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, subtraction, multiplication and division.
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
Multiplication
Early Years grouping
Arrays
Number lines ~ jumping in groups
Commutativity
The grid method
Column
Standard
Division
Early Years sharing
Division as repeated grouping on a number line
Chunking

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 carrying 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. Multiplication
Early multiplication is groups of or lots of and involves repeated addition of objects.
Arrays Times tables begin
with 2, 5 and 10.
2s ~ socks, hands, shoes.
5s ~ fingers on gloves.
10s ~ fingers, toes.

21. Commutativity Multiplication is commutative, 2 x 4 = 4 x 2
Children are encouraged to explore this using objects and by drawing diagrams as well as using a number line.

22. Grid method
This relies on the children understanding multiplication as repeated addition, recalling their times tables quickly and partitioning. 14 x 3 = 10 x 3 and 4 x 3 Task 5 ~ Calculate 27 x 8 using the Grid method

23. Grid method
A two-digit by two-digit number uses the same method, the grid just becomes larger to accommodate for more rows and columns. 14 x 15 = Once this is secure, children move on to multiplying with HTO.

24. Column multiplication
Once the grid method is secure, partitioning is used in the expanded column method. (The grid method vertically)

25. The standard method
Finally this method is used once multiplications are recalled rapidly, place value is clearly understood, exchanging is clear and adding is secure.

26. Other multiplication tips
When a number is multiplied by 10, 100, 1000 etc, you are not simply adding zeros! What is happening is that the number is becoming bigger and is therefore moving into the appropriate place value position. The numbers always stay together and any spaces remaining are filled with zeros i.e. 156 x 10= Th H T O …otherwise it would be ( x 10) 156.0!

27. Multiplication ~ reminders
Times tables are key Place value columns must be checked You don’t just add zeros when multiplying by multiples of ten

28. Division Early years start with ‘sharing’.
6 sweets are shared between 2 people.
How many do they have each?
You might hear children say, “One for me, one for you.” and so on.
Eventually pictures are replaced with dots.
It is important for children to know how to count on and back in multiples of 1,2,5 and 10 so they can derive the multiples of 2, 5 and 10.

29. Structured number lines
Early division is seen as repeated subtraction. Here is a calculation for 15 ÷ 3 The answer is 5 groups of / lots of / sets of 3.

30. Unstructured number lines
e.g. 18 ÷ 6 = 3
The children are also given examples whereby there is a remainder.
e.g. 16 ÷ 3 = 5 r 1

31. Chunking on a number line and vertically
38 / 3 = 12 r 2 38 / 3 = 3| (10 x 3) 8 6 (2 x 3) 2
10 lots of a number is a great starting point.
Knowing how to subtract when digits are presented vertically is key.

32. Chunking vertically by 2 digits
840 ÷ 15 = 56 Task 6 ~ calculate 742 / 14 using this method.
When you know 10 lots of a number it’s easy to calculate 20 lots ~ double it!

33. Standard method of division
Finding out how many of the divisor go into each digit as a separate number. The next step is to find remainders. This involves the children having to apply their knowledge of decimals.

34. Division ~ reminders
Place value is key Times tables knowledge must be secure Use multiplication to check as an inverse calculation

35. 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.

36. Thank you so much for participating
7 years of learning calculation progression in one evening!