Fractions: the four ideas children mix up

Fractions are where many children first decide they are "bad at maths". Almost always, the confusion is specific and fixable.

1. A fraction is a number, not two numbers

One half is a point on the number line, not a 1 above a 2. If a child can place 3/4 between 1/2 and 1, they already understand more than most worksheets test.

2. Of means multiply

"3/4 of 48" is 48 ÷ 4 × 3. Children who have secure number bonds can do this mentally in seconds.

3. Same denominator is a fairness rule

You cannot add 1/2 and 1/3 until the pieces are the same size. Showing this with two chocolate bars removes the mystery.

4. Bigger denominator, smaller piece

A tenth is smaller than a quarter, even though ten is bigger than four. This trips up adults too.

Address these four in conversation, with drawings rather than rules, and the topic settles quickly.