
Given,
Length = 15.6 in
width = 7.2 in
Area = 15.6 × 7.2 = 112.32 sq. in/

B. Show how to find the length and width of the actual court.
The ratio is 1 in : 5 ft
Length = 15.6 × 5 = 78 ft
Width = 7.2 × 5 = 36 ft

C. Show how to find the area of the actual tennis court.
78 × 36 = 2808 sq. ft
Thus the area of the actual tennis court is 2808 sq. ft

D. Attend to Precision What is the ratio of the area of the actual court to the area of the drawing (as a unit rate)? Is it the same as the ratio of the length of the actual court to the length of the drawing? How do you know?
__________________________
__________________________
__________________________
__________________________
The ratio of the area of the actual court to the area of the drawing is equal
78:36 = 15.6:7.2

Question 5.
The students in Suzanne’s school are painting a rectangular mural outside the building that will be 15 feet by 45 feet.
A. Write the unit rate for the proportional relationship between lengths on the mural y and lengths in the scale drawing x.

The actual scale of mural is 15 × 45
Picture scale of the mural is 2 × 6
y/x = 45/6 = 15/2 = 7.5

B. Model with Mathematics Write an equation that relates x and y. The diagonal of the scale drawing is approximately 6.3 units. Estimate the length of the diagonal of the mural.
_____________________
y = 7.5x
The diagonal of the scale drawing is approx 6.3 units
The length of the diagonal of the mural is 47.25 ft
y = 7.5 × 6.3 = 47.25

Question 6.
The students at Suzanne’s school are also going to paint a smaller mural inside the building. A scale drawing of the mural is shown on the grid.

A. Redraw the inside mural on the grid using a scale of 1 unit:1 foot.

B. How many grid units are there for every 3 feet of mural in the original scale? How many grid units are there for every 3 feet of mural in the new scale?
Answer: There is 1 grid unit for every 3 feet of mural in the original scale.

C. What is the length of your scale drawing compared to the length of the original scale drawing?

D. How does the area of your drawing compare to the original area?
_______________________

Lesson 6.5 More Practice/Homework

Question 1.
Model with Mathematics Martine’s town is building a volleyball court based on a scale drawing that is 40 centimeters by 80 centimeters and uses the scale 1 cm:22.5 cm.
A. Write an equation for the proportional relationship between drawing court lengths x in centimeters and court lengths y in centimeters.

B. What are the length and width in meters of the actual court? Show your work.
____________________________
____________________________
Given,
Martine’s town is building a volleyball court based on a scale drawing that is 40 centimeters by 80 centimeters and uses the scale 1 cm:22.5 cm.
y = 22.5x
y = 80 × 22.5 = 1800 cm
x = 40 × 22.5 = 900 cm

C. Write the ratio of the area of the actual court to the area of the court in the scale drawing.
____________________________
40:80 = 1:2
900:1800 = 1:2
Thus the ratio of the area of the actual court to the area of the court in the scale drawing is 1:2

Question 2.
The students in Roberto’s school are painting a mural that will be 8 feet by 15 feet. First they make a scale drawing of the mural with a scale of 2 feet:5 feet.
A. Write an equation for the proportional relationship between drawing mural lengths x in feet and mural lengths y in feet.
_______________________
Given,
The students in Roberto’s school are painting a mural that will be 8 feet by 15 feet.
y = 15 ft
x = 8 ft
So, y = 2x – 1

B. What are the length and width of the scale drawing in feet? Show your work.
_______________________
Scale is 2ft : 5 ft
2 ft represents 5 ft
So, the length is 8 ft which will be represented by 2/5 × 8 = 3.2 ft
width is 15 ft represented by 6 feet.

C. Open Ended Choose a different scale and use it to make a scale drawing of the mural that will fit on a piece of graph paper.
_______________________

Question 3.
Geography A map has a scale of 1 in.:10 mi. Find the distance on the map between two cities that lie 147 miles apart. Show your work.
_______________________
Given,
A map has a scale of 1 in.:10 mi.
147 ÷ 10 = 14.7

Test Prep

Question 4.
Ricardo draws a scale model of the floor plan of his house. His house is 60 feet long and 40 feet wide. He uses the scale to draw his model. Which statements are true? Select all that apply.
A. The equation l = $$\frac{1}{4}$$(60) can be used to find the length of the scale model.

B. The equation w = (4)(40) can be used to find the width of the scale model.

C. The width of the scale model is 10 inches.

D The length of the scale model is 240 inches.

E. The scale means that 1 inch in the model represents 4 feet in the house.
1 in = 4 ft
x in = 60 ft
60 = 4x
x = 60/4
x = 15
1 in = 4 ft
y = 40 ft
4y = 40
y = 40/4 = 10 in
Thus Option A, C and E are correct statements.

Question 5.
A scale drawing of an elephant shows the animal as 6 inches high and 10.8 inches long. The scale used for the drawing was 3 in.:5 ft.
What are the height and length of the actual elephant?
Height: ___ feet Length: ____ feet
Given,
A scale drawing of an elephant shows the animal as 6 inches high and 10.8 inches long.
The scale used for the drawing was 3 in.:5 ft.
6/3 = 2 in
2 × 5in = 10 ft
First find out how many times 3 fits into 10.8, which is 3.6 times.
3.6 × 5 = 18 ft
Thus length is 10 ft and the height is 18 ft.

Question 6.
Town planners are planning a 500-foot by 700-foot parking lot by making a scale drawing that is 90 inches by 126 inches. What is the scale of inches in the drawing to inches in the actual object?
A. 3:200
B. 1:300
C. 2:30
D. 1:200
Given,
Town planners are planning a 500-foot by 700-foot parking lot by making a scale drawing that is 90 inches by 126 inches.
convert from feet to inches
500 × 12 = 6000 inch
90:6000 = 3:200
126: (700 × 12)
126:8400
21:1400
3:200
Thus option A is the correct answer.

Spiral Review

Question 7.
A machine produces parts at a steady rate of 160 parts in 8 hours. Complete the table for this relationship.

Given,
A machine produces parts at a steady rate of 160 parts in 8 hours.
160:8 = 20:1

Question 8.
The table shows possible numbers of basketball teams in a league and the number of jerseys needed for the number of teams.
A. Graph the relationship between the number of teams in the league and the number of jerseys needed.