The idea, step by step
Some objects may be left
Seven counters cannot all be shared equally between three trays if every counter must stay whole. Give two to each tray and one counter stays outside.
The leftover is not an extra share for one tray. Keep it separate so the shares stay equal.
Check whether you have finished
If you have enough left to give everyone one more, keep sharing. Only stop when you cannot complete another fair round.
Check the total: count the objects in all groups, then count the leftovers. Together they must make the original collection.
A common trap
Giving all leftover objects to one person and still calling the shares equal.
Instead: That makes one share larger. If the objects must stay whole, show the leftover separately.
See the thinking
One left over
Share nine whole counters equally between four trays.
- Give each tray two counters. That uses eight.
- One counter remains, which is not enough for another round.
- Keep the one counter outside the trays.
Two left over
Share fourteen whole tokens equally among three people.
- Give four tokens to each person. That uses twelve.
- Two tokens remain.
- Two are not enough to give one more to all three people.
Check your understanding
Share seven whole counters among three trays. How many per tray and left over?
Show answer
2 per tray, with 1 left over.
The shares use six counters; one remains.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Share five whole counters between two trays. State each share and the leftover.
- Share ten whole counters between three trays. State each share and the leftover.
- Share eight whole counters between three trays. State each share and the leftover.
- Share twelve counters between four trays. Is anything left over?
- Eleven counters are shared among three trays. Each has two and five remain. Can you share more fairly? Explain.
- A drawing has four equal groups of three counters and one left over. How many counters altogether?
Read the worked solutions
- Share five whole counters between two trays. State each share and the leftover.
Two and two use four; one remains.
2 per tray, with 1 left over. - Share ten whole counters between three trays. State each share and the leftover.
Three groups of three use nine; one remains.
3 per tray, with 1 left over. - Share eight whole counters between three trays. State each share and the leftover.
Three groups of two use six; two remain.
2 per tray, with 2 left over. - Share twelve counters between four trays. Is anything left over?
Four groups of three use all twelve.
No. Each tray gets three. - Eleven counters are shared among three trays. Each has two and five remain. Can you share more fairly? Explain.
There are enough leftovers for one more complete round.
Yes. Give one more to every tray. Then each has three and two remain. - A drawing has four equal groups of three counters and one left over. How many counters altogether?
3 + 3 + 3 + 3 = 12; add the leftover one.
13 counters.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Practical Year 1 grouping and equal sharing with whole objects.
Official curriculum source ↗