Two fractions are equivalent if they have the same value.

Checking understanding of percentages

Maths

In this unit, pupils develop the skills to calculate a given percentage of an amount. In the percentages unit, this is extended to performing simple and compound interest calculations. 

The multiplicative relationship is extended in this unit by considering percentages and the connections between multiplicative relationships and direct proportion. By building on a secure understanding of fractions and ratio, pupils can see their understanding of multiplicative relationships being extended.

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

Understanding multiplicative relationships: percentages and proportionality

Variables are in proportion if they have a constant multiplicative relationship.

Securing understanding of percentages

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

A ratio shows the relative sizes of two or more values and allows you to compare a part with another part in a whole.

Two fractions are equivalent if they have the same value

Multiplicative relationships presented graphically

If two things are proportional then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained.

Scaling diagrams for multiplicative relationships

Expressing one number as a percentage of another

The associative law states that a repeated application of the operation produces the same result regardless of how pairs of values are grouped. We can group using brackets.

Finding a percentage with a multiplier

Increase by a percentage

Decrease by a percentage

The reciprocal is the multiplicative inverse of any non-zero number.  Any non-zero number multiplied by its reciprocal is equal to 1.

Finding the original amount after an increase

The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.

Finding the original amount after a decrease

Finding the percentage change

Two variables are in direct proportion if they have a constant multiplicative relationship.

Multiplicative relationships and direct proportion

Graphing direct proportion

Direct proportion in context

Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.

Understanding multiplicative relationships: percentages and proportionality

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These lessons will be removed by end of Summer Term 2025.