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Scale Drawings: Reading, Computing, and Reproducing Geometric Figures

Work through each section in order. Show your proportion setup for all scale problems.

Grade 7·~35 min·Common Core Math - Grade 7·standard·7-g-a-1

Work through problems with immediate feedback

Recall / Warm-Up

Which statement correctly describes the ratio 3 : 7?

For every 3 of one quantity there are 7 of another quantity.

The first quantity is 7 times as large as the second quantity.

The two quantities are equal.

The second quantity is 3 more than the first quantity.

Solve the proportion: $\\frac{1}{5} = \\frac{x}{20}$ . What is $x$ ?

What is the area of a rectangle with length 6 cm and width 4 cm?

10 cm²

20 cm²

24 cm²

48 cm²

Fluency Practice

$Proportion table with two rows: 1 cm corresponds to 5 m, and 4 cm corresponds to an unknown actual length.$

A scale drawing uses the scale 1 cm : 5 m. A room measures 4 cm long on the drawing.

What is the actual length of the room in meters?

A floor plan uses the scale 1 in : 8 ft. An actual wall is 24 ft long.

How many inches long is the wall on the floor plan?

A scale drawing uses the scale 1 cm : 3 m. A room measures 4.5 cm on the drawing.

Which proportion correctly sets up the calculation for the actual length?

$\\dfrac{1 \\text{ cm}}{3 \\text{ m}} = \\dfrac{4.5 \\text{ cm}}{? \\text{ m}}$

$\\dfrac{3 \\text{ m}}{1 \\text{ cm}} = \\dfrac{4.5 \\text{ m}}{? \\text{ cm}}$

$\\dfrac{1}{3} = \\dfrac{?}{4.5}$

$\\dfrac{1 \\text{ cm}}{4.5 \\text{ cm}} = \\dfrac{3 \\text{ m}}{? \\text{ m}}$

A city map uses the scale 2 cm : 7 km. Two landmarks are 8 cm apart on the map.

What is the actual distance between the landmarks in kilometers?

A scale drawing uses the scale 1 cm : 10 m. A rectangular room on the drawing is 5 cm long and 3 cm wide.

What is the actual area of the room in square meters?

Varied Practice

A scale drawing uses the scale 1 cm : 6 m. A room in reality is 7.5 m wide. How long is the room's width on the drawing?

1.25 cm

45 cm

1.5 cm

13.5 cm

$Scale drawing of a rectangle labeled 3 cm along the top edge and 2 cm along the right edge, with scale 1 cm : 4 m noted inside.$

A scale drawing uses the scale 1 cm : 4 m. A rectangle on the drawing is 3 cm long and 2 cm wide.

Actual length: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ m.
Actual area: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ m².

Actual length (m):

Actual area (m²):

A drawing was originally made at a scale of 1 cm : 6 m. It is redrawn at a new scale of 1 cm : 2 m.

How many times larger is the new drawing compared to the original? Enter the number.

$Three-element flowchart: original drawing at scale 1 cm : 4 m on the left, actual size oval in the center, and new drawing at scale 1 cm : 2 m on the right.$

A hallway on a floor plan is drawn at the scale 1 cm : 4 m. The hallway appears as a rectangle 3 cm long and 0.5 cm wide on the drawing.

Find the actual dimensions. Actual length: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ m. Actual width: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ m.

Actual length (m):

Actual width (m):

The hallway is redrawn at a scale of 1 cm : 2 m. New drawing length: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ cm. New drawing width: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ cm.

New length (cm):

New width (cm):

Word Problems

$Floor plan of a living room rectangle labeled 2.5 in long and 1.5 in wide, with a scale of 1 in : 10 ft noted in the corner.$

An architect draws a floor plan at the scale 1 in : 10 ft. The living room on the floor plan measures 2.5 in long and 1.5 in wide.

What is the actual length of the living room in feet?

What is the actual width of the living room in feet?

What is the actual area of the living room?

3.75 ft²

37.5 ft²

250 ft²

375 ft²

A city map uses the scale 1 cm : 25 km. Priya measures the distance between two cities on the map and finds it is 3.4 cm.

What is the actual distance between the two cities in kilometers?

A model car is built at a scale of 1:24. The model is 18 cm long.

What is the actual length of the car in meters?

A triangular garden is shown on a scale drawing at the scale 1 cm : 3 m. On the drawing, the triangle has a base of 4 cm and a height of 3 cm.

What is the actual area of the garden in square meters?

Error Analysis

$Two-column contrast card: Tariq's error (multiplying drawing area by k to get 240 m²) on the left versus the correct method (scaling each dimension by k first to get 2400 m²) on the right.$

Tariq solved this problem: "A park is drawn at the scale 1 cm : 10 m. The park appears as a 4 cm × 6 cm rectangle on the drawing. Find the actual area of the park."

Tariq's work:

Drawing area = $4 \times 6 = 24$ cm²
Actual area = $24 \times 10 = 240$ m²

What error did Tariq make, and what is the correct actual area?

Tariq found the drawing area correctly but should have multiplied by $10^2 = 100$ , not 10. Correct area = $24 \\times 100 = 2400$ m².

Tariq used the wrong scale factor. He should have multiplied by $\\frac{1}{10}$ instead of 10. Correct area = 2.4 m².

Tariq made no error. 240 m² is correct.

Tariq should have found the actual length and width first, then divided their product by 10. Correct area = 240 m².

$Two-column contrast card: Leila's error (multiplying 30 × 5 = 150 cm) on the left versus the correct method (dividing 30 ÷ 5 = 6 cm) on the right.$

Leila solved this problem: "A floor plan uses the scale 1 cm : 5 m. A room in the actual building is 30 m long. How long is the room on the floor plan?"

Leila's work:

$30 \times 5 = 150$ cm
The room is 150 cm long on the floor plan.

What error did Leila make, and what is the correct drawing length?

Leila multiplied instead of dividing. Going from actual to drawing, you divide by the scale factor: $30 \\div 5 = 6$ cm.

Leila used the wrong scale factor. She should have used $\\frac{1}{30}$ instead. Correct length = $\\frac{5}{30} \\approx 0.17$ cm.

Leila made no error. 150 cm is the correct drawing length.

Leila should have added the scale factor: $30 + 5 = 35$ cm.

Challenge

A garden is drawn at a scale of 1 cm : 5 m. On the original drawing, the garden appears as a rectangle 4 cm long and 3 cm wide.

The garden is then redrawn at a new scale of 1 cm : 2 m.

What is the actual area of the garden in square meters? (The area is the same regardless of which drawing scale is used.)

An L-shaped room is drawn on a floor plan at the scale 1 cm : 3 m. The L-shape is made up of two non-overlapping rectangles:

Left portion: 4 cm wide and 5 cm tall on the drawing
Right portion: 2 cm wide and 3 cm tall on the drawing

Find the total actual area of the L-shaped room in square meters. Show all steps.

0 of 23 answered