Cut through the middle
Take a circle and cut it with one straight cut that goes right through its middle. The circle falls into two pieces that are exactly the same size and shape. Each piece is a half circle.
A half circle has two edges: one straight side, which is the cut, and one curved edge, which is half of the circle's edge. The straight side is as long as the circle is wide.
One cut through the middle makes two half circles. One of them is shaded.
A half circle on its own: one straight side and one curved edge.
Only a cut through the middle makes halves
A cut that misses the middle also makes two pieces, but one is bigger than the other. Neither piece is a half circle, because the two halves of a circle must be the same size.
the cut misses the center, so the pieces differ: bigger piece ≠ smaller piece, by the red strip the folded piece does not cover
Cut the circle into 2 half circles
The gold piece is folded over the cut onto the other piece. Off the middle it falls short, and the red strip is how much bigger the other piece is. Through the middle it covers the other piece exactly, so the two pieces are half circles.
Cut the half in half again
Now cut the half circle in half, straight down through the middle of its straight side. That makes two smaller pieces, each a quarter circle. Cutting the whole circle this way makes four quarter circles, all the same size.
A quarter circle has two straight sides and one curved edge. The two straight sides meet at a corner, which is a square corner, like the corner of a page. That corner was the middle of the whole circle.
Two cuts through the middle make four quarter circles. One of them is shaded.
the cuts cross away from the center, so the 4 pieces come in two sizes: bigger ≠ smaller, and none is a quarter circle
Cut the circle into 4 quarter circles
One cut stands through the middle. The other cut makes four quarter circles only where it also passes through the middle, at a square corner to the first.
A quarter circle on its own: two straight sides meeting at a corner, and one curved edge.
Putting the pieces back
The pieces fit back together into the circle they came from. 2 half circles make 1 whole circle. 4 quarter circles make 1 whole circle. 2 quarter circles, side by side, make a half circle.
So to tell the three shapes apart, count the straight sides. A whole circle has none, a half circle has one, and a quarter circle has two.
The 2 shaded quarter circles together cover the same part of the circle as a half circle.
Worked example: Half Circles and Quarter Circles Put Together into Whole Circles
Question 2 half circles put together make 1 whole circle. 4 quarter circles put together make 1 whole circle. (a) Ben uses half circles. How many half circles make 3 whole circles? (b) Mei uses quarter circles. How many quarter circles make 2 whole circles?
1.Draw a circle and cut it through the middle. It makes 2 half circles, so 2 half circles make 1 whole circle.
A cut through the middle of a circle makes 2 half circles. So 2 half circles make 1 whole circle. 2.Draw 3 whole circles. Cut each one into 2 half circles.
Draw 3 whole circles and cut each one into 2 half circles. 3.(a) Count the half circles: 2 + 2 + 2 = 6. Ben needs 6 half circles.
(a) 2 + 2 + 2 = 6. Ben needs 6 half circles. 4.Draw a circle and cut it into 4 equal parts. Each part is a quarter circle, so 4 quarter circles make 1 whole circle.
Cut a circle into 4 equal parts. Each part is a quarter circle, so 4 quarter circles make 1 whole circle. 5.(b) Draw 2 whole circles and cut each one into 4 quarter circles. 4 + 4 = 8. Mei needs 8 quarter circles.
(b) 4 + 4 = 8. Mei needs 8 quarter circles.
Answer: (a) 6 half circles; (b) 8 quarter circles
Common mistakes
- Saying 3 half circles for 3 whole circles. Each whole circle needs 2 half circles, so count 2 for every circle.
- Using 2 quarter circles for each whole circle in part (b). 2 quarter circles make only a half circle. A whole circle needs 4 quarter circles.
More shapes and where they sit problems, worked step by step →