Mathematics K–6 · Years 1–2

Equal groups and arrays with counters

Number and algebra

Practical, model not builtLow risk

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The idea

Equal groups arranged in rows make an array, and turning the array shows that 3 rows of 4 and 4 rows of 3 hold the same number.

What you need

40 counters
10 paper plates
a sheet of 1 cm grid paper and a pencil
a set of 20 shoe pictures to count in twos

How to do it

Put 12 counters into equal groups on plates: first 2 per plate, then 3, then 4, then 6. Record how many plates each time.
Slide the plates of 4 into a row and tip the counters out in straight rows to make an array of 3 rows of 4. Count by rows: 4, 8, 12.
Turn the array a quarter turn. Count by rows again: 3, 6, 9, 12. Say what changed and what stayed the same.
Count the 20 shoe pictures in twos, pointing to each pair, then in fives by grouping five pictures at a time.
Draw two different arrays for 18 on the grid paper and write the counting sequence beside each.

What you should see

12 counters make 6 plates of 2, 4 plates of 3, 3 plates of 4 and 2 plates of 6. The array of 3 rows of 4 and its quarter turn both hold 12, so the pair records 3 fours and 4 threes as the same total. Counting the 20 shoes in twos takes 10 counts and in fives takes 4. Arrays for 18 include 2 rows of 9, 3 rows of 6 and their turns, and every one counts to 18.

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.

Turning an array changes how many counters there are.
Counting in twos skips some counters, so it gives a smaller answer than counting in ones.

Safety card

Low riskLearners carry it out

Hazards

counters are a choking hazard for very young children

Controls

supervise and count counters back in

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.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA1-FG-01 MAO-WM-01
Australian Curriculum v9AC9M1N03AC9M2N05AC9M2A03

Sources

The pages the author read to write this activity.

All Concept Studio activities