As for 2AS–3, Dienes and partitioning diagrams can be used to support pupils as they learn about strategies for carrying out these calculations.
To add 2 two-digit numbers, pupils need to combine one-digit addition facts with their understanding of two-digit place value. Pupils should first learn to add 2 multiples of ten and 2 ones before moving on to the addition of 2 two-digit numbers, for example:
- 40 + 20 + 5 + 3 = 60 + 8 = 68
- 40 + 5 + 20 + 3 = 60 + 8 = 68
- 45 + 23 = 60 + 8 = 68
Language focus: “First I partition both numbers. Then I add the tens. Then I add the ones. Then I combine all of the tens and all of the ones.”
Pupils can then learn to be more efficient, by partitioning just one addend, for example:
45 + 23 = 45 + 20 + 3
= 65 + 3
When pupils learn to subtract one two-digit number from another, the progression is similar to that for addition. Pupils can first learn to subtract a multiple of ten and some ones from a two-digit number, and then connect this to the subtraction of one two-digit number from another.
There is an important difference compared to the addition strategy: pupils should not partition both two-digit numbers for subtraction as this can lead to errors, or calculations involving negative numbers, when bridging a multiple of 10, for example:
- 63 – 17 60 – 10 + 7 – 3
- 63 – 17 = 60 – 10 + 3 – 7
You can find out more about fluency and recording for addition and subtraction of two-digit numbers here in the calculation and fluency section: 2AS–4