Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Solve problems involving fractions and mixed numbers

      Lesson details

      Learning outcome

      I can solve problems involving fractions and mixed numbers.

      Key learning points

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

      Keywords

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

      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.

      Teacher tip

      Where possible, provide opportunities for pupils to interpret information that does not automatically provide questions to be answered. Encourage pupils to come up with questions for themselves that they can create based on the information provided.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      Tick the equation this bar model represents.

      An image in a quiz
      Correct answer: 72 − 44 = ___
      44 − 72 = ___
      44 + 72 = ___
      72 ÷ 44 = ___

      Q2.
      Tick the equation this bar model represents.

      An image in a quiz
      Correct answer: 6 + 6 + 6 + 6 + 6 = ___
      6 ÷ 5 = ___
      Correct answer: 5 × 6 = ___
      Correct answer: ___ ÷ 5 = 6

      Q3.
      Tick the correct expressions that represent the image

      An image in a quiz
      4 × $$ \frac{6}{5} $$
      5 × $$ \frac{5}{6} $$
      Correct answer: 4 × $$ \frac{5}{6} $$
      Correct answer: $$ \frac{5}{6} $$ × 4

      Q4.
      Estimate the value of this expression. Give your estimate as a whole number. $$ 3\frac{2}{15} $$ × 2

      Correct Answer: 6, six

      Q5.
      Give the missing numerator.

      An image in a quiz
      Correct Answer: 48, forty eight

      Q6.
      Tick the product of this equation. $$ 1\frac{3}{7} $$ × 3 = ___

      $$ 1\frac{9}{7} $$
      $$ 2\frac{2}{7} $$
      $$ 6\frac{6}{7} $$
      $$ 3\frac{3}{7} $$
      Correct answer: $$ 3\frac{9}{7} $$

      6 Questions

      Q1.
      Write the answer to the following equation. 4 × $$ \frac{5}{10} $$ =

      Correct Answer: 2, two, two wholes

      Q2.
      Tick the correct expressions that represent the image

      An image in a quiz
      4 × $$ \frac{5}{9} $$
      Correct answer: 2 × $$ \frac{5}{8} $$ + 2 × $$ \frac{5}{8} $$
      4 + $$ \frac{5}{8} $$
      2 + 2 × $$ \frac{5}{8} $$

      Q3.
      Tick the equation this bar model represents.

      An image in a quiz
      Correct answer: $$ \frac{4}{9} $$ × 4 = ___
      $$ \frac{4}{9} $$ × 3 = ___
      Correct answer: 4 × $$ \frac{4}{9} $$ = ___
      Correct answer: ___ ÷ 4 = 4 × $$ \frac{4}{9} $$

      Q4.
      Tick the context that could be represented by this image.

      An image in a quiz
      Correct answer: Alex has 5 lessons that all last for $$ \frac{3}{4} $$ of an hour.
      Correct answer: 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.

      Q5.
      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?

      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz

      Q6.
      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?

      Correct Answer: 25, twenty five , £25

      To help you plan your 5 maths lesson on: Solve problems involving fractions and mixed numbers, download all teaching resources for free and adapt to suit your pupils' needs...