Explain how finding a fraction of a quantity relates to multiplying by a unit fraction | Maths

Starter quiz

Tick the unit fractions.

$\frac{1}{5}$ ✓

$\frac{3}{6}$

$\frac{1}{12}$ ✓

$\frac{6}{7}$

$\frac{8}{4}$
Look at the image and complete. Each part is one-__________ of the whole.

half

quarter ✓

fifth

sixth
Look at the image. One-__________ of the whole is circled.

half

third

fifth

sixth ✓
Which equations match the image?

orange + orange = yellow

yellow + orange = yellow

yellow + yellow = orange ✓

2 × yellow = orange ✓
One-quarter of 28 is equal to ______

'7' ✓
One-fifth of 30 is equal to ______

'6' ✓

Exit quiz

How many lots of yellow are equal to orange?

'2' ✓
Tick the representation that matches the equation: $\frac{1}{2}$ × r = w
Tick the equations that match the image.

g = r

g = 3 × r ✓

$\frac{1}{3}$ × r = g

$\frac{1}{3}$ × g = r ✓
Tick the operation that can replace ‘of’ in a calculation.

+

−

× ✓

÷
Tick the equations that match the image.

5 = 20 × 4

20 = 4 × 5 ✓

$\frac{1}{4}$ × 20 = 5 ✓

$\frac{1}{5}$ × 20 = 4
Tick the equations that match the image.

18 = 6 × 3 ✓

18 = $\frac{1}{3}$ × 6

$\frac{1}{6}$ × 18 = 3

$\frac{1}{3}$ × 18 = 6 ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

Half of a number is the same as a half multiplied by the number.
If half of 10 is 5 then 1/2 x 10 = 5
Finding a fraction of a number is the same as multiplying the number by the fraction.

Common misconception

Pupils struggle to see the relationship between the different number rods.

Take time with pupils for them to explore the use of number rods if they have not done so before. You might ask pupils to find rods that are half the size of different coloured rods, so they can estimate sizes and draw attention to the relationship.

Keywords

Relationship - A relationship is a connection between two or more things.
Unit fraction - A unit fraction is a fraction that has a numerator of one.