Substitute into simple expressions and formulae

Home learning focus

Learn how to solve formulae and substitute numbers.

This lesson includes:

  • a learning summary
  • interactive activities
  • one worksheet with answers

Learn

Formulae are facts or rules written in a mathematical way. They help you work out a quantity using other amounts connected to it.

Sometimes, you see letters being used to represent numbers. Letters are used so numbers can then be substituted (swapped in) depending on the rule.

Finding the volume of a cuboid

For example, to find the volume of a cuboid, you multiply the length by the width by the height.

As a formula, you would write:

Volume = length x width x height

or, for short:

Volume = lwd

The letters are written next to each other to show that you have to multiply them.

Algebra doesn’t use an ‘x’ to show multiplication because it can get confusing since other letters are being used!

Not all cuboids have the same dimensions - this is where substitution comes in.

Depending on the measurements each time, the numbers representing the letters will change, but the rule to find the volume never will.

Look at this cuboid:

This time the length = 4cm, width = 2cm, and the height = 3cm.

To find the volume, you’d use the formula:

Volume = lwd

So:

4cm x 2cm x 3cm = 24cm³.

What if the length changed to 3cm, the width to 2cm, and the height to 2cm?

You would still use the same formula to find the volume, but swap in the different measurements.

3cm x 2cm x 2cm = 12cm³

Using words in a formula

Sometimes, formulae use words instead of just letters.

Example:

Libby works in a pet shop. She earns £30 a day plus £10 for every pet she sells.

The formula to show this would be:

Amount earned = £30 + (10 x number of pets sold).

How much would Libby earn if she sold 5 pets on Monday?

To solve this, you would have to substitute the number 5 into the “number of pets sold.”

Amount earned = £30 + (10 x 5)

So Libby would earn £80 on Monday.

How much would Libby earn if she sold 9 pets on Tuesday?

This time, you would substitute the number 9 into the “number of pets sold.”

Amount earned = £30 + (10 x 9).

Libby would earn £120 this time.

Practise

Activity 1

Equations, formulae and identities worksheet

In this worksheet from Maths Whizz there are 18 questions to answer. You can print it out or just write your answers on a piece of paper.

Substitutions worksheet

Click here to find the answer sheet.

Activity 2

Have a go at finding and understanding substitutions in algebra with these interactive games from My Maths, Oxford University Press.

Rules and Formulae - Interactive guide

There’s more to learn

Have a look at these other resources around the BBC and the web.

KS2 Maths
Primary games
Newsround