1. Addition
Using partitioning

2. Prior Steps
You will find this example on page 4 of your handbook. This is the method commonly used prior to introducing partitioning and is often used up until the end of year 2. This skill of counting on is also important in developing the children’s knowledge of bridging to the next multiple of 10.

3. Partitioning
This is the method used in year 3. This strategy encourages the children to think about place value and how the tens and units must be added separately, in order that the answer is correct.

4. Expanded Method
By the end of year 3, some children will be ready to use expanded methods (which are those that progress neatly onto the formal column method). The onus is still on place value and understanding which numbers are hundreds, tens and units, however carrying is not introduced straight away.

5. Column Method
Dependent on ability, the column method is often used by the end of year 4, in order that the children understand how to ‘carry’ digits over to the next place value column. This is the method used until the end of year 6, although it will be revisited each year to accommodate the teaching of decimal/money addition.

6. Decimals and beyond

7. Your turn!
Please choose one of the methods used in your child’s year group:
Number line
Partitioning
Expanded Method (HTU split up)
Formal column method
Formal column method with decimals.
Roll the dice on your table to create two or three-digit numbers to practise adding on your paper. Check your working out with a partner upon completion.

8. Addition 
Any questions?

9. Subtraction
Early subtraction in year 1 will begin by counting back or forwards to find the difference on a number line.
When working with bigger numbers in year 2, the children will be expected to count on from the smaller number (using bridging) to work out the difference up to the bigger number. They will then be introduced to counting back from the bigger number for numbers with a larger difference.

10. Expanded Method
As children become confident in using a number line (usually by the end of year 4), the children begin using an expanded method (with a focus on place value) in preparation for column subtraction.
From this stage, decomposition is introduced so that children get used to recognising when you cannot take a larger number away from a smaller number.

11. Column Method
This then progressively moves onto using the formal column method. This is usually introduced by year 5.
This will again, be revisited when dealing with decimal numbers in order to solve money problems by the end of year 5 and beginning of year 6.

12. Your turn!
Please choose one of the methods used in your child’s year group:
Number line to find the difference by counting on
Number line to find the difference by counting back
Expanded method splitting up place value
Expanded method involving decomposition
Column method
Column method with decimals.
Roll the dice on your table to create two or three-digit numbers to practise adding on your paper. Check your working out with a partner upon completion.

13. Subtraction 
Any questions?