Primary 2 · Mathematics · Number
Halves, quarters and eighths
Folding and cutting shapes and sharing collections to make halves, quarters and eighths, and understanding that the parts of a fraction must be equal.
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These lessons were written around Australian Curriculum strands and matched to Singapore levels by age (Primary 1 is the first year of primary school). They are not aligned to MOE syllabuses or the PSLE, so check them against the syllabus your child is working towards.
Learning goals
Learners will
- Make halves, quarters and eighths of a shape by folding and cutting.
- Share a collection into halves, quarters and eighths.
- Explain that the parts of a fraction must be equal.
Success looks like
- I can fold paper into halves, quarters and eighths.
- I can find half or a quarter of a small collection, like half of 8 strawberries.
- I can tell if a shape has been split into equal parts or not.
The big idea
A fraction is an equal part of a whole. The most important idea in this lesson is that the parts must be equal. If a sandwich is cut into one big piece and one small piece, those are not halves.
Fold a square of paper so the edges match exactly, then open it. The fold line has made 2 equal parts. Each part is one half, written 12. Two halves make the whole.
Fold the paper in half again and open it out. Now there are 4 equal parts. Each part is one quarter, written 14. Fold once more to make 8 equal parts. Each part is one eighth, written 18.
Notice what happens: halves are folded in half to make quarters, and quarters are folded in half to make eighths. The more equal parts there are, the smaller each part is. One eighth is smaller than one quarter, and one quarter is smaller than one half.
Fractions also work with collections. To find half of 8 buttons, share them into 2 equal groups: each group has 4, so half of 8 is 4. To find a quarter of 8, share them into 4 equal groups: each has 2. To find an eighth of 8, share into 8 groups of 1.
Always check the parts are equal. Ask, 'Would everyone be happy with their piece?' If one piece is bigger, it is not a fair share and the parts are not halves, quarters or eighths.
- 12: 1 of 2 equal parts.
- 14: 1 of 4 equal parts.
- 18: 1 of 8 equal parts.
Worked examples
Folding quarters
Fold a square sheet of paper to show quarters.
- Fold the paper in half so the edges match exactly. Crease it.
- Keep it folded and fold it in half again. Crease it.
- Open it up. Count the parts: there are 4, and they are all the same size.
- Colour one part. That part is one quarter.
Answer: The paper is folded into 4 equal parts; each part is 14.
Half of a collection
What is half of 10 strawberries?
- Half means 2 equal groups.
- Share the strawberries one at a time into 2 groups.
- Count one group: 5.
Answer: Half of 10 is 5.
Equal parts or not?
A pizza is cut into 4 pieces, but two pieces are big and two are small. Is each piece a quarter?
- Quarters must be 4 equal parts.
- The pieces are different sizes, so they are not equal.
Answer: No. The pieces are not quarters because they are not equal.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
A shape is split into 2 equal parts. What is each part called?
a half — 2 equal parts are halves.
What is half of 8?
4 — Share 8 into 2 equal groups: 4 and 4.
How many quarters make a whole?
4 — A quarter is 1 of 4 equal parts, so 4 quarters make a whole.
What is a quarter of 12 crackers?
3 — Share 12 into 4 equal groups: each group has 3.
A cake is cut into 2 pieces. One piece is much bigger than the other. Are they halves?
No, because the pieces are not equal — Halves must be equal in size. Two different-sized pieces are not halves.
Which is the smallest piece of the same pancake?
18 — The more equal parts the pancake is cut into, the smaller each part is. Eighths are the smallest.
You fold a paper in half, then in half again, then in half again. How many equal parts are there when you open it?
8 — 2 parts, then 4 parts, then 8 parts. Each part is one eighth.
What is one eighth of 16 buttons?
2 — Share 16 into 8 equal groups: each group has 2.
Watch out for
- Calling any piece a 'half', even when it is bigger or smaller. Keep asking 'Are the parts equal?'
- Thinking 18 is bigger than 14 because 8 is bigger than 4. Fold paper to show eighths are smaller pieces.
- Believing halves must be cut the same way every time. Show a square cut into halves down the middle, across, and from corner to corner.
Tips for parents
- Use food: cut sandwiches, pizza or fruit into halves and quarters and talk about whether the pieces are equal.
- Say fraction names often: 'Can you eat one quarter of the orange?'
- When sharing collections, deal items one at a time so the groups stay equal.
Go further
- Find as many different ways as you can to fold a square into halves, then into quarters.
- Make a fraction wall from paper strips: one whole, two halves, four quarters and eight eighths, lined up underneath each other.
- Make a pizza from paper and cut it into eighths, then put toppings on 12, 14 and 18 of it.
About 35 minutes
You'll need
- Square and rectangular sheets of paper
- Scissors and coloured pencils
- 16 small objects such as buttons, crackers or blocks
- A slice of bread or a pancake (optional, for a tasty demonstration)
Key words
- fraction
- An equal part of a whole shape or a whole collection.
- whole
- The complete shape or group before it is split.
- half
- One of 2 equal parts of a whole.
- quarter
- One of 4 equal parts of a whole.
- eighth
- One of 8 equal parts of a whole.
- equal
- Exactly the same size or the same number.
Still tricky?
For parents
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