Primary 3 maths · Operations · About 10 minutes
Interpret remainders
Separate complete groups from the leftovers. Compare the leftovers with one group’s size.
Start the interactive lesson →Open practice activity
What you will learn
- Interpret remainders
Models used: number sentences, stories, tables.
Before you start
When there are some left over
We have 14 counters. Put them into bags of 4.
Each bag is one group. Counters outside the bags are left over.
We have 14 counters. Put them into bags of 4.
The remainder is smaller than a full group. Otherwise we could still make another complete group.
Each bag is one group. Counters outside the bags are left over.
Three full bags use 12 counters. Two counters are still outside.
Equal sharing means every share has the same amount. Check both conditions: the shares match, and all the starting objects are accounted for.
Group 1: 4Group 2: 4Group 3: 4Each bag is one group. Counters outside the bags are left over.
Two counters cannot fill another bag of 4. We call the 2 left over the remainder.
14 ÷ 4 = 3 remainder 2
Equal sharing means every share has the same amount. Check both conditions: the shares match, and all the starting objects are accounted for.
Group 1: 4Group 2: 4Group 3: 4
What did the picture help us see?
Two counters cannot fill another bag of 4. We call the 2 left over the remainder.
Worked example: A new example, together
What is the remainder in 758 ÷ 6?
| Total | Equal groups | Left over |
|---|---|---|
| 758 | 126 groups of 6 | ? |
Count complete groups first. Read each value with the heading above its column.
Separate complete groups from the leftovers. Compare the leftovers with one group’s size.
The remainder is what is left after making as many full groups as possible.
Count complete groups first Total Equal groups Left over 758 126 groups of 6 ? Count complete groups first. Read each value with the heading above its column.
6 × 126 = 756 fits into 758.
Count complete groups first Total Equal groups Left over 758 126 groups of 6 ? What is the remainder in 758 ÷ 6?
2
Count complete groups first. Read each value with the heading above its column.
6 × 126 = 756 fits into 758.
Count complete groups first Total Equal groups Left over 758 126 groups of 6 ? Count complete groups first. Read each value with the heading above its column.
758 − 756 = 2.
Count complete groups first Total Equal groups Left over 758 126 groups of 6 ? Count complete groups first. Read each value with the heading above its column.
The remainder 2 is smaller than 6.
Count complete groups first Total Equal groups Left over 758 126 groups of 6 ? Count complete groups first. Read each value with the heading above its column.
Check the result against the question we started with.
126 × 6 + 2 = 758.
We found 2. The remainder is what is left after making as many full groups as possible.
Count complete groups first Total Equal groups Left over 758 126 groups of 6 ?
Common mistakes to discuss
- Ignoring what is left over. The situation decides what to do with the remainder. If 23 pupils need boats holding 4, the answer is 6 boats, because the 3 left still need one.
Check your understanding
- Interpret remainders
- explain a remainder and check it is smaller than the divisor
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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