1. Calculation Progressions at St Francis CE Primary
Welcome to this evenings interactive presentation.
Please feel free to have a look through the resources on your table.
If you would like to order a Maths Resources Pack for £5, do sign up on the sheets near the entrance.

2. Aims
To understand the progression of calculation for addition and subtraction.
To see the methods in use and use the calculation strategies that children learn at
St Francis.

3. Outline of the session
Addition Early Years counting on – practical maths Number lines Partitioning Column ~ expanded and standard methods Subtraction Early Years taking away Number lines ~ finding the difference and taking away Expanded column and standard column methods with and without exchanging

4. Addition
Early addition starts with practical maths. Children are taught to count and use real objects and then count on to add more.

5. Number lines
Children begin to use structured number lines to support addition calculations by counting on in Ones from the biggest number. The children will continue to use this method as they solve problems with 2-digit numbers =24

6. Blank or ‘Unstructured’ Number lines
At this stage, children will also be introduced to a 100 square so that patterns, as well as calculations, can be identified and discussed.
25+12=37 (25+10= =37)
Remember to add multiples of ten
followed by Ones.

7. Blank or ‘Unstructured’ Number lines
Let’s have a go… Task 1 ~ Using a blank number line, add 15 and 7. Task 2 ~ Now try using larger numbers. Add together 356 and 173.
Remember to add on the Hundreds first, then the Tens and finally the Ones.

8. Partitioning
Partitioning is how children are shown how to split a number into Hundreds (H), Tens (T) and Ones (O). H T O = 300 and 50 and 2 This skill is used to support children with all four calculations and it is essential that children have an understanding of the place value of digits. For example in the number 367. The 3 stands for 300 (three Hundreds) the 6 stands for 60 (six Tens) and the 7 stands for 7 (seven Ones)

9. Partitioning
This method can begin with Tens and Ones only, progressing on to H, T and O. It requires children to understand the value of each digit. 145 is NOT made up from 1, 4 and 5!
Arrow cards also clearly show the value of each digit in its correct place value column.

10. Expanded and standards methods of column addition
At this stage, children learn to add the Ones first and then the Tens. This is ready for when exchanging begins. Partitioning is key here.

11. Addition ~ reminders
Encourage mental calculations first. Use number lines first, then an unstructured number line. Begin with the larger number and add on. Remember partitioning of numbers.

12. Subtraction
Physical objects are used first. Counting back on a number line or a bead string supports the idea of ‘taking something away’. Structured number lines are used to ‘find the difference’ starting from the biggest number. Counting on can also find the difference between two numbers.

13. Finally combine the Tens together and the Ones together.
Subtraction
The progression is the same as addition
Use unstructured number lines to count back in steps of ten followed by Ones. Have a 100 square handy to reinforce this idea.
Then combine the Ones.
Finally combine the Tens together and the Ones together.

14. start with Tens for a) and Hundreds for b)
Subtraction
Let’s have a go…
Task 3 ~
Using a blank number line, solve these…
54 – 36 =
637 – 471 =
a) = 18
b) = 166
Remember,
start with Tens for a) and Hundreds for b)
OR use number bonds.

15. Expanded column and standard column methods, no exchanging
It is crucial that the children learn to subtract the Ones column first and record their answer. The children will then subtract the Tens column, recognising that it is 50 take away 20 not 5 take away 2.
When the children are ready, they are encouraged to drop the ‘and’.
And the standard way with
no exchanging.

16. Expanded column and standard column methods with exchanging
In this example, the children are asked, ’What is 3 take 7? Can you do it? We need to exchange a ten from the Tens column and place it next to the Ones column. The children exchange one ten from the Tens column cross out the 5 (50) and write the number, which is 10 less, 4 for (40). The children are then asked, ‘What is 13 take away 7?’ They can now do the calculation. This is why it is essential that the children have learnt to subtract from the Ones column first.

17. Expanded column and standard column methods with exchanging
Task 4 ~
Calculate 275 – 83 =
Exchanging from the
Tens and the Ones

18. An example with a zero
When a zero appears as a place value holder, the same method applies for exchanging =

19. Subtraction ~ reminders
Physical objects help picture the quantities. Use number lines and bead strings to see the numbers decreasing and the difference between them. Begin with the largest number and subtract from that. You never steal, borrow or take from the column to the left, you ‘exchange’!

20. To conclude
Using objects and number lines helps the size of numbers to be recognised. Number bonds help quick recall of addition and can be multiplied and divided by base 10. Times tables are key. Place value keeps the numbers where they should be for what they are worth.

21. Thank you so much for participating
7 years of learning addition and subtraction progression in one evening!