Addition/subtraction strategies | Year 4

01 / LEARN

Understand the idea.

Break a calculation into friendly parts

Partitioning turns one calculation into smaller calculations you can track. To add $247$ , add $200$ , then $40$ , then $7$ . To subtract $247$ , remove those same parts one at a time. Record each new total before moving on.

For a number near a round number, use compensation. Adding $198$ can become adding $200$ and removing the extra $2$ . Subtracting $198$ can become subtracting $200$ and restoring $2$ , because the first subtraction removed too much.

Regroup and check

In a written calculation, line up matching places. When a column needs an exchange, remember that $10$ ones equal $1$ ten and $10$ tens equal $1$ hundred. Regrouping changes the form of a number while keeping its value.

Estimate the size first, then check the exact calculation with an inverse operation. For subtraction, add the difference to the amount removed to recover the start. An estimate catches many large mistakes; an exact inverse check can catch smaller ones too.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Add by partitioning

Find 386 + 247.

Worked solution

1
Add the hundreds part.
$386 + 200 = 586$
The 247 being added contains two hundreds.
2
Add the tens part.
$586 + 40 = 626$
Four tens remain to be added.
3
Add the ones part.
$626 + 7 = 633$
The parts 200, 40 and 7 account for all of 247.
4
Check by taking the added amount away.
$633 - 247 = 386$
Subtraction reverses the addition and returns the starting number.

Answer

633.

EXAMPLE 02

Subtract from a round number

Find 800 − 367.

Worked solution

1
Remove the hundreds.
$800 - 300 = 500$
Break 367 into 300, 60 and 7.
2
Remove the tens.
$500 - 60 = 440$
Six tens are sixty, so the remaining amount decreases by 60.
3
Remove the ones.
$440 - 7 = 433$
Removing all three parts subtracts exactly 367.
4
Rebuild the starting amount.
$433 + 367 = 800$
The difference and the removed part should make the original whole.

Answer

433.

03 / YOUR TURN

Try it yourself.

Check your understanding

Use compensation to find 426 + 199.

Show answer & reasoning

625.

Use $199 = 200 - 1$ . First $426 + 200 = 626$ , then remove the extra one: $626 - 1 = 625$ . The total is one less than adding a full two hundred.

Keep practising

6 worksheet questions · 10 marks

Open worksheet Worked solutions

Read the questions online

Calculate $458 + 236$ .
1 mark
Calculate $703 - 268$ .
1 mark
Use compensation to find $645 + 298$ .
2 marks
Use compensation to find $721 - 299$ .
2 marks
A library had 625 books. It received 178 more, then lent out 246. How many remained?
2 marks
A learner finds $472 + 189 = 551$ . Show a correct method and use an estimate to explain why 551 is not sensible.
2 marks

Read the worked solutions

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

Calculate $458 + 236$ .
1 mark
$458 + 200 = 658$ .
$658 + 30 + 6 = 694$ .
694.
Calculate $703 - 268$ .
1 mark
$703 - 200 = 503$ .
$503 - 60 - 8 = 435$ .
435.
Use compensation to find $645 + 298$ .
2 marks
$645 + 300 = 945$ .
Subtract the extra 2: 943.
943.
Use compensation to find $721 - 299$ .
2 marks
$721 - 300 = 421$ .
Add 1 back because one too many was removed: 422.
422.
A library had 625 books. It received 178 more, then lent out 246. How many remained?
2 marks
$625 + 178 = 803$ .
$803 - 246 = 557$ .
557 books.
A learner finds $472 + 189 = 551$ . Show a correct method and use an estimate to explain why 551 is not sensible.
2 marks
$472 + 200 - 11 = 661$ .
Rounding to hundreds gives about $500 + 200 = 700$ , much closer to 661 than 551.
The correct answer is 661.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Place-value revision; odd/even properties; addition/subtraction strategies; missing values; rounding/checking.

Official curriculum source ↗

In this lesson

Understand the idea.

Break a calculation into friendly parts

Regroup and check

See the method in action.

Add by partitioning

Add the hundreds part.

Add the tens part.

Add the ones part.

Check by taking the added amount away.

Subtract from a round number

Remove the hundreds.

Remove the tens.

Remove the ones.

Rebuild the starting amount.

Try it yourself.

Check your understanding

Keep practising