1. Maths Calculation Years 4, 5 & 6
Four Number Operations: Addition, Subtraction, Multiplication & Division

2. Addition

3. Year 4
Year 5
Year 6

4. Addition – Concrete Models
The children will use concrete place-value counters to partition the numbers and then undertake the calculation

5. Addition – Pictorial Models
This is similar to the concrete representation, but can be drawn on whiteboards or in books.

6. Addition – Abstract Models
This is a compact model for addition.
Children are taught to carry the numbers below the equals line and cross off once added.
Before this, many children will partition the numbers into their place-value columns to emphasise the value of each digit: this is called partitioning.
Examples on a flipchart and calculations to tackle using these methods

7. Apply Understanding in Context: Fluency & Variation
Saturn class raised £4754 for Children in Need, Jupiter class raised £2987. How much did both classes raise in total?
Draw a bar model and discuss methods.
This is extended in years 5 and 6 with the use of decimals in context (money and measure etc) and multi-step problems.

8. Subtraction

9. Year 4
Year 5
Year 6
The same expectations for subtraction are applied to each year group.

10. Subtraction – Concrete Models
The children will use concrete place-value counters or base 10 blocks to partition the numbers and then undertake the calculation, exchanging where necessary.
Show example

11. Subtraction – Pictorial Models
This is similar to the concrete representation, but can be drawn on whiteboards or in books. This can be extended to 4 and 5-digit numbers and decimals.

12. Subtraction – Abstract Models
These are compact models for subtraction.
Children are taught to exchange the numbers.
Before this, many children will partition the numbers into their place-value columns to emphasise the value of each digit: this is called partitioning.
Examples on a flipchart and calculations to tackle using these methods, including 4 and 5 digit numbers and decimals.

13. Apply Understanding in Context: Fluency & Variation
Saturn class raised £4754 for Children in Need, Jupiter class raised £2987 less. How much did Jupiter class raise?
Draw a bar model and discuss methods.
This is extended in years 5 and 6 with the use of decimals in context (money and measure etc) and multi-step problems.

14. Multiplication

15. Year 4
Year 5
Year 6
The same expectations for subtraction are applied to each year group.

16. Multiplication – Concrete Models
The children will use concrete place-value counters or base 10 blocks to partition the numbers and then undertake the calculation, exchanging where necessary.
Show example.

17. Multiplication – Pictorial Models
This is similar to the concrete representation, but can be drawn on whiteboards or in books. This can be extended to 4 and 5-digit numbers and decimals.

18. Multiplication – Abstract Models
This is the compact models for short multiplication and long multiplication.
Children are taught to carry the numbers underneath and cross off once added.
Before this, many children will partition the numbers using the grid method, partitioning the numbers into their place-value columns to emphasise the value of each digit.
Examples on a flipchart and calculations to tackle using these methods, including 4 and 5 digit numbers and decimals.

19. Apply Understanding in Context: Fluency & Variation
Saturn class raised £4754 for Children in Need, Jupiter class raised three times as much. How much did they raise altogether?
Draw a bar model and discuss methods.
This is extended in years 5 and 6 with the use of decimals in context (money and measure etc) and multi-step problems.

20. Division

21. Year 4
Year 5
Year 6
The same expectations for subtraction are applied to each year group.

22. Division – Concrete Models
The children will use concrete place-value counters or base 10 blocks to partition the numbers and then undertake the calculation, exchanging where necessary.
Show example.

23. Division – Pictorial Models
42÷3=
This is similar to the concrete representation, but can be drawn on whiteboards or in books. This can be extended to 4 and 5-digit numbers and decimals.

24. Division – Concrete Model: Long Division
Say that this can linked back to all of the previous concrete models, but may not be necessary by this stage as many of the children will be competent and understand the processes involved.

25. Division – Abstract Models
These are the compact models for short and long division.
Children are taught to exchange the numbers underneath.
Examples on a flipchart and calculations to tackle using these methods, including 4 and 5 digit numbers and decimals.

26. Apply Understanding in Context: Fluency & Variation
The entire school raised £4755 for Children in Need, what was the average amount raised per class?
Draw a bar model and discuss methods.
This is extended in years 5 and 6 with the use of decimals in context (money and measure etc) and multi-step problems.