Mental strategies | Year 3

01 / LEARN

Understand the idea.

Split or bridge

Choose useful parts instead of counting every one. To add $23$ to $46$ , add the $20$ first and then the $3$ . Each part must be used once so the amount added is still $23$ .

Bridge a ten when a number is nearly a multiple of ten. For $38 + 7$ , split $7$ into $2 + 5$ . Add $2$ to reach $40$ , then add the remaining $5$ to reach $45$ .

Adjust a nearby number

A nearby easy number can make mental work shorter. For $57 + 19$ , add $20$ to reach $77$ , then remove $1$ . You added one more than the question asked, so you must undo that extra one.

For subtraction the adjustment reverses. To subtract $19$ , subtract $20$ and then add $1$ back. Explain what was added or removed in excess; this tells you which direction the adjustment must go.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Bridge a ten

Work out 67 + 8 mentally.

Worked solution

1
Find the amount needed to reach seventy.
$70 - 67 = 3$
Seventy is the next full ten after sixty-seven.
2
Split the eight into the bridge and the remainder.
$8 = 3 + 5$
Using three of the eight leaves five still to add.
3
Add both parts in turn.
$\begin{aligned} 67 + 3 & = 70 \\ 70 + 5 & = 75 \end{aligned}$
The two additions use exactly the original eight.

Answer

EXAMPLE 02

Subtract a near-ten amount

Work out 84 − 29 mentally.

Worked solution

1
Subtract the nearby full ten.
$84 - 30 = 54$
Thirty is one more than the required twenty-nine.
2
Return the extra one removed.
$54 + 1 = 55$
Subtracting thirty took away one too many.
3
Check by adding the removed amount back.
$55 + 29 = 84$
The difference and the removed part rebuild the starting number.

Answer

03 / YOUR TURN

Try it yourself.

Check your understanding

Work out 48 + 19 by adding 20 first.

Show answer & reasoning

First $48 + 20 = 68$ . This is one too much, so $68 - 1 = 67$ . The total increase is $19$ .

Keep practising

6 worksheet questions

Open worksheet Worked solutions

Read the questions online

Calculate $42 + 26$ by splitting 26.
Calculate $56 + 9$ by bridging a ten.
Calculate $73 - 19$ by adjusting 20.
Calculate $95 - 32$ by splitting 32.
There are 39 birds. Another 18 arrive. Find the total and explain a mental method.
Mia says $64 + 29 = 95$ because she added 30 then 1. Correct her method.

Read the worked solutions

Calculate $42 + 26$ by splitting 26.
$42 + 20 = 62$ ; $62 + 6 = 68$ .
68
Calculate $56 + 9$ by bridging a ten.
$56 + 4 = 60$ ; 5 remains; $60 + 5 = 65$ .
65
Calculate $73 - 19$ by adjusting 20.
$73 - 20 = 53$ ; add back 1 to get 54.
54
Calculate $95 - 32$ by splitting 32.
$95 - 30 = 65$ ; $65 - 2 = 63$ .
63
There are 39 birds. Another 18 arrive. Find the total and explain a mental method.
$39 + 20 = 59$ ; remove the extra 2 to get 57.
57 birds
Mia says $64 + 29 = 95$ because she added 30 then 1. Correct her method.
$64 + 30 = 94$ . One too many was added, so $94 - 1 = 93$ .
93

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Mental strategies; two-/three-digit calculations; regrouping; inverse operations; missing values.

Official curriculum source ↗

In this lesson

Understand the idea.

Split or bridge

Adjust a nearby number

See the method in action.

Bridge a ten

Find the amount needed to reach seventy.

Split the eight into the bridge and the remainder.

Add both parts in turn.

Subtract a near-ten amount

Subtract the nearby full ten.

Return the extra one removed.

Check by adding the removed amount back.

Try it yourself.

Check your understanding

Keep practising