Contextual remainders | Year 5

01 / LEARN

Understand the idea.

Division does not always finish exactly

A remainder is what is left after making as many complete equal groups as possible. Since $29 = 4 \times 7 + 1$ , dividing $29$ by $4$ gives $7$ whole groups with $1$ left. A remainder must be smaller than the divisor.

That calculation alone does not decide the final answer. Sharing counters may leave one aside, but transporting people needs a seat for everyone. A remainder of one person requires another vehicle even when that vehicle will not be full.

The same division can answer different questions
Situation	Interpretation of 29 ÷ 4
Counters shared among four groups	7 each, 1 left
Cars with four seats	8 cars are needed
Four equal pieces of a 29 m ribbon	7 and one-quarter metres each

Read the question before deciding

Read exactly what is being counted. For complete packs, keep the whole groups and state the leftovers. For enough containers to hold everything, add one more container if there is a remainder. Do not apply the same rounding decision to both situations.

When the item can be cut or shared, a remainder can become a fraction. A $29$ metre ribbon split into four equal pieces gives $7 \frac{1}{4}$ metres each. People, full packs and lengths require different interpretations of the same division.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Enough boats for everyone

A club has 38 people. Each boat holds six people. How many boats are needed?

Worked solution

1
Fill as many boats as possible.
$6 \times 6 = 36$
Six full boats carry 36 people.
2
Find the people still needing places.
$38 - 36 = 2$
Two people remain after the six boats are full.
3
Include a boat for the remaining people.
$6 + 1 = 7$
The remainder cannot be left behind, so 7 boats are needed.

Answer

7 boats.

EXAMPLE 02

Count only complete packs

A baker has 50 biscuits. A sale pack needs eight biscuits. How many complete packs can be made, and how many biscuits remain?

Worked solution

1
Find the largest full-packs total below fifty.
$6 \times 8 = 48, 7 \times 8 = 56 > 50$
Six packs are possible; seven packs would need more biscuits than are available.
2
Calculate the leftover biscuits.
$50 - 48 = 2$
The remainder is 2 biscuits, less than the 8 needed for a pack.
3
State the complete packs and the remainder.
$50 = 8 \times 6 + 2$
There are 6 complete packs and 2 biscuits left; an incomplete pack does not count.

Answer

6 complete packs, with 2 biscuits left.

03 / YOUR TURN

Try it yourself.

Check your understanding

Twenty-three students need tables seating four. How many tables are needed?

Show answer & reasoning

6 tables.

Five tables seat $5 \times 4 = 20$ students, leaving $23 - 20 = 3$ . They need another table, so $5 + 1 = 6$ tables are required.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Divide 35 by 6. State the whole quotient and remainder.
1 mark
Forty-three apples are packed six to a bag. How many full bags can be made, and how many apples remain?
2 marks
Fifty-three passengers need vans holding eight passengers each. How many vans are needed?
2 marks
A 19-metre ribbon is cut into four equal pieces. What is the length of each piece?
2 marks
A game needs teams of five. There are 37 players. How many complete teams can be made and how many people will not be in a complete team?
2 marks
A school has 41 students and buses with ten student seats. A learner says four buses are enough because $41 \div 10$ gives four remainder one. Explain the mistake.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Divide 35 by 6. State the whole quotient and remainder.
1 mark
$6 \times 5 = 30$ and $35 - 30 = 5$ .
5 remainder 5.
Forty-three apples are packed six to a bag. How many full bags can be made, and how many apples remain?
2 marks
$6 \times 7 = 42$ , leaving one.
7 full bags, 1 apple left.
Fifty-three passengers need vans holding eight passengers each. How many vans are needed?
2 marks
Eight times six is forty-eight, leaving five passengers.
A seventh van is needed.
7 vans.
A 19-metre ribbon is cut into four equal pieces. What is the length of each piece?
2 marks
Four complete metres for each piece use sixteen metres.
Share the remaining three metres equally among four pieces.
4 and three-quarter metres.
A game needs teams of five. There are 37 players. How many complete teams can be made and how many people will not be in a complete team?
2 marks
$5 \times 7 = 35$ , leaving two.
7 teams, 2 players left.
A school has 41 students and buses with ten student seats. A learner says four buses are enough because $41 \div 10$ gives four remainder one. Explain the mistake.
3 marks
Four buses seat forty students only.
The one remaining student must also have a seat, so include a fifth bus.
Five buses are needed.

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Curriculum Mathematics 2026

One-/two-digit multipliers; division strategies; contextual remainders; inverse fact families; unknown factors/dividends/divisors.

Official curriculum source ↗

In this lesson

Understand the idea.

Division does not always finish exactly

Read the question before deciding

See the method in action.

Enough boats for everyone

Fill as many boats as possible.

Find the people still needing places.

Include a boat for the remaining people.

Count only complete packs

Find the largest full-packs total below fifty.

Calculate the leftover biscuits.

State the complete packs and the remainder.

Try it yourself.

Check your understanding

Keep practising