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

Maths

Checking understanding of percentages

Securing understanding of percentages

Scaling diagrams for multiplicative relationships

Expressing one number as a percentage of another

Finding a percentage with a multiplier

Increase by a percentage

Decrease by a percentage

Finding the original amount after an increase

Finding the original amount after a decrease

Finding the percentage change

Multiplicative relationships and direct proportion

Graphing direct proportion

Direct proportion in context

Inverse proportion in context

Problem solving with percentages and proportionality

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

Which of the following are equivalent to 20%?

Use the ratio table to help you work out 31% of 860.

Use the double number line to work out 55% of 700.

The amount that represents 100% on this graph is {{ }}.

The graph shows the grades achieved by pupils in a maths test. Aisha earned 61 marks in the test. What grade did Aisha achieve?

Match each mark or percentage with the correct information from the graph.

$$\frac{3}{4}$$ and $$\frac{9}{12}$$ are examples of {{ }} fractions as they have the same value.

Select all the fractions that are equivalent to the fraction of this grid that is shaded.

Select the fractions that are equivalent to $$\frac{7}{20}$$.

Match each percentage calculation to its answer.

Starter Quiz

$$\frac{3}{4}$$ and $$\frac{9}{12}$$ are examples of fractions as they have the same value.