1. Calculation 12th October 2017
Maths KS2
Calculation
12th October 2017

2. Welcome to the KS2 Maths Workshop on Calculation
Have a go at the Key Stage 2 Maths Quiz and fill in the first part of the evaluation

3. Aims of the Session Enjoy maths and play around with numbers.
Learn a little about how we teach maths across KS2.
Learn how we teach:
Addition
Subtraction
Multiplication
Division

4. Maths in KS2 at Applecroft School
Fun and something to be played with
Relevant to everyday life and especially the children’s everyday life.
Involves practical and oral/mental work as well as ‘traditional’ book work.
Taught once a day for between60 minute sessions
Contained within a 3 part lesson : Oral/mental starter
Main activity
Plenary
Is supported by numerous additional sessions for booster and enhancement.
Challenging.

5. Mentally or pen and paper?
Mental calculations – the children are encouraged to ask the question ‘Can I do this in my head?’ If not they are encouraged to do informal jottings and then formal written calculations when necessary.
If a baby was born in 1998 how old were they in 2001? or
2001
1998

6. Mental Calculation
The ability to calculate mentally forms the basis of all methods of calculation. This involves
instant recall of number facts (+ - x ÷)
having a secure understanding of place value
and the number system
having a range of strategies to apply to a
calculation
understand the language and rules of maths

8. Resources Number line Counters Unifix cubes Number square
Place value cards
Dienne rods

9. Written Calculation
Throughout their primary years, children should progress from informal jottings to efficient written methods for each of the four operations.
Standard written methods should only be introduced when a child has a secure knowledge and understanding of the process involved and can clearly explain the strategies they have used.
Children become secure with these methods when they have regular practice and persevere!

10. It is ok to make mistakes – this is part of learning!

11. Addition

12. Addition
Written calculations:
Models & images:
Mental calculations:

13. Now, have a go at this question on your whiteboards using one of the methods here, then try a different method: =

14. Informal jottings The empty number line
The empty number line helps to record the steps on the way to calculating the total. The steps often bridge through a multiple of 10.
8 + 7 = 15
= 84 or:

15. Addition continued Expanded written form Partition and recombine=
=300
= 50
= 8
= 358

16. Column method- standard written form
t o h t o o.1/

17. Have a go The empty number line Partitioning and recombining
The Column Method
On-line resources to support the learning in school - espresso

18. Subtraction

19. Subtraction Written calculations: Models & images:
Mental calculations:

20. Now, have a go at this question on your whiteboards using one of the methods here, then try a different method: =

21. Practical Subtraction
Taking away using different objects and materials
Counting back on number tracks
Use resources to understand relationship between addition and subtraction

22. Subtraction

23. Subtraction

24. And finally

25. Have a go
Number Line
Decomposition

26. Multiplication

27. Understanding number
Number bonds are the window to success in KS2 and it is vital that your child knows these securely as they enter this phase.
By the end of Year 4, your child is expected to know all their times tables up to 12 x 12. To ensure this, we practise the tables daily and explore connections between the tables, e.g. to find 6 x 8, we know 5 x 8 is 40, so 6 x 8 is one more 8, so is 48.

28. Multiplication Times tables are key.
Related facts 5 x 6 = x 6 = 300
Arrays (knowing 3 x 4= 4 x 3)
15 x 5= (partitioning)
Repeated addition.

29. Multiplication Written calculations: Models & images:
Mental calculations:

30. The Grid method
This can then be developed into traditional long multiplication when the children are confident in how and why it works.

31. Written methods for Multiplication38
X 7
x 7
x 7
266 38
X 7
266 5
When they are ready The next step is to represent the method in a column format, but showing the working. Attention should be drawn to the links with the grid method above. Children should describe what they do by referring to the actual values of the digits in the columns. For example, the first step in 38 × 7 is ‘thirty multiplied by seven’, not ‘three times seven’, although the relationship 3 × 7 should be stressed.

32. Have a go
The Grid Method
Column
Napiers!

33. Division

34. Last but not least…… ……the one most children dread!
Many children can partition and multiply with confidence. But this is not the case for division. One reason for this may be that mental methods of division, stressing the correspondence to mental methods of multiplication, have not in the past been given enough attention.
The aim is that children use mental methods when appropriate, but for calculations that they cannot do in their heads they use an efficient written method accurately and with confidence.
The stages building up to long division span Years 4 to 6 - first introducing TO ÷ O, then extending to HTO ÷ O, and finally HTO ÷ TO.

35. Language of Division Sharing Grouping
How many lots of (how many times)
Chunking
Remainder (left over)
Divisor

36. Division
Written calculations:
Models & images:
Mental calculations:

37. Division
Chunking

38. Division
Bus stop
Short division

39. Long division- It’s back!
Long division for HTU ÷ TU
The next step is to tackle HTU ÷ TU, which for most children will be in Year 6. The layout on the right, which links to chunking, is in essence the 'long division' method. Conventionally the 20, or 2 tens, and the 3 ones forming the answer are recorded above the line, as in the second recording.

40. Now, have a go at this question on your whiteboards using one of the methods here, then try a different method:
853 ÷ 5 =

41. Maths Dos and Don’ts Do Play maths- make it fun
Make maths a casual part of things you are doing.
Lots of hands on maths.
Recognise there is more than one way to solve a calculation.
Don’t
Be afraid to show them different ways.
Expect them to get it after you have explained it once!
Tell them you are hopeless at maths!