Finding missing calculation values | Year 4

01 / LEARN

Understand the idea.

Parts and a whole

Read an equation as a statement that two amounts are equal. In $? + 258 = 700$ , the whole is $700$ and one known part is $258$ . Subtract that part from the whole to find the missing part.

For a missing starting amount, undo the subtraction. In $? - 186 = 329$ , the remaining $329$ and the removed $186$ make the original whole. Adding puts the removed amount back; subtracting again would make the whole smaller than its parts.

The unknown's position matters

Identify what is missing before choosing an operation. In $904 - ? = 487$ , the unknown is the amount removed, rather than the start. The removed part is the difference between the starting $904$ and the remaining $487$ .

Check by putting your number into the original equation. Both sides must have the same value, whichever way the equation is written. For example, $56 = ? + 19$ still asks for a part of the whole $56$ , even though the whole appears first.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Find a missing addend

Find the missing number in ? + 258 = 700.

Worked solution

1
Identify the known whole and part.
$? + 258 = 700$
700 is the total of the missing part and the known part 258.
2
Subtract the known part in manageable pieces.
$\begin{aligned} 700 - 200 & = 500 \\ 500 - 50 & = 450 \\ 450 - 8 & = 442 \end{aligned}$
Removing 200, 50 and 8 removes exactly 258.
3
Substitute the missing value.
$442 + 258 = 700$
The original equality holds, so the missing addend is 442.

Answer

442.

EXAMPLE 02

Find the amount removed

Find the missing number in 904 − ? = 487.

Worked solution

1
Identify the part removed.
$904 - ? = 487$
The unknown must fill the gap from the remaining amount 487 to the start 904.
2
Find that difference.
$\begin{aligned} 904 - 400 & = 504 \\ 504 - 80 & = 424 \\ 424 - 7 & = 417 \end{aligned}$
487 splits into 400, 80 and 7, so the missing part is 417.
3
Check in the original subtraction.
$904 - 417 = 487$
Removing 417 leaves exactly the stated remainder.

Answer

417.

03 / YOUR TURN

Try it yourself.

Check your understanding

Find the missing number: 650 = ? + 275.

Show answer & reasoning

375.

The missing part is $650 - 275 = 375$ . Check the equation as written: $650 = 375 + 275$ , with both sides equal to six hundred and fifty.

Keep practising

6 worksheet questions · 8 marks

Open worksheet Worked solutions

Read the questions online

Find $?$ : $? + 147 = 500$ .
1 mark
Find $?$ : $368 + ? = 720$ .
1 mark
Find $?$ : $? - 245 = 318$ .
1 mark
Find $?$ : $900 - ? = 427$ .
1 mark
Find $?$ : $156 + 84 = ? + 90$ .
2 marks
A school wants 800 tickets. It has printed 365. Write a missing-value equation and find how many more to print.
2 marks

Read the worked solutions

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

Find $?$ : $? + 147 = 500$ .
1 mark
$500 - 147 = 353$ .
$353 + 147 = 500$ .
353.
Find $?$ : $368 + ? = 720$ .
1 mark
$720 - 368 = 352$ .
$368 + 352 = 720$ .
352.
Find $?$ : $? - 245 = 318$ .
1 mark
$318 + 245 = 563$ .
$563 - 245 = 318$ .
563.
Find $?$ : $900 - ? = 427$ .
1 mark
$900 - 427 = 473$ .
$900 - 473 = 427$ .
473.
Find $?$ : $156 + 84 = ? + 90$ .
2 marks
The left side is 240.
$240 - 90 = 150$ , so both sides equal 240.
150.
A school wants 800 tickets. It has printed 365. Write a missing-value equation and find how many more to print.
2 marks
$800 - 365 = 435$ .
Check: $365 + 435 = 800$ .
$365 + ? = 800$ ; 435 more tickets.

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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.

Parts and a whole

The unknown's position matters

See the method in action.

Find a missing addend

Identify the known whole and part.

Subtract the known part in manageable pieces.

Substitute the missing value.

Find the amount removed

Identify the part removed.

Find that difference.

Check in the original subtraction.

Try it yourself.

Check your understanding

Keep practising