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      Efficiently solve subtraction problems (within a whole)

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      Lesson details

      Learning outcome

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

      Key learning points

      1. Mixed numbers can be partitioned in the same way as whole numbers.
      2. If fractions have the same denominator, they can be subtracted.
      3. To subtract 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 subtract the incorrect parts of the mixed numbers and/or proper fractions.

      What is the number that we are subtracting? If this number is a mixed number, partition it into its whole number part and fractional part.Use unitising to support subtraction.

      Teacher tip

      This lesson is similar to lesson 1 so ensure comparisons are made between the structure used for addition and subtraction. Ensure that children have a secure understanding of the structure of mixed numbers and a good understanding of unitising is also key.

      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 $$9 {{1} \over {4}}$$ We say it as nine and one .

      Correct Answer: quarter, fourth

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

      An image in a quiz
      2
      7
      $$ {2} \over {7}$$
      $$ {7} \over {2}$$
      Correct answer: 8

      Q3.
      Which fraction shows how much of the bar has been shaded grey?

      An image in a quiz
      $$ {2} \over {4}$$
      $$ {4} \over {2}$$
      $$ {2} \over {6}$$
      Correct answer: $$ {4} \over {6}$$

      Q4.
      Match the equations to their sum.

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

      $$ {3} \over {4}$$ − $$ {2} \over {4}$$

      Correct Answer:$$ {2} \over {6}$$ =,$$ {5} \over {6}$$ − $$ {3} \over {6}$$

      $$ {5} \over {6}$$ − $$ {3} \over {6}$$

      Correct Answer:$$ {6} \over {10}$$ =,$$ {9} \over {10}$$ − $$ {3} \over {10}$$

      $$ {9} \over {10}$$ − $$ {3} \over {10}$$

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

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

      Q5.
      5 + $$ {2} \over {8}$$ + $$1{{3} \over {8}}$$ + $$ {2} \over {8}$$ = ?

      $$ {13} \over {8}$$
      $$5{{8} \over {8}}$$
      $$5{{5} \over {27}}$$
      Correct answer: $$6{{7} \over {8}}$$

      Q6.
      $$4{{3} \over {8}}$$ + $$2{{4} \over {8}}$$ = ?

      $$6{{7} \over {16}}$$
      $$ {13} \over {16}$$
      $$ {13} \over {8}$$
      Correct answer: $$6{{7} \over {8}}$$

      Assessment exit quiz

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      6 Questions

      Q1.
      Calculate: $$1{{4} \over {5}}$$ − $$ {2} \over {5}$$ = ?

      $$ {2} \over {5}$$
      $$1{{6} \over {10}}$$
      Correct answer: $$1{{2} \over {5}}$$
      $$1{{6} \over {5}}$$

      Q2.
      Match the equations to their difference.

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

      $$1{{4} \over {5}}$$ − $$ {1} \over {5}$$

      Correct Answer:$$2{{2} \over {8}}$$ =,$$2{{6} \over {8}}$$ − $$ {4} \over {8}$$

      $$2{{6} \over {8}}$$ − $$ {4} \over {8}$$

      Correct Answer:$$4{{4} \over {8}}$$ =,$$4{{7} \over {8}}$$ − $$ {3} \over {8}$$

      $$4{{7} \over {8}}$$ − $$ {3} \over {8}$$

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

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

      Q3.
      $$1{{5} \over {7}}$$ − ___ = $$1{{2} \over {7}}$$

      $$ {7} \over {3}$$
      $$ {1} \over {7}$$
      Correct answer: $$ {3} \over {7}$$
      $$2{{7} \over {7}}$$

      Q4.
      What is the missing number? $$4{{5} \over {8}}$$ − = $$ {5} \over {8}$$

      Correct Answer: 4

      Q5.
      $$5{{7} \over {10}}$$ − $$2{{4} \over {10}}$$ = ?

      $$5{{3} \over {10}}$$
      $$ {10} \over {3}$$
      Correct answer: $$3{{3} \over {10}}$$
      $$3{{10} \over {2}}$$
      $$5{{3} \over {7}}$$

      Q6.
      Jacob has three and one-fifth metres of rope. Sofia has five and four-fifths metres of rope. How much more rope does Sofia have?

      $$2{{3} \over {10}}$$
      Correct answer: $$2{{3} \over {5}}$$
      $$2{{5} \over {3}}$$
      $$8{{5} \over {5}}$$

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