A rectangle can be halved down the middle, or across, or corner to corner.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
All of them are halves
Each cut makes two equal shares, so each one really is a half.
The thing people get wrong
Shares must be equal in *size*. They do not have to be the same shape.
How to judge
Ask whether the two pieces cover the same amount, not whether they look alike.
Equal shares need not be the same shape
Cut a square in half with a diagonal and you get two triangles. Cut it with a vertical line and you get two rectangles. All four pieces are halves of the same square, even though triangles and rectangles look nothing alike. Equal means equal in amount, not identical in outline.
How to check they really are equal
For simple shapes you can cut the pieces out and lay one on top of the other, turning or flipping if needed. If they cover each other exactly, they were equal. For trickier cases, count squares on grid paper — the same number of squares means the same amount.
Naming a share of a shape
If a shape is split into four equal parts and one is shaded, that shaded part is one fourth of the shape — regardless of which part it is or what shape it is. The name depends only on how many equal parts there are and how many you have taken.
Step 2: Try It Yourself
A circle and a rectangle, both cut into equal shares.
The whole is cut into 2 equal shares, called halves.
The whole is cut into 2 equal shares, called halves.
These pieces are not the same size, so they are not halves.
How many pieces
Step 3: Watch an Example
One step at a time.
Watch Leo Judge Two Cuts
Two identical squares are halved, one down the middle and one corner to corner.
- Step 1
He looks at the first: two rectangles, clearly the same size.
Step 4: Your Turn
Practice makes it stick.
Two Cuts
Problem 1 of 2
A square is cut corner to corner into two triangles. Are they halves?
Not Fair
Problem 2 of 2
A rectangle is cut into a big piece and a small piece. Are they halves?
Is It Really Halved?
1 of 3
Must two halves be the same shape?
2 of 3
Must two halves be the same size?
3 of 3
How many different ways can a square be halved?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Two halves of a square are triangles. Is that allowed?
Question 2 of 2
What has to be equal about equal shares?
What You Learned
- A shape can be cut into equal shares in more than one way.
- Equal shares must be the same size.
- They do not have to be the same shape.