1. How children learn (and we teach) the Four Operations

2. Aims To understand expectations of the new curriculum in mathematics.
To be familiar with methods used for addition and subtraction
To become familiar with methods used for multiplication and division
To clarify progression

3. The Hat Game

4. The New Curriculum for mathematics
The New Curriculum for mathematics aims to ensure that all pupils:
become fluent in the basics of mathematics
reason mathematically
can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication
become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions

5. Your feelings of maths

6. Consider for a moment… 15 – 5 = 29+11= 18 – 16 = 2007 – 1992 =
How would you approach these questions?
15 – 5 =
29+11=
18 – 16 =
2007 – 1992 =
359 – 211 = =
6+4+7 =
24.6 – 12.4 =
312 x 54
1850 ÷ 25
2786 – 1899
x 13
4782 ÷ 13

7. Little Big Maths ~ Jupiter Class
CLIC ~
Counting
Learn ‘It’s facts’ (no bonds)
‘Its nothing new’ (applying)
Calculations (Methods =, + , - ,x , division)

8. ADDITION
We may have been taught different ways at school

9. Number Lines (Progression)
Counting on
Numbered lines
Bead strings
Partly numbered
lines
Numbered Lines
Use a numbered line to count on in ones.
Beads string (bar is better)
Use a bead string to illustrate the bridge through ten (count on 2, then 3).
Numbered lines (or caterpiller tracks)
Bridge through ten using a partly numbered lines.

10. Counting On Not crossing tens boundary e.g. 34 + 23
Jumps of 10s and 1s
Encourage children to become more efficient
Add 3 in 1 jump
Add 20 in 1 jump

11. Counting on Crossing tens boundary e.g. 37 + 25 Jumps of 10s and 1s
Help children become
more efficient:
Add 5 in jumps of 3 and 2
(bridging over 10)
Add 20 in 1 jump

12. Column addition
We only use these if children are able to manipulate numbers and have a good understand of place value
= (6 + 3) 140 ( ) 1300 ( ) =
= 1449

13. Compact (Formal) method New Curriculum
7 8 9
(These are carried)
Accurate use of language is key.

14. SUBTRACTION

15. Using a numberline for larger numbers ~ using find the difference
74 – 27 = 47
+ 40
+ 3
+ 4 27 30 70 74
74 – 27 = = 47

16. Formal written method
368
- 152
216
No ‘borrowing’

17. Compact Formal method New Curriculum 1 2 8 1

18. Multiplication

19. Early Multiplication Counting sticks Repeated addition
Rapid recall of multiplication tables facts
Games
Good as oral / mental starters
Using known facts (e.g. doubling)
Arrays
17 x

20. Moving on with Multiplication
Progression
2 digit x 1 digit
3 digit x 1 digit
3 / 4 digit x 2 digit
Grid method
26 x 7
32 x 14 7 10 4 20
140 6 42
=182 30
300 2 20
= 448

21. Formal Methods – New curriculum x
2 1 x
How would you explain these to children?

22. Division

23. Dividing - Sharing and grouping
Children appear to find sharing (partitive) tasks easier but this becomes inefficient with larger numbers,
e.g Smarties divided by 6 children – on a one for you, one for me basis this takes a while!!!
We therefore need to help children to move from sharing individual items to groups of items,
e.g. We could do 20 for you, 20 for me etc, we are taking away groups of the divisor from the dividend (CHUNKING).
Division involves multiplicative reasoning as opposed to additive reasoning and is therefore harder and is usually taught after addition and subtraction

24. Children’s working
A tent holds 6 children. How many tents are needed to hold 70 children?

25. Number line division 48 ÷ 6 = 1 x 6 1 x 6 1 x 6 1 x 6 1 x 6 1 x 66 12 18 24 30 36 42 48

26. To divide 81 by 3 Bucks method
Lets start looking at short division by using a number line.
We are going to divide 81 by 3
This is an excellent way of ensuring understanding.
It is also a very effective process of carrying our the calculation
Bucks recommend a number for understanding
Could also choose to do chunking
–but number line is most reliable
This course is looking at standards methods
so we will go on to see what the national strategy recommend

27. Remainders 5 10 15 17 r2
17 ÷ 5 = 3 r or 3 2 5

28. Chunking
x x

29. Formal method – short and long division New curriculum
1 2
1 4 2

30. Progression chart Learning through play Helping at home ~ Early years/KS1 Maths help at home ~ KS2