Larger calculations | Year 4

01 / LEARN

Understand the idea.

Partition larger numbers

Split a larger factor into useful place-value parts. To calculate $6 \times 23$ , count six groups of twenty and six groups of three, then combine their totals. Both parts must be multiplied because both belong to every group of twenty-three.

For division, choose parts that share easily. In $156 \div 3$ , split the total as $150 + 6$ . Each of three people receives $50$ from the first part and $2$ from the second, making $52$ each.

A remainder must fit the situation

A remainder is the amount left after making as many full groups as possible. In $86 \div 4$ , twenty-one groups use $84$ and leave $2$ . The remainder must be smaller than $4$ ; otherwise another full group could be made.

Check the total using the groups and leftovers: $divisor \times quotient + remainder$ . Then read the story. Leftover counters may stay unshared, while packing every item into containers may need an extra container. Give each number a clear meaning.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Multiply in parts

Find 23 × 6.

Worked solution

1
Split the larger factor.
$23 = 20 + 3$
Twenty-three contains twenty and three, and both parts must be multiplied by six.
2
Multiply each part.
$\begin{aligned} 20 \times 6 & = 120 \\ 3 \times 6 & = 18 \end{aligned}$
Twenty groups of six and three groups of six cover all twenty-three groups.
3
Combine the partial products.
$120 + 18 = 138$
Adding the two totals counts every part of the 23 groups of six.

Answer

138.

EXAMPLE 02

Divide and interpret

86 counters are shared equally among 4 pupils. How many does each get, and how many remain?

Worked solution

1
Give each pupil twenty counters.
$\begin{aligned} 4 \times 20 & = 80 \\ 86 - 80 & = 6 \end{aligned}$
Sharing eighty counters equally leaves six still to share.
2
Give each pupil one more counter.
$\begin{aligned} 20 + 1 & = 21 \\ 6 - 4 & = 2 \end{aligned}$
One extra each uses four counters, leaving fewer than one per pupil.
3
Check the equal shares and leftovers.
$4 \times 21 + 2 = 86$
Four shares of 21 and two unshared counters reconstruct all 86 counters.

Answer

21 counters each, with 2 counters left over.

03 / YOUR TURN

Try it yourself.

Check your understanding

Find 152 ÷ 4 using 120 + 32.

Show answer & reasoning

38.

Split the total as requested: $120 \div 4 = 30$ and $32 \div 4 = 8$ . Each share contains both parts, so $30 + 8 = 38$ . Check $4 \times 38 = 152$ .

Keep practising

6 worksheet questions · 8 marks

Open worksheet Worked solutions

Read the questions online

Find $34 \times 3$ .
1 mark
Find $46 \times 5$ .
1 mark
Find $168 \div 4$ .
1 mark
Find $246 \div 3$ .
1 mark
Put 95 apples into full bags of 6. How many full bags can be made, and how many apples remain?
2 marks
A coach must seat 47 pupils in minibuses with 8 pupil seats each. How many minibuses are needed? Explain the remainder.
2 marks

Read the worked solutions

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

Find $34 \times 3$ .
1 mark
$30 \times 3 = 90$ ; $4 \times 3 = 12$ .
$90 + 12 = 102$ .
102.
Find $46 \times 5$ .
1 mark
$40 \times 5 = 200$ ; $6 \times 5 = 30$ .
$200 + 30 = 230$ .
230.
Find $168 \div 4$ .
1 mark
$160 \div 4 = 40$ ; $8 \div 4 = 2$ .
$40 + 2 = 42$ .
42.
Find $246 \div 3$ .
1 mark
$240 \div 3 = 80$ ; $6 \div 3 = 2$ .
$80 + 2 = 82$ .
82.
Put 95 apples into full bags of 6. How many full bags can be made, and how many apples remain?
2 marks
$6 \times 15 = 90$ .
$95 - 90 = 5$ ; the remainder is less than 6.
15 full bags and 5 apples left.
A coach must seat 47 pupils in minibuses with 8 pupil seats each. How many minibuses are needed? Explain the remainder.
2 marks
$47 \div 8 = 5 remainder 7$ .
Five minibuses seat only 40 pupils. The other 7 need one more minibus.
6 minibuses.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Facts to 10×10; related division; larger calculations; multiples/powers of ten; efficient strategies.

Official curriculum source ↗

In this lesson

Understand the idea.

Partition larger numbers

A remainder must fit the situation

See the method in action.

Multiply in parts

Split the larger factor.

Multiply each part.

Combine the partial products.

Divide and interpret

Give each pupil twenty counters.

Give each pupil one more counter.

Check the equal shares and leftovers.

Try it yourself.

Check your understanding

Keep practising