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 a decrease

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 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

Which of the following words indicate an increase?

Which of the following is the correct calculation for finding 3% of 300?

Match each percentage question to the correct multiplier.

A t-shirt costs £12 in a sale offering a 25% discount.  The cost of the t-shirt before the discount was £{{ }}.

The value of a motorbike depreciates by 14% each year.  It is now worth £5590.  Last year the motorbike was worth £{{ }}.

Mr. Oak sells a vase is sold for £102.  This gives him a profit of 20%.  Mr. Oak originally purchased the vase for £{{ }}.

Which of the following is the correct calculation for finding 20% of 300?

A number is increased by 25%.  1 part is equal to 25%. What will be the total number of parts representing the new number? 

The cost of a TV increases by 20%.  The new price is £420.  What was the cost of the TV before the price increase?  Without calculating the answer, decide whose answers cannot possibly be correct?

Jun thinks of a number and increases it by 20%.  Jun's new number is 720.  What was his original number?

The cost of a TV increases by 20%.  The new price is £420. The cost of the TV before the price increase is £{{ }}.

The cost of a concert ticket is £80.  This is an increase of 25% on last year.  The cost of the ticket last year was £{{}}.

Starter Quiz

Which of the following is the correct calculation for finding 20% of 300?