Cogito
Grade 7 Math · Chapter 1 · Lesson 4
Redrawing at a New Scale
The same object, a different size of picture.
10 problems · about 18 minutes · 7.G.A.1
What this lesson teaches
The child reproduces a scale drawing at a different scale and finds the new lengths.
- To change scale, go through the real length.
- Old drawing to real, then real to new drawing.
- A scale covering more ground per centimetre makes a smaller drawing.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Reading a Scale: Scale 1 cm to 30 km. Real distance for 5 cm, in km?
Answer 150
Why 150 km.
Review — 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.
Warm Up
Straightforward practice. Get the method working first.
3 problems9 cm at 1 cm to 2 m, redrawn at 1 cm to 3 m. New length in cm?
Answer 6
Why 6 cm.
6 cm at 1 cm to 4 m. Real length in metres?
Answer 24
Why × 4.
That 24 m at 1 cm to 8 m. Drawing length in cm?
Answer 3
Why ÷ 8.
Build It Up
The same ideas with more to keep track of.
2 problems5 cm at 1 cm to 10 m, redrawn at 1 cm to 5 m. New length in cm?
Answer 10
Why Real is 50 m.
If each centimetre covers more ground, does the drawing get bigger or smaller? Answer 1 for bigger, 2 for smaller.
Answer 2
Why Fewer centimetres are needed.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Redraw: 10 cm at 1 cm to 2 m. What is the real length, in metres?
Answer 20
Why 20 m.
The New Plan: That same 20 m, drawn at 1 cm to 5 m. How many cm?
Answer 4
Why 4 cm.