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Understanding multiplicative relationships: percentages and proportionality

Understanding multiplicative relationships: percentages and proportionality

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Why this why now

Pupils build upon key stage 2 work with finding percentages of amounts, then extending their knowledge to percentage change, connecting to previous learning around decimals and fractions. Pupils then explore a more general exploration of multiplicative relationships.

Prior knowledge requirements

  • Convert between fractions, decimals, and percentages
  • Understand ratio and scaling
  • Solve problems involving direct proportion

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Why this why now

Pupils build upon key stage 2 work with finding percentages of amounts, then extending their knowledge to percentage change, connecting to previous learning around decimals and fractions. Pupils then explore a more general exploration of multiplicative relationships.

Prior knowledge requirements

  • Convert between fractions, decimals, and percentages
  • Understand ratio and scaling
  • Solve problems involving direct proportion

Understanding multiplicative relationships: percentages and proportionality

In this unit pupils explore multiplicative relationships with percentages, direct and inverse proportion.

16 lessons in unit

  1. 1

    Checking understanding of percentages

    I can manipulate percentages of an amount without a representation.
  2. 2

    Securing understanding of percentages

    I can manipulate percentages of an amount with a representation.
  3. 3

    Multiplicative relationships presented graphically

    I can use a graph to represent a multiplicative relationship and connect to other known representations.
  4. 4

    Scaling diagrams for multiplicative relationships

    I can use a scaling diagram to represent a multiplicative relationship and connect to other known representations.
  5. 5

    Expressing one number as a percentage of another

    I can describe one number as a percentage of another.
  6. 6

    Finding a percentage with a multiplier

    I can find a percentage of a quantity using a multiplier.
  7. 7

    Increase by a percentage

    I can calculate percentage changes (increase).
  8. 8

    Decrease by a percentage

    I can calculate percentage changes (decrease).
  9. 9

    Finding the original amount after an increase

    I can calculate the original value, given the final value after a stated percentage increase.
  10. 10

    Finding the original amount after a decrease

    I can calculate the original value, given the final value after a stated percentage decrease.
  11. 11

    Finding the percentage change

    I can find the percentage increase or decrease given start and finish quantities.
  12. 12

    Multiplicative relationships and direct proportion

    I can appreciate the connection between multiplicative relationships and direct proportion.
  13. 13

    Graphing direct proportion

    I can recognise direct proportion graphically and be able to identify features of the graph.
  14. 14

    Direct proportion in context

    I can recognise direct proportion in a range of contexts, including compound measures.
  15. 15

    Inverse proportion in context

    I can recognise inverse proportion graphically and use inverse proportionality in a range of contexts.
  16. 16

    Problem solving with percentages and proportionality

    I can use my knowledge of percentages and proportionality to solve problems.

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