Cogito
Grade 7 Math · Chapter 1 · Lesson 2
Scale Drawings and Area
Doubling the sides does not double the area.
10 problems · about 18 minutes · 7.G.A.1
What this lesson teaches
The child uses a scale to find real lengths and understands how area changes under scaling.
- A scale converts map lengths to real ones.
- Lengths scale by the factor.
- Area scales by the factor squared.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Scale Copies: A 9 cm side becomes 27 cm. What is the scale factor?
Answer 3
Why 3.
Review — Scale Copies: What makes a copy a scale copy?
Answer Every length multiplied by the same factor.
Why One factor applied to every length.
Warm Up
Straightforward practice. Get the method working first.
4 problemsA shape is scaled by 3. How many times bigger is its area?
Answer 9
Why 9 times.
Why does doubling the sides quadruple the area?
Answer Both the length and the width doubled.
Why 2 × 2 = 4.
Scale 1 cm to 3 km. How far is 12 cm?
Answer 36
Why 12 × 3.
A shape scaled by 2. How many times bigger is the area?
Answer 4
Why 2 squared.
Build It Up
The same ideas with more to keep track of.
2 problemsA shape scaled by 5. How many times bigger is the area?
Answer 25
Why 5 squared.
Scale 1 cm to 10 km. A distance is 70 km. How many cm on the map?
Answer 7
Why 70 ÷ 10.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Map: A map scale is 1 cm to 6 km. How far is 8 cm?
Answer 48 km
Why 48 km.
The Area: A shape is scaled by 4. How many times bigger is its area?
Answer 16 times
Why 16 times.