Groups, Sharing and Halves
Primary 2 · Mathematics
Groups, Sharing and Halves
Lesson 3 of 3
11 min
Let's begin
Umutoni's mother comes home from the market with one warm chapati. But there are two hungry children in the house, Umutoni and her little brother.
One chapati. Two children. Mother picks up a knife and cuts it straight down the middle. Nobody cries. Why not?
Mother cut the chapati into 2 pieces that are exactly the same size. Umutoni takes one piece. Her brother takes the other piece.
Each child is holding one half of the chapati.
We write one half like this: 12
The bottom number (2) says: the whole thing was cut into 2 equal parts. The top number (1) says: you have 1 of those parts.
Suppose mother had cut a big piece and a tiny piece. Is the big piece one half?
No. Two pieces are not enough. They must be two pieces of the same size. If one child gets more chapati than the other, those pieces are not halves. They are just pieces, and somebody will complain!
Put Umutoni's piece and her brother's piece back together. What do you get? The whole chapati again.
12 and 12 make 1 whole.
The next day two cousins arrive. Now there are 4 children and still only one chapati.
Mother cuts it down the middle to make 2 halves. Then she cuts each half down the middle again. Now there are 4 pieces, all the same size.
Each child gets one piece. Each child has one quarter of the chapati.
We write one quarter like this: 14
The bottom number (4) says the whole thing was cut into 4 equal parts. The top number (1) says you have 1 of them.
A quarter is smaller than a half. More cuts means smaller pieces. That is always true.
You can halve a shape like a chapati. You can also halve a group of things.
Keza has 8 oranges. She wants to give one half of them to Mugisha.
Finding one half is just sharing into 2 equal groups, which you already know how to do! Deal the oranges out, one for Keza, one for Mugisha, round and round.
Each of them ends up with 4 oranges.
One half of 8 is 4. (8 ÷ 2 = 4)
Now Keza wants to give one quarter of her 8 oranges to Mugisha.
Finding one quarter is sharing into 4 equal groups. Deal the 8 oranges into 4 groups. Each group has 2 oranges.
One quarter of 8 is 2. (8 ÷ 4 = 2)
So halving and quartering are not new work at all. They are the fair sharing you learned in the last lesson, wearing a different hat.
Tip
Fold a piece of paper. Fold it once, corner to corner, and open it up: 2 equal parts, and each one is a half. Fold it again the other way and open it: 4 equal parts, and each one is a quarter. Your fingers will remember this even when your head forgets.
Draw the shapes if it helps, then tap Show answer to check.
A mango is cut into 2 equal pieces. You eat one piece. How much of the mango did you eat?
Answer: One half, or 12. Two equal pieces, and you took one of them.
What is one half of 10 bottle tops?
Answer: 5. Share the 10 into 2 equal groups. 10 ÷ 2 = 5.
What is one quarter of 12 bananas?
Answer: 3. Share the 12 into 4 equal groups. 12 ÷ 4 = 3.
Ishimwe cuts a mandazi into 2 pieces. One piece is huge and the other is tiny. Has he made halves?
Answer: No. Halves must be exactly the same size. He has just made two pieces.
Mutesi eats 2 quarters of a cake. How much cake did she eat?
Answer: One half. 2 quarters and 1 half are the same amount. Two quarters of the cake are still sitting on the plate.
What you learned today
Quick check
A chapati is cut into 4 equal parts. One part is:
