Explain how to compare pairs of non-related fractions by comparing to a half | Maths

Starter quiz

Double 16 is equal to ______
- '32' ✓
Tick the largest fraction.
- ${3} \over {7}$ ✓
- ${3} \over {8}$
- ${3} \over {9}$
- ${3} \over {10}$
Half of 500 is ______
- '250' ✓
Tick the fractions that represent one half.
- ${1} \over {2}$ ✓
- ${2} \over {4}$ ✓
- ${4} \over {6}$
- ${4} \over {8}$ ✓
- ${10} \over {15}$
Use the correct symbol to compare: ${3} \over {6}$ ___ ${4} \over {12}$
- <
- > ✓
- =
Use the correct symbol to compare: ${2} \over {6}$ ___ ${3} \over {9}$
- <
- >
- = ✓

Exit quiz

What is the relationship between the numerator and the denominator of a fraction that is equivalent to one half?
- The numerator is double the size of the denominator.
- The denominator is half the size of the numerator.
- The denominator is double the size of the numerator. ✓
- The denominator is two times the size of the numerator. ✓
Tick the fractions that represent one half.
- ${4} \over {7}$
- ${5} \over {10}$ ✓
- ${10} \over {20}$ ✓
- ${20} \over {10}$
- ${1} \over {5}$
Tick the fractions greater than one half.
- ${3} \over {12}$
- ${2} \over {4}$
- ${4} \over {7}$ ✓
- ${5} \over {9}$ ✓
- ${2} \over {3}$ ✓
Tick the fractions less than one half.
- ${1} \over {3}$ ✓
- ${2} \over {8}$ ✓
- ${5} \over {6}$
- ${4} \over {8}$
- ${4} \over {7}$
Order the fractions from largest to smallest.
- 1
  
  ⇔
  
  ${3} \over {10}$
- 2
  
  ⇔
  
  ${1} \over {2}$
- 3
  
  ⇔
  
  ${4} \over {7}$
$Tick the fractions that would fit in the equation.$

Tick the fractions that would fit in the equation.
- ${3} \over {6}$ ✓
- ${1} \over {10}$
- ${6} \over {12}$ ✓
- ${15} \over {16}$

Worksheet

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Presentation

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Lesson Details

Key learning points

In fractions equivalent to a half, the numerator is half the value of the denominator.
When the numerator is more than half the value of the denominator, the fraction is greater than a half.
When the numerator is less than half the value of the denominator, the fraction is less than a half.

Common misconception

Pupils struggle to compare fractions to a half as they mainly consider it in its simplest form.

Encourage pupils to visualise their fractions on a number line. Also spend time thinking about the relationship between the numerator and the denominator in fractions equivalent to one-half and use this generalisation to help moving forward.

Keywords

Proper fraction - A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number).
Order - To order things means to put things into their correct place following a set rule.