Lesson 8.3 · Geometry
Halves and fourths
When you share a sandwich with a friend, you want the pieces to be fair. Fair pieces are equal parts: they are all the same size.
Halves
Cut a shape into 2 equal parts. Each part is a half. Two halves make the whole.
Fourths
Cut a shape into 4 equal parts. Each part is a fourth. Another name for a fourth is a quarter. Four fourths make the whole.
Definition
Equal parts
Parts are equal when they are all the same size. A half is 1 of 2 equal parts. A fourth (or quarter) is 1 of 4 equal parts.
Not equal? Not halves!
This circle is cut into 2 parts, but one part is much bigger. These are not halves.
More parts, smaller pieces
Cut the same pizza into halves or into fourths. The fourths are smaller. The more equal parts you cut, the smaller each part is.
More parts means smaller parts
A half is bigger than a fourth of the same whole.
Worked example: Name the parts
A square is cut into 4 equal parts. What is each part called?
Each part is a fourth, or a quarter.
Worked example: Fair share
Ben cuts a pancake into 2 parts. One part is big and one is small. Did he cut it in halves?
No. Halves must be the same size. His parts are not equal.
Worked example: Which is bigger?
You can have half of a pizza or a fourth of the same pizza. Which piece is bigger?
A half is cut into 2 parts. A fourth is cut into 4 parts. Fewer parts means bigger pieces, so half is bigger.
Common mistake
Don't just count the pieces. A shape cut into 2 parts is only cut in halves if both parts are the same size.
Practice
How many halves make one whole?
Type a number.
How many fourths make one whole?
Type a number.
What is another name for a fourth?
Which shows a shape cut into halves?
Which piece of the same sandwich is bigger?
A pie is cut into fourths. Dad eats 1 fourth. How many fourths are left?
Type a number.
Two friends each cut a cracker into halves. How many halves do they have in all?
Type a number.