Halves and quarters
Maths · Key Stage 1 · The School
Equal parts, or it is not a fraction
A half means one of TWO EQUAL parts. Cut a sandwich into a huge piece and a tiny piece and you have two parts, but you do not have halves. This is the whole idea, and it is where most early mistakes come from: children are quick to count the parts and slow to check they match. Always ask, "are the pieces the same size?"
Halves and quarters of a set
Fractions work on groups too, not just shapes. Half of 8 sweets means sharing 8 into two equal piles: 4 each. A quarter of 8 means four equal piles: 2 each. Try it with counters before writing anything — moving objects into equal piles is what makes the written fraction mean something afterwards.
Writing them, and one to notice
One half is written 1/2, one quarter 1/4, three quarters 3/4. The bottom number says how many equal parts the whole was cut into; the top says how many you have. Now fold a paper strip in half, then in half again: you get four parts, and two of them cover exactly the same amount as one half. So 2/4 and 1/2 are the same amount, written two different ways.
Take 12 counters. A quarter means four equal piles, so deal them out one at a time into four piles: 3, 3, 3, 3. A quarter of 12 is 3. Now push two of those piles together: 6. That is 6 out of 12, which is half. So two quarters make one half — not because someone said so, but because you can see the two piles becoming one. Half of 12 is 6, and 3 + 3 = 6.