The reciprocal is the multiplicative inverse of any non-zero number.  Any non-zero number multiplied by its reciprocal is equal to 1.

Finding the original amount after an increase

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 a decrease

Finding the percentage change

Multiplicative relationships and direct proportion

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

‘Of’ can be exchanged for which operation in maths?

A number is increased by 20%.  One part is 20%. What is the total number of parts representing the new number? 

The cost of a TV increases by 15%.  The new price is £460.  What was the cost of the TV before the price increase?  Without calculating the answer, decide whose answers cannot possibly be correct?

Alex thinks of a number and increases it by 5%.  His new number is 252.  What was Alex's original number?

The cost of a TV increases by 15%.  The new price is £460.  The cost of the TV before the price increase was £{{ }}. 

This year the cost of a concert ticket is £94.50.  This is an increase of 26% on last year.  The cost of the ticket last year was £{{ }}.

A multiplier is the decimal equivalent of a __________.

Match each question to the correct multiplier.

Which of the following is the correct calculation for calculating 360 increased by 5%?

A box of washing powder contains 20% extra free.  The box usually contains 6.5 kg.  The special offer box contains {{ }}kg.

Finding the original amount after an increase

Lesson outcome