Understand the idea.
Halve every piece
Fold a whole strip in half so its ends match. Now halve both halves. Each half gives two smaller pieces, making four equal quarters. If you halve only one half, the uncut half is still larger than the new pieces.
Smaller pieces, same whole
Halve every quarter to make eight equal eighths. Each round of halving doubles the number of pieces: . The amount of paper stays the same. More equal pieces mean each piece is smaller.
See the method in action.
Fold to make quarters
A strip is folded in half. Each half is folded in half again. How many equal parts are made?
Worked solution
- 1
Make the first pair of equal shares.
Folding the whole in half makes two equal halves.
- 2
Halve both halves and count.
Each of the two halves makes two pieces, so all four pieces are equal.
- 3
Name the four equal pieces.
Each piece is one quarter of the original strip.
4 equal parts, called quarters.
Make eighths
A rectangle has four equal quarters. Each quarter is cut into two equal pieces. How many pieces are there?
Worked solution
- 1
Give each quarter two equal pieces.
Every quarter is halved, so no larger quarter is left uncut.
- 2
Count the pieces from all four quarters.
There are two pieces from each of four equal quarters.
- 3
Name one piece.
Eight equal pieces make the original whole, so each is one eighth.
8 equal pieces, called eighths.
Try it yourself.
Check your understanding
A whole is halved three times, with every piece halved each time. How many equal parts result?
Show answer & reasoning
8 equal parts.
Start with one whole. After each round the number of pieces doubles: . Three rounds make eight equal parts.
Keep practising
6 worksheet questions
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 ↗