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

Graphing direct proportion

Maths

Checking understanding of percentages

Securing understanding of percentages

Multiplicative relationships presented graphically

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

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

Graphs showing direct proportion have a positive gradient with an {{ }} of 0.

Which of the following graphs does NOT show direct proportion?

Which tables show that A and B are in direct proportion?

The constant of proportionality represented by this graph is {{ }}.

The constant of proportionality is $$3$$.

The graph does not show a directly proportional relationship.

Which of the following is NOT true of this graph?

What are the key features of a graph showing direct proportion?

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

Which of the following show a directly proportional relationship between A and B?

A and B are directly proportional.   The missing value of B is {{ }}.

A and B are directly proportional. The missing value of B is {{ }}.

No, reading off the graph at £5 shows you can buy between 2 and 3 boxes.

Yes, reading off the graph at £5 shows you can buy exactly 3 boxes.

The graph shows the relationship between cost and number of boxes bought. Can you spend exactly £5 on boxes?

This graph shows that A and B are in direct proportion. The proportional relationship between A and B is B = A × {{ }}.

Graphing direct proportion

Lesson outcome