The idea, step by step
Split or bridge
Split a number into useful parts. For 46 + 23, add 20 to make 66, then add 3 to make 69. You do not need to count every one.
You can also bridge to a full ten. For 38 + 7, use 2 of the 7 to reach 40. There are 5 left, so the answer is 45.
Adjust a nearby number
When adding 19, it may be easier to add 20 and then take away 1. For 57 + 19, 57 + 20 = 77, then 77 − 1 = 76.
Explain the adjustment. You added one too many, so remove one. For subtracting 19, subtract 20 then add one back because you removed one too many.
A common trap
Adding 20 for +19, then adding another 1.
Instead: Adding 20 is already one too much. Take away 1, rather than adding it.
See the thinking
Bridge a ten
Work out 67 + 8 mentally.
- Use 3 of the 8 to reach 70.
- There are 5 left.
- 70 + 5 = 75.
Subtract a near-ten amount
Work out 84 − 29 mentally.
- Subtract 30: 84 − 30 = 54.
- That removed one too many. Add 1 back.
- 54 + 1 = 55.
Check your understanding
Work out 48 + 19 by adding 20 first.
Show answer
67
48 + 20 = 68, then 68 − 1 = 67.
Your turn
6 questions · Work at your own pace.
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
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Mental strategies; two-/three-digit calculations; regrouping; inverse operations; missing values.
Official curriculum source ↗