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

Inverse 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

Direct 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 inversely proportional if there is a constant multiplicative relationship between one variable and the __________ of the other variable.

Which of the following is a graph representing inverse proportion?

The number of scones made and the amount of milk needed.

The time taken to read a book and the number of pages.

The time taken to complete a lap of a track and the speed.

The number of pieces a plank of wood is cut into and the length of the pieces.

The height of a wall and the number of bricks used.

Which of the following situations illustrate an inversely proportional relationship?

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

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

It takes 3 people 4 days to build a wall. It should take 5 people {{ }} days to build the same wall.

Two variables are in proportion if they have a __________.

5 miles = 8 kilometres. So 12 miles is {{ }} kilometres.

The cost of a box of pens is £4.80.  Five boxes of pens cost £{{ }}.

If $20 = £15.20, which of the following are true?

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

Inverse proportion in context

Lesson outcome