Primary 3 · Mathematics · Number
Exploring fractions
Making halves, thirds, quarters, fifths and other unit fractions by folding paper and sharing collections, and counting fractions such as one quarter, two quarters, three quarters.
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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, thirds, quarters and fifths of shapes by folding paper.
- Find unit fractions of collections by sharing into equal groups.
- Count by unit fractions, such as one quarter, two quarters, three quarters, four quarters.
Success looks like
- I can fold a paper strip into thirds, quarters or fifths with equal parts.
- I can find 13 of 12 by sharing 12 into 3 equal groups.
- I can count in quarters and know that four quarters make one whole.
The big idea
A fraction describes equal parts of a whole. The bottom number, the denominator, tells how many equal parts the whole is split into. The top number, the numerator, tells how many of those parts we are talking about.
A unit fraction has 1 as its numerator. 12 is one of 2 equal parts, 13 is one of 3 equal parts, 14 is one of 4 equal parts and 15 is one of 5 equal parts.
Fold paper strips to make fractions. Halves and quarters are easy: fold in half, then in half again. Thirds are trickier — roll the strip into an S shape and adjust it until the three layers line up exactly, then press flat. For fifths, measure: a 30 cm strip has fifths every 6 cm.
Lay the strips one under another. Notice that the bigger the denominator, the smaller each part. 15 is smaller than 13, because the whole is shared among more parts.
Fractions of collections use sharing. To find 13 of 12 counters, share them into 3 equal groups. Each group has 4, so 13 of 12 is 4. To find 15 of 15, share into 5 groups: each has 3.
We can count by fractions just like whole numbers. Colour a strip of quarters one part at a time and say: one quarter, two quarters, three quarters, four quarters. Four quarters cover the whole strip, so 44 is the same as 1 whole.
- 13 means 1 of 3 equal parts.
- 14, 24, 34, 44 = 1 whole.
- More equal parts means smaller parts.
Worked examples
A fraction of a collection
What is 13 of 12 strawberries?
- The denominator is 3, so share the strawberries into 3 equal groups.
- Deal them out one at a time until all 12 are shared.
- Count one group: 4.
Answer: 13 of 12 is 4.
Counting in fifths
A strip is folded into fifths. Count the parts as you colour them, one at a time.
- Colour one part: one fifth, 15.
- Keep going: 25, 35, 45.
- Colour the last part: 55. The whole strip is coloured.
Answer: One fifth, two fifths, three fifths, four fifths, five fifths. 55 is one whole.
Comparing unit fractions
Which is bigger, 13 or 15 of the same pizza?
- In 13, the pizza is cut into 3 equal slices.
- In 15, the same pizza is cut into 5 equal slices.
- Sharing among more slices makes each slice smaller.
Answer: 13 is bigger than 15.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
How many thirds make one whole?
3 — A third is 1 of 3 equal parts, so 3 thirds make a whole.
What is 13 of 12?
4 — Share 12 into 3 equal groups: 4 in each group.
Which is the biggest piece of the same cake?
12 — The fewer equal parts the cake is cut into, the bigger each part. Halves are the biggest here.
Count in quarters: one quarter, two quarters, ___. Write the next fraction.
3/4 — After two quarters comes three quarters, 34.
What is 15 of 20?
4 — Share 20 into 5 equal groups: 4 in each group.
A shape is split into 5 equal parts and 1 part is shaded. What fraction is shaded?
15 — 1 part out of 5 equal parts is 15.
44 is the same as …
one whole — Four quarters cover the whole shape, so 44 = 1 whole.
A pizza is cut into 3 equal slices. Ana eats 1 slice. What fraction of the pizza is left?
2/3 — There were 3 thirds. 1 third was eaten, so 2 thirds, 23, are left.
Watch out for
- Thinking 15 is bigger than 13 because 5 is bigger than 3. Compare folded strips side by side to see the parts get smaller.
- Making parts that are not equal and still calling them thirds or fifths. Always check the parts match exactly by folding or measuring.
- Thinking a fraction of a collection is the number of groups rather than the number in one group (13 of 12 answered as 3). Point to one group and count it.
Tips for parents
- Use food to make fractions real: cut a sandwich into thirds or share a packet of crackers into fifths.
- Say fractions out loud as words and as numbers: 'two thirds' and 23.
- Folding thirds is genuinely hard — let your child try, adjust and try again before measuring.
Go further
- Make a fraction wall with strips for halves, thirds, quarters and fifths, glued one under another, and compare the pieces.
- Find 12, 13, 14 and 15 of 60 using counters or drawings. Which is largest?
- Count in thirds past one whole: one third, two thirds, three thirds (one whole), four thirds … and draw it with strips.
About 40 minutes
You'll need
- Paper strips about 30 cm long (several of each colour)
- Scissors, coloured pencils and a ruler
- 20 small objects such as counters, beans or buttons
- Small bowls or paper circles for sharing
Key words
- fraction
- A number that shows equal parts of a whole or a collection.
- unit fraction
- A fraction showing one equal part, such as 13 or 15.
- numerator
- The top number of a fraction; it tells how many parts we have.
- denominator
- The bottom number of a fraction; it tells how many equal parts make the whole.
- third
- One of 3 equal parts.
- fifth
- One of 5 equal parts.
Still tricky?
For parents
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