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Year 6

Explain how to add related unit fractions with a representation or image

I can solve problems involving adding and simplifying fractions with different denominators.

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Share activities with pupils
New
New
Year 6

Explain how to add related unit fractions with a representation or image

I can solve problems involving adding and simplifying fractions with different denominators.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Fractions need to have the same denominator if you are to add and subtract them.
  2. Common denominators for non-related fractions can be found using common multiples of the denominators.
  3. When adding or subtracting fractions with the same denominators you just add or subtract the numerators.

Common misconception

Pupils think that although parts look different, they cannot represent the same fraction of the whole.

Ensure multiple examples are provided where the fractional parts of the whole look different but instead are equivalent in value. You may like to create a concrete example of each shape and show how it can be manipulated so the parts are equivalent.

Keywords

  • Common denominator - When two or more fractions share the same denominator, you can say they have a common denominator.

Encourage pupils to draw onto each shape with dotted lines to help identify a common unit value for each whole. At this point, the focus is on children visualising each part being divided into a common denomination of the whole.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Tick the equations that represent the image.
An image in a quiz
Correct answer: $$ {4} \over {8}$$ + $$ {1} \over {8}$$ = $$ {5} \over {8}$$
$$ {4} \over {8}$$ + $$ {1} \over {8}$$ = $$ {5} \over {16}$$
Correct answer: $$ {1} \over {8}$$ + $$ {4} \over {8}$$ = $$ {5} \over {8}$$
$$ {1} \over {8}$$ + $$ {4} \over {8}$$ = $$ {5} \over {16}$$
Q2.
Tick the equation that represent the image (the cross indicates it has been subtracted).
An image in a quiz
Correct answer: $$ {6} \over {12}$$ − $$ {3} \over {12}$$ = $$ {3} \over {12}$$
$$ {6} \over {12}$$ − $$ {3} \over {12}$$ = 3
6 − $$ {3} \over {12}$$ = $$ {3} \over {12}$$
$$ {6} \over {12}$$ − 3 = $$ {3} \over {12}$$
Q3.
Tick the fraction that is the simplest form of $$ {12} \over {14}$$
$$ {2} \over {4}$$
$$ {1} \over {7}$$
Correct answer: $$ {6} \over {7}$$
$$ {6} \over {14}$$
Q4.
Match the fraction to its simplest form.
Correct Answer:$$ {15} \over {20}$$,$$ {3} \over {4}$$

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

Correct Answer:$$ {16} \over {30}$$,$$ {8} \over {15}$$

$$ {8} \over {15}$$

Correct Answer:$$ {4} \over {12}$$,$$ {1} \over {3}$$

$$ {1} \over {3}$$

Correct Answer:$$ {3} \over {21}$$,$$ {1} \over {7}$$

$$ {1} \over {7}$$

Q5.
Tick the options that could represent the sum: $$ {5} \over {12}$$ + $$ {3} \over {12}$$
$$ {8} \over {24}$$
Correct answer: $$ {8} \over {12}$$
Correct answer: $$ {4} \over {6}$$
Correct answer: $$ {2} \over {3}$$
$$ {4} \over {12}$$
Q6.
Tick the options that could represent the difference: $$ {10} \over {15}$$ − $$ {5} \over {15}$$
Correct answer: $$ {5} \over {15}$$
$$ {1} \over {5}$$
Correct answer: $$ {1} \over {3}$$
$$ {5} \over {30}$$
$$ {2} \over {10}$$

Exit quiz

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6 Questions

Q1.
What fraction of the shape is shaded?
An image in a quiz
Correct answer: $$ {7} \over {12}$$
$$ {5} \over {12}$$
$$ {1} \over {3}$$
$$ {1} \over {2}$$
Q2.
What fraction of the shape is shaded?
An image in a quiz
$$ {1} \over {3}$$
Correct answer: $$ {1} \over {4}$$
Correct answer: $$ {3} \over {12}$$
$$ {3} \over {9}$$
Q3.
What fraction of the shape is shaded?
An image in a quiz
Correct answer: $$ {4} \over {10}$$
$$ {1} \over {8}$$
$$ {4} \over {7}$$
Correct answer: $$ {2} \over {5}$$
Q4.
What fraction of the whole shape is shaded?
An image in a quiz
Correct answer: $$ {7} \over {15}$$
$$ {3} \over {11}$$
$$ {7} \over {8}$$
$$ {1} \over {3}$$
Q5.
What fraction of the whole shape is shaded?
An image in a quiz
$$ {2} \over {16}$$
Correct answer: $$ {6} \over {16}$$
Correct answer: $$ {3} \over {8}$$
$$ {1} \over {4}$$
Q6.
One-third of a garden patio is covered by a garden bench. Two twelfths of the garden patio is covered by a table. How much of the garden patio is covered?
Correct answer: $$ {6} \over {12}$$
$$ {3} \over {36}$$
$$ {3} \over {15}$$
Correct answer: $$ {1} \over {2}$$