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Year 7

Equivalent multiplicative relationships

I can appreciate that there are an infinite number of pairs of numbers for any given multiplicative relationship.

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New
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Year 7

Equivalent multiplicative relationships

I can appreciate that there are an infinite number of pairs of numbers for any given multiplicative relationship.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. There is a multiplicative relationship between the ratio parts, and other equivalent ratios.
  2. Ratios can be expressed as fractions.
  3. There are infinitely many equivalent fractions.
  4. There are infinitely many equivalent ratios.

Keywords

  • Proportionality - Proportionality means when variables are in proportion if they have a constant multiplicative relationship.

Common misconception

Using multiplication as repeated addition leads to incorrect additive strategies of ratios.

Focus on the multiplicative relationships between parts to whole or whole to parts. Ratio tables can help see this more easily.

Using gridded or squared paper, pupils can do some pixelated art with specific ratios. e.g For every 3 black, there must be 1 white. Start with a 5 x 5, then a 6 x 6. Emphasising the ratio
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).

Lesson video

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Starter quiz

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6 Questions

Q1.
Proportionality means when __________ are in proportion if they have a constant multiplicative relationship.
multiplicatives
Correct answer: variables
additives
constants
Q2.
Match the equivalent fractions.
Correct Answer:$$\frac{2}{3}$$,$$\frac{6}{9}$$

$$\frac{6}{9}$$

Correct Answer:$$\frac{3}{5}$$,$$\frac{9}{15}$$

$$\frac{9}{15}$$

Correct Answer:$$\frac{5}{7}$$,$$\frac{15}{21}$$

$$\frac{15}{21}$$

Correct Answer:$$\frac{1}{2}$$,$$\frac{3}{6}$$

$$\frac{3}{6}$$

Q3.
For every 2 apples, there are 5 bananas. If there are 10 apples, how many bananas are there?
Correct Answer: 25, twenty-five, twentyfive, twenty five
Q4.
For every 2 apples, there are 9 bananas. If there are 33 pieces of fruit in total, how many bananas are there?
30
22
11
Correct answer: 27
Q5.
Packs of fruit are in the ratio of 2 apples to 3 pears to 5 bananas. When there are 27 pears, how many apples and bananas are needs to make as many packs of fruit as possible?
12 apples and 20 bananas
19 apples and 29 bananas
Correct answer: 18 apples and 45 bananas
20 apples and 30 bananas
Q6.
Packs of fruit are in the ratio of 2 apples to 3 pears to 5 bananas. When there are 48 pears, how many apples and bananas are needs to make as many packs of fruit as possible?
18 apples and 23 bananas
33 apples and 83 bananas
Correct answer: 32 apples and 80 bananas
40 apples and 80 bananas

Exit quiz

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6 Questions

Q1.
How many equivalent ratios are there to "For every 1 apple, there are 2 bananas."?
24
16
1
Correct answer: infinite
1000
Q2.
Select the equivalent ratios to "For every 10 stars, there are 2 moons."
Correct answer: For every 5 stars, there is 1 moon.
Correct answer: For every 20 stars, there are 4 moons.
Correct answer: For every 25 stars, there are 5 moons.
For every 2 stars, there are 0.1 moons.
For every 8 stars, there are 4 moons.
Q3.
What is the equivalent ratio for this?
An image in a quiz
For every 1 pair of shorts, there are 3 t-shirts.
Correct answer: For every 1 t-shirt, there are 3 pairs of shorts.
Correct answer: For every 5 t-shirts, there are 15 pairs of shorts.
For every 4 t-shirts, there are 5 pairs of shorts.
Q4.
What is the ratio of shaded to not shaded?
An image in a quiz
Correct answer: For every 9 shaded, there are 16 not shaded.
For every 3 shaded, there are 2 not shaded.
For every 2 shaded, there are 3 not shaded.
For every 1 shaded, there is 1 not shaded.
Q5.
What is the ratio of shaded to not shaded?
An image in a quiz
Correct answer: For every 10 shaded, there are 15 not shaded.
For every 2 shaded, there are 5 not shaded.
Correct answer: For every 2 shaded, there are 3 not shaded.
For every 3 shaded, there are 2 not shaded.
Q6.
Three pieces of wood are cut so that length of piece A × 3 = length of piece B, length of piece B × 2 = length of piece C. Find the length of piece C in cm if the total length of all 3 pieces is 65 cm
Correct Answer: 40, 40 cm, 40cm