Understand the idea.
Some objects may be left
Sometimes whole objects cannot all be shared fairly. With seven counters and three trays, two can go on each tray and one stays outside. This leftover is kept separate so every tray still has the same number of whole counters.
Check whether you have finished
Keep sharing while you can give everyone one more. Stop only when there are too few leftovers for another complete round. Check your work by counting all the equal shares and then the leftovers; together they must make the starting collection.
See the method in action.
One left over
Share nine whole counters equally between four trays.
Worked solution
- 1
Give two counters to each of the four trays.
Two full rounds use eight of the nine counters and keep the shares equal.
- 2
Find how many counters remain.
One whole counter has not been placed.
- 3
Check whether another round is possible.
Four counters would be needed to give every tray one more. Keep the one leftover outside, leaving two per tray.
2 counters per tray, with 1 left over.
Two left over
Share fourteen whole tokens equally among three people.
Worked solution
- 1
Give four tokens to each of the three people.
These equal shares use twelve tokens.
- 2
Count the remaining tokens.
Two whole tokens are left after the equal shares are made.
- 3
Check for another fair round.
Three tokens would be needed to give everyone one more. Each person gets four, with two left over.
4 tokens each, with 2 left over.
Try it yourself.
Check your understanding
Share seven whole counters among three trays. How many per tray and left over?
Show answer & reasoning
2 per tray, with 1 left over.
Two on each of three trays uses counters. Since , one is left over; it is too few for another round of three.
Keep practising
6 worksheet questions
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?
; 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 ↗