1. Aims of the Session
To build understanding of mathematics and it’s development throughout KS2
To have a stronger awareness of when and how to progress from non-formal to formal methods at the appropriate stage for your pupils (and the pitfalls of formal methods)
To enhance subject knowledge of the pedagogical approaches to teaching mathematics

2. Models of multiplication
I had four bags and they each contained six books. How many books do I have?
I had six pens. Tom had four times as many? How many did Tom have?
Year 3
solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects
First is the repeated addition model
Second is the scaling model

3. Models for multiplication
Scaling
This can be generalised to include any multiplier including those less than one – i.e. making smaller
3 times
as tall 3

4. 14th November 2012 Mathematics Across the Curriculum
14/11/2012 6 6 6 6 6
Additive reasoning 6 6 6 6
6 x x 4
Multiplicative reasoning
Secondary mathematics team, Babcock 4S

5. Arrays 2 lots of 3 make 6 3 lots of 2 make 6 There are two 3s in 6
There are three 2s in 6
2 x 3 = 6
3 x 2 = 6
6 divided by 2 = 3
6 divided by 3 = 2

6. An image for 7  8 = 56
Suggest come out of slide show mode here so that you can move the lines about to demonstrate how this 56 can be partitioned in lots of different ways:
4 lots of 7 doubled
5 lots of 7 and 3 lots of 7
5 lots of 8 and another two 8’s
25 (5 x 5) + 15 (3 x 5) + 10 (2 x 5) + 6 (2 x 3)
This highlights different ways of figuring out some ‘tables facts’ you might not know from facts you do. This idea of partitioning the array into 4 portions is an important pre-cursor to the 10s and 1’s partitioning used in the grid method which is in turn a useful stepping stone along the way to the standard algorithm.

7. Multiplication
At the heart of success of this topic is clearly mastery of times tables. It is the one area where deviating from your year group and extending has value. Fluency with tables opens up so many other topics in maths (e.g. fractions and area) and conversely closes off success in other topics if they haven't been mastered at a young age.
Guide: Yr 2 (2, 5, 10) Yr 3 (3, 4, 8) Year 4-6 (upto 12 x 12)
Is this the wisest plan?
Practice, practice, practice is the key. Use every (daily throughout the year) opportunity open to you, especially:
- Lining up to assembly, getting changed for PE, etc.
- Parents! They can really support the regularity of practice.
Note: DK Times Table App – many can access at home.

8. Building the Journey Year 3 Autumn two-digit x one-digit informally
Spring/Summer developing two-digit x one-digit formally
Year 4 Autumn/Spring term two-digit & three-digit x one-digit formally
Year 5 Autumn/Spring term up to 4-digit x one-digit or two-digit formally
(including long multiplication)
Multiply whole numbers and those involving decimals by 10, 100, 1000
Identify multiples and factors of a number, and common factors of two numbers.
Recognise and use square numbers and cube numbers (and notation)
Year 6 All of the above should now be fluent, and:
Autumn/Spring identify common factors, common multiples and prime numbers

9. Arrays to Solve Multiplication
13 x 4 = 10 3 4
Keep with arrays as a starting point
Make the array with Dienes/Cuisenaire, draw the parallel grid, then create the short multiplication algorithm. Again in pairs builder/scribe
Autumn term – arrays to grid
Spring/summer – grid to short multiplication
No panic if not by summer – they can pick it up again in y4
Do not go above teens with Dienes – move to PV counters
10 x 4 = 40
4 x 3 = 12
= x 4 = 52

10. Year 3
(set questions involving their tables targets - in autumn change to 34 x 8 or 85 x 3)
Autumn Spring Summer
34 x 2
45 x 3
Autumn term – pictorial representation to grid
Spring term – pictorial representation to grid and start to develop short multiplication in tandem
Summer term – grid to short in tandem

11. Year 4
(set questions involving all their tables targets - though this will need differentiation throughout the classes)
Always go back to the kinaesthetic example when re-introducing (even if only for a few seconds)
43 x 6
247 x 3 T U
Same hierarchical build up as year 3 although a more efficient progression on to short multiplication – don’t skip the informal H T U

12. Year 5
Multiply upto 4 digits by one-digit or two-digit, using a formal written method, including long multiplication for two-digit numbers.
re-visit:
Hands-On? Short-Multiplication Long-Multiplication
4253 x x x 37
Hands-On… grid

13. Year 5
Multiply multi-digit numbers up to 4 digits by a 2-digit whole number. 10 18 18 8 10
100 80 13 13
New learning but following the same starting point and pedagogy 3 30 24

14. Progressing towards the standard algorithm
1 0 8
1 0
1 0 0
8 0 3
3 0
2 4

15. 10 8 3
100 80 30 24
When? ? 1 8  3 5 4 2
How?

16. Year 5 Multiplying (and Dividing) by 10, 100 and 1000 4 x 10 13 x 10
1 10
1 100 H T U
Scaling is critical to understanding – could show with dienes as it exemplifies the 10 times bigger, smaller etc

17. Differentiation
Year 5
Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.
Know the vocabulary of prime numbers and non-prime numbers.
Does every number have an even number of factors (factor bug) ?
Can you think of five numbers that have only got two factors?
A prime number has exactly two factors.

18. Year 5 Recognise square numbers and cube numbers - and notation.
Square Numbers Cube Numbers
Link square numbers to squares physically – ditto cubes

19. Year 6
Multiply multi-digit numbers up to 4 digits by a 2-digit whole number.
Identify common factors, common multiples and prime numbers.

20. Reflection
On the multiplication journey, where are your individual pupils?
e.g. Year 3 Autumn term...
Some may still be working "informally", others may be mastered in "formal". What are the implications for the Spring term?
In an individual lesson, how are you going to assess effectively whether a pupil or group is ready for the next stage, as opposed to waiting to move on when the whole class is ready?

21. Regarding the "mastery learning" approach, if a skill is mastered by the end of the Autumn or Spring term, consider the following for the Summer Term:
Set questions in a "worded context"
Apply skills to a more "problem solving" question, e.g.
"The school hall measures 12m by 26m. Miss Smith is going to carpet the hall using square carpet tiles which are 50cm long. How many tiles are needed?“
Extend further??

22. 1 1

23. Using Inequalities 3 x 42 5 x 21 9 3 2 3 5 4 x No crocodiles
A range of answers
Number pyramids careful thought so that the multiplications do not become too large

25. Links with other topics…
Area
Pictograms
Measure

26. Aims of the Session
To build understanding of mathematics and it’s development throughout KS2
To have a stronger awareness of when and how to progress from non-formal to formal methods at the appropriate stage for your pupils (and the pitfalls of formal methods)
To enhance subject knowledge of the pedagogical approaches to teaching mathematics