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Representing ratio in different ways

You can explain how to use multiplication and division to calculate unknown values with two variables.

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Year 6

Representing ratio in different ways

You can explain how to use multiplication and division to calculate unknown values with two variables.

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Lesson details

Key learning points

Bar models can represent unequal sharing or many to many sharing.
Representations show the relationship between the two variables.
The representation helps to identify the calculations needed to solve the problem.

Keywords

Many to many - Use many to many to describe ratios where each value is more than one

Common misconception

Using addition and subtraction rather than multiplication and division to solve problems.

Continue to model the use of the language and notation of multiplication to calculate missing values.

Make sure that pupils can explain how the numbers in the caluclation relate to the objects and bar models. Make sure they understand what the answer represents and whether they are calculating a part or the whole.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), 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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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
Which image can be described by this statement 'For every 3 birds there are 4 squirrels'?

Correct Answer: An image in a quiz

Q2.
Write a sentence using 'for every' to describe this image

For every 2 triangles there are 3 circles

Correct answer: For every 3 triangles there are 2 circles

Correct answer: For every 9 triangles there are 6 circles

For every three triangles there are 3 circles

Q3.
What does the number 8 in this equation $$2 \times 4 = 8$$ represent in relation to this image?

Correct Answer: The total number of circles, All the circles, 4 lots of 2 circles

Q4.
What does the number 4 this equation $$3 \times 4 = 12$$ represent in relation to this image?

Correct Answer: The pattern is shown 4 times, There are 4 basic patterns, There are 4 lots of pattern

Q5.
What does the number 12 this equation $$3 \times 4 = 12$$ represent in relation to this image?

Correct Answer: The number of triangles, There are 12 triangles, 4 lots of 3 triangles

Q6.
What does the number 20 this equation $$5 \times 4 = 20$$ represent in relation to this image?

Correct Answer: The total number of shapes, All the triangles and circles, All the shapes in the image

Assessment exit quiz

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6 Questions

Q1.
Which statment matches this image?

For every 1 orange marble there are 3 blue marbles

For every 3 orange marbles there are 2 blue marbles

For every 3 blue marbles there are 2 orange marbles

Correct answer: For every 3 orange marbles there is 1 blue marble

Q2.
Which of the images show a 'many to many' ratio?

Correct answer: For every 2 orange marbles there are 3 blue marbles

For every 1 orange marble there are 2 blue marbles

Correct answer: For every 2 blue marbles there are 5 orange marbles

For every 3 orange marbles there is 1 blue marble

Q3.
What multiplication would you use to work out the missing number? If there are 12 blue marbles, there will be __ orange marbles.

$$5 \times 2 = 10$$

$$2 \times 3 = 6$$

Correct answer: $$2 \times 4 = 8$$

$$5 \times 4 = 20$$

Q4.
Which equation represents the total number of marbles?

$$5 \times 2 = 10$$

$$2 \times 3 = 6$$

$$2 \times 4 = 8$$

Correct answer: $$5 \times 4 = 20$$

Q5.
A recipe uses 3 eggs for every 4 spoons of sugar. If you use 15 eggs, how many spoons of sugar will you need?

Correct answer: 20

Q6.
A recipe uses 3 eggs for every 4 spoons of sugar. If you use 40 spoons of sugar, how many eggs will you need?

Correct answer: 30

Lesson appears in

UnitMaths / Ratio and proportion

Maths

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Representing ratio in different ways

Representing ratio in different ways

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Which image can be described by this statement 'For every 3 birds there are 4 squirrels'?

Q2.Write a sentence using 'for every' to describe this image

Q3.What does the number 8 in this equation $$2 \times 4 = 8$$ represent in relation to this image?

Q4.What does the number 4 this equation $$3 \times 4 = 12$$ represent in relation to this image?

Q5.What does the number 12 this equation $$3 \times 4 = 12$$ represent in relation to this image?

Q6.What does the number 20 this equation $$5 \times 4 = 20$$ represent in relation to this image?

Assessment exit quiz

6 Questions

Q1.Which statment matches this image?

Q2.Which of the images show a 'many to many' ratio?

Q3.What multiplication would you use to work out the missing number? If there are 12 blue marbles, there will be __ orange marbles.

Q4.Which equation represents the total number of marbles?

Q5.A recipe uses 3 eggs for every 4 spoons of sugar. If you use 15 eggs, how many spoons of sugar will you need?

Q6.A recipe uses 3 eggs for every 4 spoons of sugar. If you use 40 spoons of sugar, how many eggs will you need?

Lesson appears in

UnitMaths / Ratio and proportion

Maths

Q1.
Which image can be described by this statement 'For every 3 birds there are 4 squirrels'?

Q2.
Write a sentence using 'for every' to describe this image

Q3.
What does the number 8 in this equation $$2 \times 4 = 8$$ represent in relation to this image?

Q4.
What does the number 4 this equation $$3 \times 4 = 12$$ represent in relation to this image?

Q5.
What does the number 12 this equation $$3 \times 4 = 12$$ represent in relation to this image?

Q6.
What does the number 20 this equation $$5 \times 4 = 20$$ represent in relation to this image?

Q1.
Which statment matches this image?

Q2.
Which of the images show a 'many to many' ratio?

Q3.
What multiplication would you use to work out the missing number? If there are 12 blue marbles, there will be __ orange marbles.

Q4.
Which equation represents the total number of marbles?

Q5.
A recipe uses 3 eggs for every 4 spoons of sugar. If you use 15 eggs, how many spoons of sugar will you need?

Q6.
A recipe uses 3 eggs for every 4 spoons of sugar. If you use 40 spoons of sugar, how many eggs will you need?