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      Solve problems involving mixed numbers

      Lesson details

      Learning outcome

      I can solve problems involving mixed numbers.

      Key learning points

      1. Word problems can involve mixed numbers. Mixed numbers may be used as part of the question or may form the answer.
      2. Mixed numbers can be used to represent measures.
      3. Representing problems as part-part-whole model can support us to form equations that we can then solve.

      Keywords

      • Mixed number - A mixed number is a whole number and a fraction combined into one "mixed" number. For example: one and a half is a mixed number.

      Common misconception

      Children may be confused about how to write mixed numbers. Children may say 'five and one-eight, rather than five and one-eighth.

      As a school, establish how mixed numbers will be recorded so that you have consistency. Ensure children are accurately expressing the fraction part.

      Teacher tip

      When solving word problems, stick with standard partitioning of mixed numbers to really embed this concept. Measures often use halves, quarters, fifths and tenths as the most common unit for the fractional part.

      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.
      Look at this mixed number $$2{{3} \over {9}}$$ We say it as and three one-ninths.

      Correct Answer: two, 2

      Q2.
      Look at this mixed number $$5{{1} \over {6}}$$ We say it as ‘five and one- .

      Correct Answer: sixth

      Q3.
      Look at the part-part-whole model. What is the missing part?

      An image in a quiz
      Correct Answer: 250

      Q4.
      Look at the part-part-whole model. $$6{{2} \over {3}}$$ is composed of 6 and two- .

      An image in a quiz
      Correct Answer: thirds

      Q5.
      Select the correct sum. 7 + $$ {2} \over {5}$$ = ?

      $$2{{7} \over {5}}$$
      $$2{{5} \over {7}}$$
      $$7{{5} \over {2}}$$
      Correct answer: $$7{{2} \over {5}}$$
      $$5{{2} \over {7}}$$

      Q6.
      $$18{{3} \over {9}}$$ − $$ {3} \over {9}$$ = ?

      3
      9
      Correct answer: 18
      $$ {3} \over {9}$$

      6 Questions

      Q1.
      Which model below represents this problem? Jacob listens to music for two hours on Monday and for half an hour on Tuesday. How long does he listen to music for in total?

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

      Q2.
      Which model below represents this situation? Jacob bakes a cake. The mass of the cake is one and a quarter kg. He gives some cake to his friends then measures the mass left to be one kg.

      An image in a quiz
      A
      Correct answer: B
      C
      D

      Q3.
      Look at the part-part-whole model, which equations can be formed from it?

      An image in a quiz
      6 - $$ {1} \over {4}$$ = ?
      Correct answer: 6 + $$ {1} \over {4}$$ = ?
      Correct answer: $$ {1} \over {4}$$ + 6 = ?
      $$ {1} \over {4}$$ - 6 = ?

      Q4.
      Look at the part-part-whole model, which equations can be formed from it?

      An image in a quiz
      ? = 11 + $$11{{1} \over {8}}$$
      11 + $$11{{1} \over {8}}$$ = ?
      $$11{{1} \over {8}}$$ + 11 = ?
      Correct answer: $$11{{1} \over {8}}$$ - ? = 11
      Correct answer: $$11{{1} \over {8}}$$ - 11 = ?

      Q5.
      Jacob has two and five-tenths of a metre length of ribbon. He uses two metres of it. How much ribbon does he have left over?

      One metre
      Two metres
      Correct answer: $$ {5} \over {10}$$ of a metre
      $$ {10} \over {5}$$ of a metre
      Ten metres

      Q6.
      Sofia has a kitten that has a mass of one kilogram. When she next measures its mass, it is eight-tenths of a kilogram heavier. What is its mass now in kilograms?

      8 kg
      10 kg
      Correct answer: $$1{{8} \over {10}}$$ kg
      $$1{{10} \over {8}}$$ kg
      $$8{{1} \over {10}}$$ kg

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