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

Problem solving with percentages and proportionality

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

Direct proportion in context

Inverse proportion in context

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 which are in proportion share a __________ relationship.

Here is part of a larger shape. Which of the following could be the whole shape?

If 100% = 45, 130% = 58.5 then the percentage change is {{}}%.

Calculate the percentage profit on a watch bought for £40 and sold for £50.

Calculate the percentage loss on a mobile phone bought for £300 and sold for £240.

A, B and C are 3 different numbers. C is two-fifths of B. C is 3 times A. The total of A & C is 32. The value of B is {{ }}.

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

Which of the following is a graph representing inverse proportion?

The number of coaches needed for a school trip and the number of people.

The time taken to to paint a wall and the number of people painting.

The number of pounds and the number of dollars exchanged.

The time taken to drive to Liverpool and speed of the car.

Number of buckets needed to fill a paddling pool and the size of the buckets.

Which of the following situations illustrate an inversely proportional relationship?

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

It takes 3 people 4 days to build a wall. It should take 2 people {{ }} days to build the same wall.

Problem solving with percentages and proportionality

Lesson outcome