Cogito
Grade 7 Math · Chapter 1 · Lesson 3
Reading a Scale
One centimetre on the map, half a kilometre on the ground.
10 problems · about 18 minutes · 7.G.A.1
What this lesson teaches
The child uses a stated scale to convert between drawing lengths and real lengths.
- A scale is a rate between drawing length and real length.
- Drawing to real multiplies; real to drawing divides.
- Estimate first so a wrong operation shows up immediately.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Scale Drawings and Area: A shape is scaled by 3. How many times bigger is its area?
Answer 9
Why 9 times.
Review — Scale Copies: A 9 cm side becomes 27 cm. What is the scale factor?
Answer 3
Why 3.
Review — Scale Drawings and Area: Why does doubling the sides quadruple the area?
Answer Both the length and the width doubled.
Why 2 × 2 = 4.
Warm Up
Straightforward practice. Get the method working first.
3 problemsScale 1 cm to 30 km. Real distance for 5 cm, in km?
Answer 150
Why 150 km.
Scale 1 cm to 5 km. Real distance for 7 cm, in km?
Answer 35
Why × 5.
Scale 1 cm to 5 km. Map length for 60 km, in cm?
Answer 12
Why ÷ 5.
Build It Up
The same ideas with more to keep track of.
2 problemsScale 1 cm to 250 m. Real distance for 4 cm, in metres?
Answer 1000
Why × 250.
Going from a real length to a map length, do you multiply or divide? Answer 1 for multiply, 2 for divide.
Answer 2
Why The map length is the smaller number.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Map: Scale 1 cm to 20 km. How many km is 8 cm?
Answer 160
Why 160 km.
The Other Way: Scale 1 cm to 20 km. How many cm on the map is 300 km?
Answer 15
Why 15 cm.