Find the whole when the size of a non-unit fraction is known | Maths

Starter quiz

Complete: $\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{1}{4}$ = ______
- '1' ✓
$The image represents <Math> \frac{3}{4} </Math> of the shape. Tick the image that shows <Math> \frac{1}{4} </Math>$

The image represents $\frac{3}{4}$ of the shape. Tick the image that shows $\frac{1}{4}$
$The image represents <Math> \frac{2}{5} </Math> of the whole. Tick the image that shows <Math> \frac{1}{5} </Math>$

The image represents $\frac{2}{5}$ of the whole. Tick the image that shows $\frac{1}{5}$
$The part of the image shown by the arrow represents <Math> \frac{6}{8} </Math> How many intervals would represent <Math> \frac{1}{8} </Math>$

The part of the image shown by the arrow represents $\frac{6}{8}$ How many intervals would represent $\frac{1}{8}$
- 1 ✓
- 2
- 3
- 4
$The image represents <Math> \frac{1}{4} </Math> of the whole. How many cubes would be needed to make the whole? <span class="blank">______</span> cubes$

The image represents $\frac{1}{4}$ of the whole. How many cubes would be needed to make the whole? ______ cubes
- '8' ✓
$The image represents <Math> \frac{3}{5} </Math> of the whole. How many circles would be needed to represent the whole?$

The image represents $\frac{3}{5}$ of the whole. How many circles would be needed to represent the whole?
- '20' ✓

Exit quiz

Think about a fraction. The __________ tells us how many equal parts the whole has been divided into.
- numerator
- denominator ✓
- whole fraction
$The image represents <Math> \frac{2}{5} </Math> of the whole. Tick the images that could represent the whole.$

The image represents $\frac{2}{5}$ of the whole. Tick the images that could represent the whole.
Tick the image that represents the whole collection. Sam says ‘This is two-quarters of the apples Mum bought on her shopping trip.’
Which line would have the largest whole?
If $\frac{5}{8}$ of a number is 45, what is the number?
- '72' ✓
If $\frac{3}{5}$ of a number is 330, what is the number?
- '550' ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

This is __ of the whole so one part of the whole is __
There will be __ of these parts in the whole
If you work out the size of a unit fraction from the non-unit fraction, you can work out the size of the whole

Common misconception

Pupils multiply the non-unit fraction by the denominator to create the whole.

Ensure pupils spend time breaking down non-unit fractions back into unit fractions. Encourage pupils to recognise this as two stages. Firstly, find the unit fraction. Secondly, re-create the whole.

Keywords

Represent - To represent something means to show something in a different way. The same thing can be shown using multiple representations.
Unit fraction - A unit fraction is a fraction that has a numerator of one.
Non-unit fraction - A non-unit fraction is a fraction that has a numerator greater than one.
Denominator - The denominator is the bottom number in a fraction.
Numerator - The numerator is the top number in a fraction.