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Understanding multiplicative relationships: fractions and ratio

Understanding multiplicative relationships: fractions and ratio

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Why this why now

This unit finishes our work with fractions in Year 7, relying upon pupil understanding of multiplication of fractions, and explicitly connecting fractions with ratios and general multiplicative relationships.

Prior knowledge requirements

  • Convert between fractions and decimals
  • Use fractions to represent parts of a whole
  • Apply ratios to compare and scale quantities

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Why this why now

This unit finishes our work with fractions in Year 7, relying upon pupil understanding of multiplication of fractions, and explicitly connecting fractions with ratios and general multiplicative relationships.

Prior knowledge requirements

  • Convert between fractions and decimals
  • Use fractions to represent parts of a whole
  • Apply ratios to compare and scale quantities

Understanding multiplicative relationships: fractions and ratio

This unit introduces the concept of multiplicative relationsihps, and connects fractions to the idea of ratios. Ratios are then explored in depth and used to solve contextual problems such as those involving exchange rates and general conversions.

17 lessons in unit

  1. 1

    Checking understanding of multiplicative relationships

    I can use proportionality as a comparison rather than just absolute values.
  2. 2

    Securing understanding of ratio as a multiplicative relationship

    I can reason about ratios in a context.
  3. 3

    Multiplicative relationships in context

    I can appreciate that any two numbers can be connected via a multiplicative relationship.
  4. 4

    Expressing multiplicative relationships as ratios and fractions

    I can express a multiplicative relationship as a ratio or as a fraction.
  5. 5

    Multiplicative relationships

    I can calculate the multiplier for any two given numbers.
  6. 6

    Equivalent multiplicative relationships

    I can appreciate that there are an infinite number of pairs of numbers for any given multiplicative relationship.
  7. 7

    Representing a multiplicative relationship

    I can use a double number line to represent a multiplicative relationship and connect to other known representations.
  8. 8

    Ratio language and notation

    I can understand and use the language and notation of ratio and use a ratio table to represent a multiplicative relationship and connect this to other known representations.
  9. 9

    Checking and securing finding a fraction of a given amount

    I can find a fraction of a given amount.
  10. 10

    Deepening understanding with fractions of a given amount

    I can find the original amount when given a fraction and the result.
  11. 11

    Expressing one number as a fraction of another

    I can express one number as a fraction of another.
  12. 12

    Dividing a quantity into a given ratio

    I can divide one quantity into a given ratio.
  13. 13

    Determining the whole

    I can determine the whole, given one part and the ratio.
  14. 14

    Determining the part

    I can determine one part, given the other part and the ratio.
  15. 15

    Describing exchange rates with ratio

    I can use ratio to describe exchange rates.
  16. 16

    Describing more conversions with ratio

    I can use ratio to describe conversions.
  17. 17

    Problem solving with fractions and ratios

    I can use my knowledge of fractions and ratios to solve problems.

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