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Fractions

A fraction is a number — a point on the number line — not only a slice of pizza. Children struggle when they still treat the numerator and denominator as two unrelated whole numbers, so 1/4 looks larger than 1/2, and adding fractions becomes ‘add everything you see’.

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Why this concept matters

Fractions are the concept Class 6–8 silently assume. If equivalent fractions never became a picture, ratio, decimals, percentages and algebra all inherit the crack.

Misconceptions, in the order we see them

Bigger digits, bigger fraction

1/3 is thought larger than 1/2 because 3 > 2. The child is comparing denominators as if they were amounts.

Add tops, add bottoms

1/2 + 1/3 = 2/5. There is no common unit, so the operation is invented.

Equivalent fractions are a trick with multiplying

They can multiply top and bottom by 2 and cannot say why the amount stayed the same.

A fraction is always less than 1

Improper fractions and mixed numbers then look like a different topic, not the same numbers past one whole.

Fraction and division are unrelated

3/4 is never ‘3 divided by 4’, so later algebra with fractions has no landing place.

Which classes cover this

Class 3 Class 4 Class 5 Class 6 Class 7

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