The idea, step by step
Halve every piece
First fold or cut one whole into two equal parts. To make quarters, halve both halves. There are now four equal parts. Halving only one of the two halves would leave three unequal pieces.
Smaller pieces, same whole
Halve each quarter to make eighths. The number of equal pieces doubles: 1 whole, 2 halves, 4 quarters, 8 eighths. The whole has not grown. Each piece gets smaller because the same whole is shared into more parts.
A common trap
Halving just one piece and calling every piece a quarter.
Instead: To keep equal parts, halve every piece at that stage.
See the thinking
Fold to make quarters
A strip is folded in half. Each half is folded in half again. How many equal parts are made?
- The first fold makes two equal parts.
- Each of those two parts splits into two: 2 + 2 = 4.
Make eighths
A rectangle has four equal quarters. Each quarter is cut into two equal pieces. How many pieces are there?
- Each of the four quarters gives two pieces.
- Count 2, 4, 6, 8.
Check your understanding
A whole is halved three times, with every piece halved each time. How many equal parts result?
Show answer
8 equal parts.
The number of parts goes 1, 2, 4, 8.
Your turn
6 questions · Work at your own pace.
Read the questions online
- How many equal pieces are there after halving one whole once?
- How many quarters are made by halving both halves?
- How many eighths fit into one quarter?
- A strip has eight equal pieces. What is each piece called?
- After making halves, Kai cuts only one half again. Are all three pieces equal? Explain.
- Use the same-sized strips shown. Which is larger: one half or one eighth?
Read the worked solutions
- How many equal pieces are there after halving one whole once?
One whole becomes two equal halves.
2 - How many quarters are made by halving both halves?
Each of two halves gives two quarters.
4 - How many eighths fit into one quarter?
Halving one quarter makes two eighths.
2 eighths. - A strip has eight equal pieces. What is each piece called?
The whole is shared into eight equal parts.
One eighth. - After making halves, Kai cuts only one half again. Are all three pieces equal? Explain.
Both halves would need to be halved to make equal quarters.
No. One half is larger than either of the two smaller pieces. - Use the same-sized strips shown. Which is larger: one half or one eighth?
The same whole is split into fewer pieces for halves, so each half is larger.
One half.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Equal parts; repeated halving; fractions of shapes, objects and measures.
Official curriculum source ↗