1. Learning the Multiplication Facts
Understanding a
contemporary approach,
to the old ‘times tables’

2. (L.I’s) Learning Intentions
to compare teaching of Multiplication Facts (‘Times Tables’) in the past, to teaching and learning today
to explain our approach to learning the Multiplication Facts in Years 3-6
to provide ideas of how to help at home

3. Times Tables Dread!
For many students forced to work with multiplication before they have adequate understanding of the multiplication concept, the ‘tables’ become an object of dread, that serve to undermine all their subsequent school Maths experiences.
We don’t want this!

4. Our Aim
To make learning the multiplication facts more manageable for students.
To make the old ‘times tables’ more meaningful.
More motivation for students.
More success for students.
More support for students.
More positive attitudes to Maths in students.

5. Changes…
You might remember the days when the Maths lesson started with chanting of tables facts, for example, once times 3 is 3, two times 3 is 6, three times 3 is 9 … and so on, and then the teacher would fire off questions, for example, 3 x 6; 9 x 3, in rapid succession.

6. Changes…
We have moved away from this type of rote learning because it does not involve understanding.
We want students to be thinking about what they are doing and using their ‘number sense’.
They still require lots of practise to pick up speed, but it now goes alongside understanding.

7. Why Do It Differently?
Research (Australia) suggested that over 22% of students in Year 5-9 were still relying on simple ‘make-all’ models, skip counting by 2s or doubling to solve problems that could be solved more efficiently using multiplication.
(Siemon & Virgona, 2001; Thomson & Fleming, 2004; Siemon et al, 2006).

8. Why Do It Differently?
It also found that the use of problem solving, extended discussion, student explanations and a range of materials, tasks and activities helps overcome this.
This is why we advocate a thorough, less superficial approach than in the past- we want more than just memorisation of answers!

9. First: Teach the Multiplication Concept
Groups of:
(initial phase)
4 threes ... 3, 6, 9, 12
3 fours ... 4, 8, 12
(D. Siemon)

10. First: Teach the Multiplication Concept
Move to arrays as a model- lead to more sophisticated thinking. The idea of ‘rows of’.
4 threes ... THINK: 6 and 6
3 fours ... THINK: 8, 12
Rotate
and rename
Arrays help focus on the product (seeing the whole, with equal groups reinforced by visual image), does not rely on repeated addition, supports commutativity (eg, 3 fours SAME AS 4 threes) and leads to more efficient mental strategies (D. Siemon)

11. First: Teach the Multiplication Concept
Also use the region model
(Same advantages as array model)
4 threes ... THINK: 6 and 6
3 fours ... THINK: 8, 12
Rotate
and rename
(D. Siemon)

12. Second: Explicit Teaching of Strategies
Students are provided with strategies for thinking about numbers and expanding their repertoire of approaches for working with numbers.

13. What Kind of Strategies?
Twos Facts:     2 x _ = Think ‘double’
Threes Facts: 3 x _ = Think ‘double, plus one more group’
Fours Facts:    4 x _ = Think ‘double, double’
Fives Facts:     5 x _ = Think ‘10 x _ then halve it’
Nines Facts:    9 x _ = Think ‘10 x _ then take away one group’
Tens Facts:    10 x _ = Think ‘make it 10 times bigger with a zero’
Making Connections: Think ‘use what you know, to help with what you don’t know’

14. Strategies
These strategies are explained in the animated video clips accessed on mfacts121.com
Here’s an example to watch!

15. Your Turn! 6 x 6 = 4 x 8 = 7 x 6 = 8 x 9 = 9 x 8 = 11 x 6 =
Answer these multiplication facts, then use the same ideas to help with decimals:
6 x 6 = x 8 =
7 x 6 = x 9 =
9 x 8 = x 6 =
12 x 6 = x 0.5 =
4 x 0.3 =

16. Thinking Strategies Share some strategies for your working out
How do you know 4 x 8 is 32? Explain.
How could students use their knowledge of 10 x 6, to quickly derive 12 x 6?
Time spent in class discussing the thinking strategies, is key to developing student understanding.

17. Mfacts121 Approach
Often mental computation consists of merely drill and practice and games of competition. Our structured program follows these steps:
concept development
strategy work
practise
quick recall
monitoring and feedback

18. Practicalities- How does Mfacts121 work?
Individual log ins- each student.
Access at school and home.
Printable resources.
Animated strategy videos.
Assessment and monitoring for the four levels of the 121 multiplication facts.

19. Practicalities- How does Mfacts121 work?
Students practise their level -using printable cards, games, at home and in class.
When ready, get online and test themselves.
Immediate feedback- certificate if level completed in timeframe.

20. Practicalities- How does Mfacts121 work?
When student succeeds, teacher is notified via .
Keeps student motivation high.
Self directed learning- can review any strategy videos.
Student progress easily tracked by teachers.

21. Practicalities- How does Mfacts121 work?
Why not the traditional tables format?
The Mfacts121 levels have been created based on ‘strategies’ rather than lists of facts.
Red, green, yellow, blue.

22. The Traditional ‘Multiplication Tables’.
1 x 3 = 3
2 x 3 = 6
3 x 3 = 9
4 x 3 = 12
5 x 3 = 15
6 x 3 = 18
7 x 3 = 21
8 x 3 = 24
9 x 3 = 27
10 x 3 = 30
11 x 3 = 33
12 x 3 = 36
1 x 4 = 4
2 x 4 = 8
3 x 4 = 12
4 x 4 = 16
5 x 4 = 20
6 x 4 = 24
7 x 4 = 28
8 x 4 = 32
9 x 4 = 36
10 x 4 = 40
11 x 4 = 44
12 x 4 = 48
This is inefficient
‘3 fours’ not seen to be the same as ‘4 threes’ ... To be learnt separately here.
Beyond 10s not necessary- should be able to calculate quickly if we know up to 10 x 10

23. Hear From the Experts
“Making connections among the facts will not only minimise the number of facts to be learned but will encourage strategies that will reduce the working in later calculations” (A. McIntosh)
“Understanding how to make links is as important as memorizing the facts” (J. Anghileri, 2000)

24. How can you help at home?
Display the set of multiplication facts your child is working on.
Vary the order you ask them.
Ask them to explain…’how do you know?’
The Vic curriculum states now that students learn their multiplication facts up to 10x10. This is partly because we now use the metric system (base 10), not the imperial (involving 12s). It is also because, from the facts up to 10x10, students should be able to quickly derive 12 x _ and even 13 x _. Student will often say ‘but we don’t learn the 13 x tables’ when faced with the question above. We do not wish to hear this thinking, as we encourage making connections and problem solving. 24

25. How can you help at home? Play games to foster quicker recall.
Print off cards and games relevant for your child.
Log onto mfacts121.com and have a look with your child. Let them show you!

26. How can you help at home? MOST IMPORTANTLY!
Keep it fun and positive - do not rush your child through the levels.
Thorough and lasting knowledge is more important.
As is a healthy attitude to Maths.

27. How can you help at home? MOST IMPORTANTLY!
The levels are designed to help students NOT to create competition or stress.
Every child is different -they will progress through the four levels at different paces.
The students have their whole Senior School years to move through the facts…then continue to revise once they ‘know’ them.

28. The Benefits
Using a strategies-based approach for the multiplication facts, pays dividends in lots of ways!
Leads to transference of knowledge to other areas.
Division facts, by association, become much easier.

29. The Benefits
Strategies can be used to solve larger multiplication questions- 4 x 26 can be thought of as a ‘double, double’ or 36 x 5 can be worked out quickly by thinking, 36 x 10 and halve it.
Work on fractions becomes more manageable- equivalence, finding common denominators, etc. requires strong knowledge of multiplication.
The list goes on!

30. Thank you! Your help DOES make a difference!
Thank you for your interest and for attending!
Always be in touch with any questions..