Solve problems involving fractions and mixed numbers | Maths

Starter quiz

Tick the equation this bar model represents.

72 − 44 = ___ ✓

44 − 72 = ___

44 + 72 = ___

72 ÷ 44 = ___
Tick the equation this bar model represents.

6 + 6 + 6 + 6 + 6 = ___ ✓

6 ÷ 5 = ___

5 × 6 = ___ ✓

___ ÷ 5 = 6 ✓
Tick the correct expressions that represent the image

4 × $\frac{6}{5}$

5 × $\frac{5}{6}$

4 × $\frac{5}{6}$ ✓

$\frac{5}{6}$ × 4 ✓
Estimate the value of this expression. Give your estimate as a whole number. $3\frac{2}{15}$ × 2

'6' ✓
Give the missing numerator.

'48' ✓
Tick the product of this equation. $1\frac{3}{7}$ × 3 = ___

$1\frac{9}{7}$

$2\frac{2}{7}$

$6\frac{6}{7}$

$3\frac{3}{7}$

$3\frac{9}{7}$ ✓

Exit quiz

Write the answer to the following equation. 4 × $\frac{5}{10}$ = ______

'2' ✓
Tick the correct expressions that represent the image

4 × $\frac{5}{9}$

2 × $\frac{5}{8}$ + 2 × $\frac{5}{8}$ ✓

4 + $\frac{5}{8}$

2 + 2 × $\frac{5}{8}$
Tick the equation this bar model represents.

$\frac{4}{9}$ × 4 = ___ ✓

$\frac{4}{9}$ × 3 = ___

4 × $\frac{4}{9}$ = ___ ✓

___ ÷ 4 = 4 × $\frac{4}{9}$ ✓
Tick the context that could be represented by this image.

Alex has 5 lessons that all last for $\frac{3}{4}$ of an hour. ✓

Izzy practises piano for $\frac{3}{4}$ of an hour, five days a week. ✓

Sofia fills $\frac{3}{4}$ of a glass with milk for breakfast every day.

There was $\frac{3}{4}$ of the cake remaining after the party.
Tick the bar model that best represents the problem. Andeep waters the plants for three nights. Each night, he fills up the watering can so it is $\frac{3}{4}$ full. How much water does he use?
Sam climbs every week for $1\frac{1}{4}$ hours. He does this for four weeks in a row. It costs him £5 per hour. How much money does he pay for the four weeks?

'25' ✓

Worksheet

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Lesson Details

Key learning points

Use the language of unitising '__ groups of __ is equal to __'
Partition the mixed number into a whole number and a fraction.
Explain which is the most efficient strategy to multiply fractions and mixed numbers.

Common misconception

Pupils struggle to represent problems as a bar model.

Encourage pupils to draw their own image of what the maths represents. Make connections between their own image and a bar model, linking them both to where the numbers are represented in each image.

Keywords

Represent - To represent something means to show it in a different way.