The idea, step by step
What does the box stand for?
A box or question mark stands for a missing number. In 34 + ? = 81, it is the amount added to 34 to reach 81. Find it by subtracting 34 from 81.
Think about parts and the whole before choosing an operation. If the whole is missing, add the parts. If a part is missing, subtract the known part from the whole.
A missing starting number
For ? − 28 = 46, the missing number was the starting whole. Put the 28 back: 46 + 28 = 74.
For 74 − ? = 46, the starting whole is already given. The missing removed part is 74 − 46 = 28. These questions use the same numbers but ask for different things. Always substitute your answer to check it.
A common trap
Always subtracting the two visible numbers, even when the starting whole is missing.
Instead: Ask what the missing number represents. To recover a whole after subtraction, add the removed amount back.
See the thinking
Find a missing added part
Find the missing number: 157 + ? = 300.
- Subtract the known part from the whole: 300 − 157.
- 300 − 100 = 200; −50 = 150; −7 = 143.
- Check: 157 + 143 = 300.
Find a missing start
Find the missing number: ? − 67 = 125.
- The starting whole is missing.
- Add the removed part back: 125 + 67 = 192.
- Check: 192 − 67 = 125.
Check your understanding
Find ?: ? − 19 = 42.
Show answer
61
42 + 19 = 61, and 61 − 19 = 42.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Find ?: 38 + ? = 70.
- Find ?: ? + 46 = 125.
- Find ?: 93 − ? = 57.
- Find ?: ? − 48 = 164.
- A bus starts with some people. Twelve get off and 27 remain. How many were on the bus at the start?
- Find a number that makes this equation true: 25 + ? = 18 + 32.
Read the worked solutions
- Find ?: 38 + ? = 70.
70 − 38 = 32; check 38 + 32 = 70.
32 - Find ?: ? + 46 = 125.
125 − 46 = 79.
79 - Find ?: 93 − ? = 57.
93 − 57 = 36; check 93 − 36 = 57.
36 - Find ?: ? − 48 = 164.
164 + 48 = 212; check 212 − 48 = 164.
212 - A bus starts with some people. Twelve get off and 27 remain. How many were on the bus at the start?
? − 12 = 27; 27 + 12 = 39.
39 people - Find a number that makes this equation true: 25 + ? = 18 + 32.
First find the right side: 18 + 32 = 50. Then 50 − 25 = 25. Check both sides equal 50.
25
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Mental strategies; two-/three-digit calculations; regrouping; inverse operations; missing values.
Official curriculum source ↗