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Year 6

Order sets of non-related fractions using a range of strategies

I can decide on the most efficient strategy to compare and order fractions.

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New
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Year 6

Order sets of non-related fractions using a range of strategies

I can decide on the most efficient strategy to compare and order fractions.

Download all resources
arrow-right
Share activities with pupils
arrow-right
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Lesson details

Key learning points

  1. There are many ways to compare and order fractions.
  2. If the numerator is the same, the greater the denominator, the smaller the fraction.
  3. If the denominator is the same, the greater the numerator, the larger the fraction.
  4. In fractions equivalent to a whole, the numerator is the same as the denominator.
  5. In fractions equivalent to a half, the numerator is half the value of the denominator.

Keywords

  • Improper fraction - An improper fraction is a fraction where the numerator is greater than the denominator.

  • Proper fraction - A proper fraction is a fraction where the numerator is less than the denominator.

Common misconception

Pupils convert to common denominators to order fractions rather then use their sense of magnitude for each fraction they are comparing.

Encourage pupils to step back at first from procedure and ask themselves what they notice about the fractions. Can they spot fractions that are equivalent to a quarter or a half?

This lesson is a great opportunity to continue practising comparing and ordering fractions within game-based activities. Encourage pupils to change the constraints of the games as they go so they can adapt the focus of their comparing.
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).

Lesson video

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Starter quiz

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6 Questions

Q1.
An improper fraction is:
a fraction with a numerator of one.
Correct answer: a fraction with a numerator that is larger than the denominator.
a fraction that has the same numerator and denominator.
a fraction with a denominator that is larger than the numerator.
Q2.
Use reasoning to compare these two fractions: $$ {2} \over {10}$$ ___ $$ {6} \over {7}$$
Correct answer: <
>
=
Q3.
Use reasoning to identify which of these fractions is greater than $$ {2} \over {5}$$
Correct answer: $$ {4} \over {5}$$
Correct answer: $$ {3} \over {5}$$
$$ {1} \over {10}$$
$$ {4} \over {10}$$
Q4.
Use reasoning to identify the fraction which would complete the inequality: $$ {5} \over {7}$$ > _____
Correct answer: $$ {5} \over {20}$$
$$ {7} \over {7}$$
$$ {7} \over {5}$$
Q5.
Use reasoning to compare these two fractions: $$ {9} \over {10}$$ ___ $$ {6} \over {7}$$
<
Correct answer: >
=
Q6.
Use reasoning to compare these two fractions: $$ {4} \over {7}$$ ___ $$ {5} \over {8}$$
Correct answer: <
>
=

Exit quiz

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6 Questions

Q1.
Tick the sequences where the fractions are increasing in size each time.
Correct answer: $$ {1} \over {4}$$ $$ {1} \over {3}$$ $$ {1} \over {2}$$
$$ {1} \over {8}$$ $$ {1} \over {4}$$ $$ {1} \over {6}$$
Correct answer: $$ {1} \over {8}$$ $$ {2} \over {7}$$ $$ {3} \over {6}$$
$$ {9} \over {9}$$ $$ {9} \over {10}$$ $$ {9} \over {11}$$
Q2.
Tick the sequence where the fractions are decreasing in size each time.
$$ {1} \over {9}$$ $$ {1} \over {8}$$ $$ {1} \over {7}$$
$$ {2} \over {5}$$ $$ {3} \over {4}$$ $$ {4} \over {1}$$
Correct answer: $$ {1} \over {8}$$ $$ {1} \over {9}$$ $$ {1} \over {10}$$
$$ {3} \over {9}$$ $$ {4} \over {10}$$ $$ {5} \over {11}$$
Q3.
Order the fractions from largest to smallest.
1 - $$ {5} \over {7}$$
2 - $$ {5} \over {10}$$
3 - $$ {5} \over {15}$$
Q4.
Tick the largest fraction and the smallest fraction in this list.
Correct answer: $$ {6} \over {10}$$
$$ {1} \over {2}$$
$$ {3} \over {9}$$
Correct answer: $$ {1} \over {12}$$
Q5.
Tick the fractions that could fit in the gap in this increasing sequence. $$ {2} \over {3}$$ $$ {5} \over {6}$$ __________ $$ {9} \over {10}$$
Correct answer: $$ {7} \over {8}$$
Correct answer: $$ {6} \over {7}$$
$$ {7} \over {10}$$
$$ {6} \over {9}$$
Q6.
Order the fractions in ascending order.
1 - $$ {3} \over {7}$$
2 - $$ {3} \over {6}$$
3 - $$ {4} \over {5}$$
4 - $$ {25} \over {30}$$
5 - $$ {9} \over {7}$$

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