Use a scale factor
If every side doubles, the scale factor is 2.
| Original | Enlarged |
|---|---|
| 3 cm | 6 cm |
| 5 cm | 10 cm |
Each matching side changes by the same multiplier.
Year 6
Solve problems involving similar shapes where the scale factor is known or can be found and solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
Use scale factors, grouping and unequal sharing in simple proportional problems.
Lesson overview
Ratio and proportion
A scale factor enlarges or shrinks every matching side by the same amount. Unequal sharing means dividing a total into linked parts rather than equal parts.
Unequal sharing
A total of 30 shared in the ratio 2:3 gives 12 and 18.
Find the value of one part first.
Worked example
Share 30 in the ratio 2:3.
| Parts | Total |
|---|---|
| 2 + 3 = 5 parts | 30 |
- There are 5 parts altogether.
- 30 divided by 5 gives 6 for one part.
- 2 parts = 12 and 3 parts = 18.
- So the total is shared as 12 and 18.
Try it
Work out how many equal ratio parts there are before finding each amount.
Question 1
If 4 cm enlarges to 12 cm, the scale factor is:
Question 2
Share 30 in the ratio 2:3. The two parts are:
Question 3
Which pair has scale factor 2?
| Original | New |
|---|---|
| 5 | 10 |
Question 4
Share 24 in the ratio 1:3. The larger part is:
| Total parts | Value of 1 part |
|---|---|
| 4 | 6 |
Question 5
If a side length triples, 7 cm becomes:
Common mistakes
Watch for these when working through the lesson.
- Adding or subtracting instead of scaling.
- Forgetting that the total number of parts matters in unequal sharing.
- Changing one side length without using the same scale factor on the others.
Related topics
These ideas fit closely with this lesson.
- Solve problems involving the relative sizes of two quantities.
- Calculate the area of parallelograms and triangles.