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

Direct proportion in context

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

Graphing direct proportion

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 {{ }} proportion if they have a constant multiplicative relationship.

5 miles = 8 kilometres. So 7 miles is {{ }} kilometres.

The cost of a box of pens is £4.50. Five boxes of pens cost £{{ }}.

If $20 = £15.80, which of the following are true?

A recipe needs 180 ml of milk to make 15 scones.  You can make {{ }} scones using 6 litres of milk.

Graphs showing direct proportion have a {{ }} gradient with an intercept 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 graph does show a directly proportional relationship.

The graph does not show a constant positive gradient.

Which of the following is NOT true of this graph?

relationship, constant positive, intercept, one

proportion, changing positive, intercept, zero

proportion, constant positive, intercept, zero

proportion, constant negative, intercept, zero

relationship, constant negative, intercept, one

What are the missing words in this statement?  A graph representing direct __________ has a __________    __________ gradient and an __________ of __________.

Starter Quiz

Graphs showing direct proportion have a gradient with an intercept of 0.