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

Multiplicative relationships and 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

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

Two variables are in direct proportion if they have a {{ }} 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 2 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 × {{ }}.

When you use a ratio table, you are using __________ relationship.

100% = 40 and 70% = 28. The percentage change is {{ }}%.

The cost of a laptop increases from £540 to £702.  What is the percentage change?

Jun thinks of a number and increases it by a percentage.  The number Jun thought of was 80 and his new number is 100.  Jun has increased his original number by {{ }}%.

Jacob’s score on a game increases from 2450 to 2744. The percentage that Jacob's original score has changed by is {{ }}%.

A reduced fat bag of crisps contains 3 g of fat.  The normal bag of crisps contains 2 g more of fat.  The percentage that the fat has been reduced by is {{ }}%.

Multiplicative relationships and direct proportion

Lesson outcome