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      Efficiently solve addition problems (within a whole)

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      Lesson details

      Learning outcome

      I can make efficient choices about the order you calculate when solving addition problems (within a whole).

      Key learning points

      1. Mixed numbers can be combined in the same way as whole numbers.
      2. If fractions have the same denominator, they can be added.
      3. To add fractions with the same denominator, the language of unitising can be used.

      Keywords

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

      Common misconception

      Children may add the incorrect parts of the mixed numbers and/or proper fractions together.

      Guide pupils through with questioning. What is the whole number part? What is the fractional part? First we add the whole number parts then we add the fractional parts using unitising.

      Teacher tip

      Ensure that children have a secure understanding of the structure of mixed numbers - that they are composed of a whole number part and a fractional part. A good understanding of unitising is also key to success.

      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

      Download starter quiz questions (PDF)

      6 Questions

      Q1.
      Look at this number $$2 {{5} \over {6}}$$ We say it as two and five .

      Correct Answer: sixths

      Q2.
      Look at the part-part-whole model. What is the missing part?

      An image in a quiz
      Correct answer: 2
      3
      $$ {2} \over {5}$$
      $$ {5} \over {3}$$
      5

      Q3.
      Look at the part-part-whole model. $$5 {{8} \over {10}}$$ is composed of five wholes and eight-

      An image in a quiz
      Correct Answer: tenths

      Q4.
      Which fraction shows how much of the bar has been shaded grey?

      An image in a quiz
      $$ {2} \over {3}$$
      $$ {3} \over {2}$$
      Correct answer: $$ {3} \over {5}$$
      $$ {3} \over {6}$$

      Q5.
      Match the expressions to their sum.

      Correct Answer:$$ {1} \over {4}$$ + $$ {2} \over {4}$$ ,$$ {3} \over {4}$$

      $$ {3} \over {4}$$

      Correct Answer:$$ {1} \over {6}$$ + $$ {3} \over {6}$$,$$ {4} \over {6}$$

      $$ {4} \over {6}$$

      Correct Answer:$$ {2}\over {10}$$ + $$ {3} \over {10}$$,$$ {5} \over {10}$$

      $$ {5} \over {10}$$

      Correct Answer:$$ {3} \over {8}$$ + $$ {2} \over {8}$$,$$ {5} \over {8}$$

      $$ {5} \over {8}$$

      Q6.
      Sofia drinks one-fifth of a litre of water in the morning and two-fifths of a litre of water in the afternoon. How many litres has she drunk in total?

      $$ {3} \over {10}$$
      Correct answer: $$ {3} \over {5}$$
      $$ {5} \over {3}$$
      $$1{{3} \over {5}}$$

      Assessment exit quiz

      Download exit quiz questions (PDF)

      6 Questions

      Q1.
      Calculate this: $$1{{3} \over {5}}$$ + $$ {1} \over {5}$$ = ?

      $$ {5} \over {5}$$
      $$1{{4} \over {10}}$$
      Correct answer: $$1{{4} \over {5}}$$
      $$2{{4} \over {5}}$$

      Q2.
      Match the equations to their sum.

      Correct Answer:$$1{{4} \over {5}}$$ =,$$1{{3} \over {5}}$$ + $$ {1} \over {5}$$

      $$1{{3} \over {5}}$$ + $$ {1} \over {5}$$

      Correct Answer:$$2{{6} \over {8}}$$ =,$$2{{3} \over {8}}$$ + $$ {3} \over {8}$$

      $$2{{3} \over {8}}$$ + $$ {3} \over {8}$$

      Correct Answer:$$4{{5} \over {8}}$$ =,$$4{{2} \over {8}}$$ + $$ {3} \over {8}$$

      $$4{{2} \over {8}}$$ + $$ {3} \over {8}$$

      Correct Answer:$$2{{4} \over {8}}$$ =,$$2{{1} \over {8}}$$ + $$ {3} \over {8}$$

      $$2{{1} \over {8}}$$ + $$ {3} \over {8}$$

      Q3.
      ___ + $$1{{3} \over {7}}$$ = $$1{{5} \over {7}}$$

      $$ {7} \over {2}$$
      $$ {1} \over {7}$$
      Correct answer: $$ {2} \over {7}$$
      $$1{{2} \over {7}}$$

      Q4.
      3 + $$ {2} \over {9}$$ + $$1{{3} \over {9}}$$ + $$ {2} \over {9}$$ = ?

      $$ {11} \over {9}$$
      $$3{{7} \over {9}}$$
      $$4{{7} \over {27}}$$
      Correct answer: $$4{{7} \over {9}}$$

      Q5.
      $$3{{3} \over {10}}$$ + $$2{{4} \over {10}}$$ = ?

      $$5{{7} \over {20}}$$
      $$ {15} \over {10}$$
      Correct answer: $$5{{7} \over {10}}$$
      $$6{{7} \over {10}}$$

      Q6.
      Jacob has three and one-fifth metres of rope. Sofia has five and two-fifths metres of rope. How many metres of rope do they have in total?

      $$8{{3} \over {10}}$$
      Correct answer: $$8{{3} \over {5}}$$
      $$8{{11} \over {5}}$$
      $$8{{11} \over {10}}$$

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