## Description

Pupils already have the arithmetic skills to solve problems involving ratio. They should now learn to describe 1-to-many (and many-to-1) correspondence structures.

Language focus “For every 1 cup of rice you cook, you need 2 cups of water.” “For every 10 children on the school trip, there must be 1 adult.”

Pupils must recognise that proportionality is preserved in these contexts, for example, there is always twice the volume of water needed compared to the volume or rice, regardless of how much rice there is. This will prepare pupils for key stage 3, when they will learn to describe correspondence structures using ratio notation and to express ratios in their simplest forms. Pupils should be able to recognise a 1-to-many or many-to-1 structure, without it being explicitly given and use the relationship to solve problems.

Pupils should also be able to answer questions such as:

- if there were 5 red beads, how many blue beads would there be?
- if there were 21 blue beads, how many beads would there be altogether?
- if there were 40 beads altogether, how many red beads and how many blue beads would there be?

Pupils must also learn to describe and solve problems related to many-to-many structures.

Language focus “For every 2 yellow beads there are 3 green beads”.

Pupils may initially use manipulatives, such as cubes or beads, for support, but by the end of year 6, they must be able to complete many-to-many correspondence tables and solve related problems without manipulatives.

Pupils should also begin to prepare for using the unitary method at key stage 3, when it is required for unit conversions, percentage calculations and other multiplicative problems. For example, if they are given a smoothie recipe for 2 people (20 strawberries, 1 banana and 150ml milk), they should be able to adjust the recipe by multiplying or dividing by a whole number, for example, dividing the quantities by 2 to find the amounts for 1 person, or multiplying the quantities by 3 to find the amounts for 6 people. At key stage 3, pupils would then, for example, be able to use the unitary method to adjust the recipe for 5 people, via calculating the amounts for 1 person.

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