Mathematics K–6 · Years 3–4
Counting by quarters along a rope
Number and algebra
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The idea
Fractions are numbers with places on a number line, so counting by quarters passes 1 and continues to mixed numerals such as one and a quarter.
What you need
- a 3 m rope stretched between two chairs
- 13 clothes pegs and 13 blank cards
- a 1 m rule
- a set of fraction cards: 1/4, 2/4, 3/4, 1, 1 1/4, 5/4, 1 1/2, 2, 2 3/4
- a strip of paper 1 m long for folding into quarters
How to do it
- Mark 0 at one chair. Use the metre rule to peg cards at 1 m, 2 m and 3 m, labelled 1, 2 and 3 (one metre is the whole).
- Fold a 1 m strip of paper into quarters and use it to peg a card every 25 cm. Label the pegs counting aloud: one quarter, two quarters, three quarters, four quarters or 1, five quarters or one and a quarter, and so on to 3.
- Draw a fraction card and clip it on the peg where it belongs. Check with a partner, then read off another name for the same peg (for example 5/4 and 1 1/4).
- Start at 0 and count by halves to 3 using only the pegs that halves land on. Then count by three-quarters and see where each count lands.
- Draw the rope as a number line in your book with every peg labelled two ways where two names exist.
What you should see
A 3 m rope with the metre as the whole has 12 quarter-intervals and 13 pegs from 0 to 3. Five quarters and one and a quarter go on the same peg at 1.25 m, and two halves, four quarters and 1 share the peg at 1 m. Counting by three-quarters from 0 lands on 0.75 m, 1.5 m, 2.25 m and 3 m, four counts to reach 3. Every peg has a fraction name and the ones past 1 have a mixed-numeral name as well.
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.
- Fractions are always less than 1, so counting by quarters stops at 3/4.
- 5/4 and 1 1/4 are different amounts.
Safety card
Hazards
- a rope at ankle height is a trip hazard
Controls
- stretch the rope at waist height between chairs, away from walkways
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.