Mathematics K–6 · Years 3–4
Fraction strips: unit fractions and completing the whole
Number and algebra
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The idea
A unit fraction is one of several equal parts of a whole, and enough copies of it laid end to end make the whole again.
What you need
- 7 paper strips 30 cm long per child, each a different colour
- a 30 cm ruler
- scissors and a glue stick
- an A3 sheet for a fraction wall
How to do it
- Keep one strip whole. Fold and cut the others into 2, 3, 4, 5, 6 and 10 equal parts, measuring to check that every part in a strip is the same length. Label each part with its unit fraction.
- Glue the whole strip at the top of the sheet and each cut strip below it, parts touching, to make a fraction wall.
- Take three fifths and lay them under the whole. Say how many more fifths complete the whole, then lay them and check.
- Find every unit fraction row that has parts lining up with one half, and write the equivalences you see.
- Compare one third with one quarter by laying them side by side from the same start and say which is longer and why.
What you should see
On a 30 cm whole the parts measure 15 cm (halves), 10 cm (thirds), 7.5 cm (quarters), 6 cm (fifths), 5 cm (sixths) and 3 cm (tenths). Three fifths need two more fifths to complete the whole. Two quarters, three sixths and five tenths each line up exactly with one half. One third (10 cm) is longer than one quarter (7.5 cm), which corrects the claim that a bigger denominator means a bigger part.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- One fifth is bigger than one quarter because 5 is bigger than 4.
- Any five pieces are fifths, even when they are different sizes.
Safety card
Hazards
- scissors
Controls
- rounded-tip scissors
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
Sources
The pages the author read to write this activity.