Explain which strategy for comparing non-related fractions is most efficient | Maths

Starter quiz

If the numerator is half the size of the denominator, we can say that the fraction is __________.
- equal to one-quarter
- equal to one-half ✓
- equal to one-whole
- a proper fraction ✓
- an improper fraction
Tick the fractions greater than one half.
- ${5} \over {6}$ ✓
- ${2} \over {3}$ ✓
- ${1} \over {4}$
- ${4} \over {12}$
- ${5} \over {11}$
Tick the fractions less than one half.
- ${1} \over {7}$ ✓
- ${2} \over {6}$ ✓
- ${4} \over {5}$
- ${3} \over {6}$
- ${3} \over {7}$ ✓
Compare these two fractions: ${4} \over {7}$ ___ ${5} \over {8}$
- < ✓
- >
- =
Order the fractions from largest to smallest.
- 1
  
  ⇔
  
  ${8} \over {10}$
- 2
  
  ⇔
  
  ${4} \over {8}$
- 3
  
  ⇔
  
  ${3} \over {7}$
- 4
  
  ⇔
  
  ${3} \over {8}$
Compare these two fractions: ${5} \over {6}$ ___ ${6} \over {7}$
- < ✓
- >
- =

Exit quiz

To complete a calculation efficiently means to calculate it __________.
- quickly
- only using a written method
- accurately
- quickly and accurately ✓
Use reasoning to compare these two fractions: ${3} \over {12}$ ___ ${7} \over {8}$
- < ✓
- >
- =
Use reasoning to compare these two fractions: ${6} \over {10}$ ___ ${7} \over {10}$
- < ✓
- >
- =
Use reasoning to compare these two fractions: ${8} \over {6}$ ___ ${8} \over {10}$
- <
- > ✓
- =
Use reasoning to compare these two fractions: ${2} \over {3}$ ___ ${4} \over {5}$
- < ✓
- >
- =
Use reasoning to compare these two fractions: ${3} \over {8}$ ___ ${5} \over {12}$
- < ✓
- >
- =

Worksheet

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Presentation

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Lesson Details

Key learning points

If the numerator is the same, the greater the denominator, the smaller the fraction.
If the numerator is the same, the greater the numerator, the larger the fraction.
In fractions equivalent to a whole, the numerator is the same as the denominator.
In fractions equivalent to a half, the numerator is half the value of the denominator.

Common misconception

Pupils look to convert all fractions so that they have a common denominator in order to compare them.

The vast majority of fractions can be compared without common denominators. To support this, pupils need to have a strong sense of the magnitude of the fractions they are comparing. Do not feel you need to move away from bar models too quickly.

Keywords

Common denominator - When two or more fractions share the same denominator, you can say they have a common denominator.
Magnitude - The magnitude of something refers to the size of something.
Efficient - To be efficient means finding a way to solve a problem quickly whilst also maintaining accuracy.