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Grade 7 · Mathematics · 30 minutes

Unit 2 · Equations and geometric models · Lesson 2 of 2

Scale Drawings and a Circular Garden

Translate a scaled plan into actual lengths and measure a circular feature.

Mr. S Teaches · Original starter mini-lesson · MS7-MATH-04

Learning objective

Use a drawing scale to calculate actual lengths and determine a circle’s circumference and area.

Before you begin

  • Proportional reasoning
  • Area units
  • Radius and diameter

Gather your materials

  • Paper and pencil
  • Ruler and graph paper

Language to know

scale
The relationship between a drawing length and an actual length.
circumference
The distance around a circle.
radius
The distance from a circle’s center to its edge.

Understand the concept

Every length in a scale drawing changes by the same factor. Areas change by the square of that factor, because two dimensions change. A circle’s circumference is 2πr and its area is πr². Rearranging many narrow circle sectors roughly forms a rectangle with height r and base half the circumference, which supports the area formula.

Teach it step by step

  1. Use a fictional plan with scale 1 cm : 2 m and a garden rectangle 3 cm by 5 cm.
  2. Calculate actual dimensions and area, then compare the drawing’s 15 cm² with the real 60 m².
  3. Add a circle of drawn radius 1 cm; calculate the actual radius rather than using the drawing length directly.
  4. Explain the sector rearrangement with a sketch and calculate circumference and area.
  5. Label each result as a length or an area and ask why the units differ.

Make the thinking visible

Worked example or model response

The rectangle measures 6 m by 10 m, so its area is 60 m². The circle’s actual radius is 2 m. Its circumference is 4π m (about 12.57 m) and area is 4π m² (about 12.57 m²); equal numerical values here do not mean equal measurements.

Guided practice

At scale 1 cm : 3 m, find the length of a 4 cm path. Calculate circumference and area for a circle with actual radius 3 m, leaving π in the answer.

Independent practice

1. A 2-by-4 cm rectangle uses scale 1 cm : 5 m. Find actual dimensions and area. 2. A circular pond has diameter 10 m. Find its circumference and area.

Quick assessment

Why is a 3 cm drawing length not necessarily a 3 m real length?

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: Path 12 m; circle circumference 6π m and area 9π m².
  2. Independent 1: 10 m by 20 m; 200 m². 2: Radius 5 m, circumference 10π m and area 25π m².
  3. Quick check: The drawing’s scale determines the conversion; units alone do not supply it.

Look for: Look for an explanation of the choices, not only a final answer. Require units and a check against the context.

Make it work for your learner

More support

Use a conversion table for each length and shade radius versus diameter in different colors.

Extension challenge

Redraw the same garden at half the drawing scale; explain how lengths and drawn area change.

Selected contributions · Official sources

Standards connections

Contributes to Common Core standard

7.G.A.1

Common Core · Grade 7

Convert scaled lengths and areas and reason about a changed drawing scale.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.

Contributes to Common Core standard

7.G.B.4

Common Core · Grade 7

Use circle formulas and explain the sector model behind area.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.