CH06-02 lesson

Reproducing Scale Drawings at a Different Scale Learning Activity

A focused Grade 7 learning session for Reproducing Scale Drawings at a Different Scale using visual models, worked examples, strategy guidance, and a short mastery check.

Start the lesson Print practice sample
15
minutes
6
lesson parts
11
practice items
Learning goal

Students will build Grade 7 mastery of reproducing scale drawings at a different scale using models, equations, and test-style reasoning.

Student goal: I can solve problems involving reproducing scale drawings at a different scale.

Helpful first: Understanding and Using Scale Drawings
concept

Learn the Idea

Reproducing Scale Drawings at a Different Scale is part of Grade 7 Geometry and Scale. This activity focuses on the central idea students need before they move into independent practice.

Students will build Grade 7 mastery of reproducing scale drawings at a different scale using models, equations, and test-style reasoning.

visual model

See the Math

What to noticeHow to use it
Numbers, units, labels, diagrams, or graphsIdentify what each part represents before calculating.
The relationship in the problemConnect the model to an equation, comparison, or explanation.

Use the figures and worked questions in the practice set below as the visual model for this skill.

worked example

Follow a Worked Example

Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.

For Reproducing Scale Drawings at a Different Scale, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.

real world

Connect It to a Real Situation

Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.

After solving, explain what the answer means in the situation, not just the number you calculated.

strategy

Avoid Mistakes and Choose a Strategy

  • Underline the exact question before solving.
  • Label units, variables, or graph axes when they appear.
  • Estimate first so unreasonable answers are easier to catch.
  • Review missed questions and write the reason for each mistake.
summary

Remember the Key Idea

I can solve problems involving reproducing scale drawings at a different scale.

Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.

Guided to independent practice

Solve before opening the answer

Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.

warmup

2 questions
G7-C06-T02-Q001 About 1 min

A rectangle has dimensions \(4\) in by \(6\) in at a scale of \(1\) in \(:2\) ft. If redrawn at a new scale of \(1\) in \(:4\) ft, what are the new dimensions?

  1. A \(1\) in by \(1.5\) in
  2. B \(2\) in by \(3\) in
  3. C \(8\) in by \(12\) in
  4. D \(16\) in by \(24\) in
Check answer and explanation

Answer B: \(2\) in by \(3\) in

At scale 1:2, the drawing is \(4 \times 6\) in representing a fixed real object. At scale 1:4, the same object is represented differently. The ratio of real-world per drawing unit goes from 2 to 4 (doubled), so the drawing must shrink by factor \(4 \div 2 = 2\). New dimensions: \(4 \div 2 = 2\) in and \(6 \div 2 = 3\) in.

G7-C06-T02-Q002 About 1 min

A blueprint shows a room measuring \(3\) cm by \(5\) cm at a scale of \(1\) cm \(:1\) m. What are the actual room dimensions?

  1. A \(3\) m by \(5\) m
  2. B \(300\) cm by \(500\) cm
  3. C \(1\) m by \(1.67\) m
  4. D \(6\) m by \(10\) m
Check answer and explanation

Answer A: \(3\) m by \(5\) m

Scale 1 cm : 1 m means 1 cm on the drawing represents 1 m in reality. Scale factor is 1 m per cm. Multiply each drawing dimension by the scale factor: \(3 \text{ cm} \times 1 \text{ m/cm} = 3\) m and \(5 \text{ cm} \times 1 \text{ m/cm} = 5\) m. This foundational skill (single scale) is the basis for comparing two scales in later problems.

guided

1 question
G7-C06-T02-Q003 About 1 min

A scale model of a car is drawn at a scale of \(1\) in \(:5\) ft. If the model is \(8\) inches long, what is the length of the actual car?

  1. A \(13\) ft
  2. B \(40\) ft
  3. C \(45\) ft
  4. D \(64\) ft
Check answer and explanation

Answer B: \(40\) ft

Scale 1 in : 5 ft means 1 inch on the model represents 5 feet in reality. Scale factor is 5 ft per inch. To find actual length, multiply: \(8 \text{ in} \times 5 \text{ ft/in} = 40\) ft. The scale factor (5 ft/in) is the key ratio that converts drawing dimensions to real-world dimensions.

practice

5 questions
G7-C06-T02-Q004 About 1 min

A rectangle on a map has length \(7\) cm and width \(4\) cm. The map scale is \(1\) cm \(:2\) km. When the map is enlarged so that the new scale becomes \(1\) cm \(:1\) km, what are the new dimensions?

  1. A \(7\) cm by \(4\) cm
  2. B \(14\) cm by \(8\) cm
  3. C \(3.5\) cm by \(2\) cm
  4. D \(3\) cm by \(2\) cm
Check answer and explanation

Answer B: \(14\) cm by \(8\) cm

Original scale 1:2 means 1 cm = 2 km. New scale 1:1 means 1 cm = 1 km. The real-world distance per cm is halved, so the drawing must double in size. Scale factor ratio: \(1 \div 2 = 0.5\), reciprocal shrink \(= 2\). New dimensions: \(7 \times 2 = 14\) cm and \(4 \times 2 = 8\) cm.

G7-C06-T02-Q005 About 1 min

A floor plan shows a rectangular office that is \(2.5\) inches by \(3.5\) inches at a scale of \(1\) in \(:10\) ft. Which pair of measurements are the actual office dimensions?

  1. A \(25\) ft by \(35\) ft
  2. B \(2.5\) ft by \(3.5\) ft
  3. C \(12.5\) ft by \(17.5\) ft
  4. D \(20\) ft by \(28\) ft
Check answer and explanation

Answer A: \(25\) ft by \(35\) ft

Multiply drawing dimensions by scale factor: \(2.5 \times 10 = 25\) ft and \(3.5 \times 10 = 35\) ft.

G7-C06-T02-Q006 About 1 min

A scale drawing of a rectangular garden is \(6\) cm long at a scale of \(1\) cm \(:0.5\) m. If the scale is changed to \(1\) cm \(:1\) m, what will be the new length?

  1. A \(3\) cm
  2. B \(6\) cm
  3. C \(12\) cm
  4. D \(24\) cm
Check answer and explanation

Answer A: \(3\) cm

Original scale 1:0.5 means 1 cm = 0.5 m. New scale 1:1 means 1 cm = 1 m. Real-world distance per cm doubled (0.5 to 1), so the drawing shrinks. Scale factor ratio: \(1 \div 0.5 = 2\), so drawing shrinks by factor \(1 \div 2 = 0.5\). New length: \(6 \times 0.5 = 3\) cm (or \(6 \div 2 = 3\) cm).

G7-C06-T02-Q007 About 1 min

A blueprint of a house wing shows a rectangular area \(5\) cm by \(7\) cm at scale \(1\) cm \(:3\) m. A new blueprint is drawn at scale \(1\) cm \(:6\) m. What are the dimensions on the new blueprint?

  1. A \(2.5\) cm by \(3.5\) cm
  2. B \(5\) cm by \(7\) cm
  3. C \(10\) cm by \(14\) cm
  4. D \(15\) cm by \(21\) cm
Check answer and explanation

Answer A: \(2.5\) cm by \(3.5\) cm

Original scale 1:3 means 1 cm = 3 m. New scale 1:6 means 1 cm = 6 m. Real-world distance per cm doubled (3 to 6), so drawing shrinks by factor \(3 \div 6 = 0.5\) (or multiply by reciprocal 6 ÷ 3 = 2, then invert: 1/2). New dimensions: \(5 \div 2 = 2.5\) cm and \(7 \div 2 = 3.5\) cm.

G7-C06-T02-Q008 About 1 min

A scale model of a rectangular stage is \(10\) cm wide. The scale is \(1\) cm \(:0.4\) m. How many meters wide is the actual stage?

  1. A \(0.4\) m
  2. B \(2.5\) m
  3. C \(4\) m
  4. D \(40\) m
Check answer and explanation

Answer C: \(4\) m

Multiply drawing width by scale factor: \(10 \text{ cm} \times 0.4 \text{ m/cm} = 4\) m.

exit

3 questions
G7-C06-T02-Q009 About 1 min

A landscape drawing shows a rectangular flower bed \(8\) inches by \(12\) inches at scale \(1\) in \(:2\) ft. What are the dimensions of the actual flower bed?

  1. A \(2\) ft by \(3\) ft
  2. B \(4\) ft by \(6\) ft
  3. C \(16\) ft by \(24\) ft
  4. D \(32\) ft by \(48\) ft
Check answer and explanation

Answer C: \(16\) ft by \(24\) ft

Multiply by scale factor: \(8 \text{ in} \times 2 \text{ ft/in} = 16\) ft and \(12 \times 2 = 24\) ft.

G7-C06-T02-Q010 About 1 min

A rectangular pool on a site plan is \(4\) cm by \(6\) cm at scale \(1\) cm \(:5\) m. When enlarged to scale \(1\) cm \(:2.5\) m, what will be the new dimensions?

  1. A \(2\) cm by \(3\) cm
  2. B \(4\) cm by \(6\) cm
  3. C \(8\) cm by \(12\) cm
  4. D \(20\) cm by \(30\) cm
Check answer and explanation

Answer C: \(8\) cm by \(12\) cm

Original scale 1:5 means 1 cm = 5 m. New scale 1:2.5 means 1 cm = 2.5 m. Real-world distance per cm halved (5 to 2.5), so drawing expands. Scale factor ratio: \(2.5 \div 5 = 0.5\), so drawing dimension ratio = \(1 \div 0.5 = 2\). New dimensions: \(4 \times 2 = 8\) cm and \(6 \times 2 = 12\) cm.

G7-C06-T02-Q011 About 1 min

A school gymnasium is drawn at \(9\) cm by \(15\) cm on a blueprint with scale \(1\) cm \(:4\) m. The drawing is redone at scale \(1\) cm \(:2\) m. How many centimeters long is the gym on the new blueprint?

  1. A \(7.5\) cm
  2. B \(15\) cm
  3. C \(30\) cm
  4. D \(60\) cm
Check answer and explanation

Answer C: \(30\) cm

Halving the real scale (4 m to 2 m) doubles the drawing: \(15 \times 2 = 30\) cm.

Keep the learning path connected
Previous skillUnderstanding and Using Scale Drawings Recommended nextDrawing Geometric Figures with Given Conditions Same strandUnderstanding and Using Scale Drawings Same strandDrawing Geometric Figures with Given Conditions
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