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      Multiply a mixed number by a whole number not bridging a whole

      Lesson details

      Learning outcome

      I can multiply a mixed number by a whole number where the fractions do not bridge a whole.

      Key learning points

      1. Partition the mixed number into a whole number and a fraction.
      2. Multiply the whole number part by the whole number factor.
      3. Multiply the fraction by the whole number using unitising language.
      4. Recombine the partial products to calculate the overall product.

      Keywords

      • Repesent - To represent something is to show it in a different way.

      • Mixed number - A mixed number is an improper fraction written as its whole number part plus the fractional part, where the fractional part is a proper fraction.

      • Partition - Partition means to split an object or value down into smaller parts.

      Common misconception

      Pupils find it difficult to represent the problem as an expression or equation as they misinterpret what the whole is.

      Draw attention to what the whole is in each example. You might like to build up each image with a whole at a time, describing the fraction of the whole that is shaded/represented.

      Teacher tip

      Spend time exploring the different ways that the stages of the calculations can be represented. Where you show the partitioned mixed number being multiplied by the integer, avoid using a part whole model as this is an additive structure not a multiplicative structure.

      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

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Tick the equation that represents the image.

      An image in a quiz
      Correct answer: 4 + 4 + 4
      4 + 3
      Correct answer: 3 × 4
      Correct answer: 4 × 3

      Q2.
      Tick the expressions that could represent this image.

      An image in a quiz
      Correct answer: 6 × 3
      Correct answer: 6 + 6 + 6
      Correct answer: 3 × 6
      7 + 7 + 7
      7 × 3

      Q3.
      Tick the images that show a mixed number.

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

      Q4.
      Tick the mixed numbers

      Correct answer: $$ 1\frac{3}{4} $$
      7
      Correct answer: $$ 3\frac{4}{5} $$
      $$ \frac{11}{4} $$

      Q5.
      Tick the numbers that could be converted to a mixed number.

      $$ \frac{7}{8} $$
      Correct answer: $$ \frac{9}{2} $$
      $$ \frac{7}{16} $$
      Correct answer: $$ \frac{15}{3} $$

      Q6.
      Match the improper fractions to the mixed number with the same value.

      Correct Answer:$$ \frac{7}{5} $$,$$ 1\frac{2}{5} $$

      $$ 1\frac{2}{5} $$

      Correct Answer:$$ \frac{9}{5} $$,$$ 1\frac{4}{5} $$

      $$ 1\frac{4}{5} $$

      Correct Answer:$$ \frac{11}{5} $$,$$ 2\frac{1}{5} $$

      $$ 2\frac{1}{5} $$

      Correct Answer:$$ \frac{13}{5} $$,$$ 2\frac{3}{5} $$

      $$ 2\frac{3}{5} $$

      Correct Answer:$$ \frac{14}{5} $$ ,$$ 2\frac{4}{5} $$

      $$ 2\frac{4}{5} $$

      6 Questions

      Q1.
      Tick the numbers greater than 1

      $$ \frac{5}{6} $$
      $$ \frac{8}{8} $$
      Correct answer: $$ \frac{14}{12} $$
      Correct answer: $$ 1\frac{1}{9} $$

      Q2.
      Tick the expressions that represent this image.

      An image in a quiz
      $$ \frac{3}{5} $$ + 4
      $$ \frac{2}{5} $$ × 2
      Correct answer: 2 × $$ \frac{3}{5} $$
      Correct answer: $$ \frac{3}{5} $$ × 2

      Q3.
      Tick the expressions that represent this problem:It costs me £1.40 to catch the bus each day. I do this four times a week.

      $$ \frac{1}{40} $$ + $$ \frac{1}{40} $$ + $$ \frac{1}{40} $$
      $$ \frac{1}{40} $$ × 4
      Correct answer: $$ 1\frac{40}{100} $$ × 4
      $$ \frac{1}{40} $$ + 4
      Correct answer: 4 × $$ 1\frac{4}{100} $$

      Q4.
      Write in the missing number to make this equation correct.

      An image in a quiz
      Correct Answer: 2, two

      Q5.
      Write in the missing number.

      An image in a quiz
      Correct Answer: 6, six

      Q6.
      Tick the correct product.

      An image in a quiz
      $$ 16\frac{8}{36} $$
      $$ 8\frac{8}{9} $$
      Correct answer: $$ 16\frac{8}{9} $$
      $$ 16\frac{2}{9} $$

      To help you plan your 5 maths lesson on: Multiply a mixed number by a whole number not bridging a whole, download all teaching resources for free and adapt to suit your pupils' needs...