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Year 10
Higher

Checking and securing understanding of equivalent ratios

I can appreciate that any two numbers can be connected via a multiplicative relationship.

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New
New
Year 10
Higher

Checking and securing understanding of equivalent ratios

I can appreciate that any two numbers can be connected via a multiplicative relationship.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A multiplicative relationship is a proportional relationship.
  2. This multiplier can be thought of as a scaling factor.
  3. The multiplier can be deduced through unitising.
  4. Any value divided by itself is equal to one.
  5. One is the multiplicative identity.

Common misconception

Finding the additive relationship between two numbers instead of the multiplicative one.

When dealing with any proportional relationships, such as ratios, pupils should be reminded to look for the multiplicative relationship. Using 1 as a middle step can help. e.g. to connect 5 and 8, divide by 5 to make 1 and then multiply by 8.

Keywords

  • Reciprocal - A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

Remind pupils that the multiplicative relationship within the parts of a ratio can be easier to use than going between ratios when finding missing parts of equivalent ratios.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
What is the ratio of triangles to circles in its simplest form?
An image in a quiz
Correct answer: 4 : 3
8 : 6
3 : 4
6 : 8
2 : 1.5
Q2.
Select the ratio of shaded to unshaded squares written in its simplest form.
An image in a quiz
Correct answer: 1 : 3
1 : 4
3 : 9
3 : 1
Q3.
Write the ratio 18 : 12 in its simplest form
Correct Answer: 3 : 2, 3:2
Q4.
Which of these are unitary ratios?
0.1 : 11
Correct answer: 13 : 1
Correct answer: 1.5 : 1
Correct answer: 1 : 8 : 4
11 : 5
Q5.
Write the ratio of triangles to circles in the form $$1 : n$$ where $$n$$ is a decimal.
An image in a quiz
Correct Answer: 1 : 0.75, 1:0.75
Q6.
A recipe uses 240 g of flour and 3 eggs. Write the ratio of number of eggs : grams flour in the form 1 : $$n$$
Correct Answer: 1 : 80, 1:80

Exit quiz

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6 Questions

Q1.
Equivalent ratios are ratios which represent the same
Correct Answer: proportion
Q2.
Write the single multiplier which connects the two numbers shown. Give your answer as a decimal.
An image in a quiz
Correct Answer: 1.25
Q3.
Find the correct value to complete the ratio table.
An image in a quiz
Correct Answer: 6
Q4.
Match up the equivalent ratios.
Correct Answer:3 : 4,15 : 20

15 : 20

Correct Answer:12 : 18,30 : 45

30 : 45

Correct Answer:4 : 3,40 : 30

40 : 30

Correct Answer:8 : 10,20 : 25

20 : 25

Correct Answer:5 : 3,25 : 15

25 : 15

Q5.
Match each of the letters to the number they represent in this ratio table.
An image in a quiz
Correct Answer:a,$$\frac{5}{4}$$

$$\frac{5}{4}$$

Correct Answer:b,$$\frac{4}{3}$$

$$\frac{4}{3}$$

Correct Answer:c,$$\frac{4}{5}$$

$$\frac{4}{5}$$

Correct Answer:d,$$\frac{3}{4}$$

$$\frac{3}{4}$$

Q6.
Select the ratio which is not equivalent to 1 : 5
11 : 55
12 : 60
60 : 300
Correct answer: 80 : 320
90 : 450