1. Mastering Multiplication Facts
30th November 2018
Reason for workshop – chn to be confident and efficient with calculations
Fractions
Divisions
Percentages
When using money – anywhere
Mental maths skills which is important in daily life.

2. Multiplication Mastery
New Government initiative – Multiplication table checks assessment for Yr. 4 Pupils
It will be statutory in
Administered on computer
25 questions
6 seconds per questions
Pilot for this year – we will take part. Multiplication comes into everything fractions, percentages, money – support developing efficiency in mathematics and calculations

3. Memorisation and number sense
“People with number sense are those who can use numbers flexibly. When asked to solve 7 x 8 someone with number sense may have memorized 56 but they would also be able to work out that 7 x 7 is 49 and then add 7 to make 56, or they may work out ten 7’s and subtract two 7’s (70-14). They would not have to rely on a distant memory.”
(Boaler, 2009)
“When students focus on memorizing times tables they often memorize facts without number sense, which means they are very limited in what they can do and are prone to making errors.” (Boaler, 2009)

4. 14 x 4 So do we teach pupils to memorise or use strategies?
One leads to the other!
14 x 4
Factual and technical
Visual and spatial
The two approaches (strategies and memorisation) involve two distinct pathways in the brain and both are needed for life-long learning. Researchers found, however, that those who learned through strategies achieved ‘superior performance’ over those who memorised (Boaler – Math Mindsets P39)
“Researchers found that mathematical learning and performance are optimized when the two sides of the brain are communicating” (Boaler)

5. Phases of basic fact mastery (Baroody 2006)
Phase 1: Modelling and counting to find the answer
Solving 6 x 4 by drawing 6 groups of 4 dots and skip-counting the dots
Visual and spatial experience
Phase 2: Deriving answers using reasoning strategies based on known facts
Solving 6 x 4 by thinking 5 x 4 = 20 and adding one more group of 4
Strategies
Students who learn multiplication facts through traditional approaches generally do not retain the facts because the method attempts to move students from phase 1 directly to phase 3 of Baroody’s (2006) three developmental phases. Memorisation and learning ‘by rote’ goes from phase 1 to phase 3, missing out phase 2.
Phase 3: Mastery (efficient production of answers)
Knowing that 6 x 4 = 24
‘From memory’
Phases of basic fact mastery
(Baroody 2006)

6. ‘From memory’ (strategies)
Memorisation
‘From memory’
(strategies) VS
Explicit development of reasoning strategies
Strategic thinking
Careful sequencing of learning
Application of number sense
Flash cards
Drilling
Times testing
Moving directly from phase 1 to 3 (of Baroody’s developmental phases)
As a result…
As a result…
Poor retention
No long-term memory
Short-term gains only
Poor flexibility in use of facts
Anxiety
Ability to regenerate a fact if they have forgotten
Flexibly apply strategies
Long-term memory gains

7. Sequence and strategies for teaching multiplication facts
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Sharing, grouping, doubling
X2, x5, x10
Repeated addition, arrays
X3, x4, x8
Recall all facts to 12x12
x6, x7, x9, x11, 12
Square numbers

8. Language _____ Groups of ___ is ____ Lots of ____ is
____ Multiply by _____ ____ X ____ =
____ Times ____ is
The product of ___ and ____ is _____
____ is the product of ____ and ___

9. Phase 1: Modelling and counting to find the answer
Modelling the pattern in a number of ways
An ant has 6 legs. How many legs do 4 ants have?
= 24
4 x 6 = 24 6 12 18 24
Skip-counting and counting to find the answer
6 times table – think about things that comes with 6. Insects – 6 legs…
6,7,8,9,10,11,12,13,14, 15,16,17,18
Skip-counting to find the total

10. Ant Game Use the expressions and the ant cards to match in pairs.
Place the two sets face down in two different sets. Turn over 1 and turn over another and decide if it matches. If they match, express aloud what is shown, e.g. “Three ants with six legs is 18 legs.”
Keep if they match, return if they don’t.
Keep the returned over ones face up. Keep taking in turns to turn over a card until all are matched.
Whoever has the most pairs wins.
Ants patterns 1 x 6, 2x 6the first number is changing by one animal, nb of legs does not change.
Increase complexity
1.Ants and expression
2. Expression and arrays
3. Arrays and answers

12. 3 x tables Tricycle Triangles
What sort of things/objects could help children to count in 3s?
Tricycle
Triangles
1 x 3 = 3
Mari K to share tricycle example
Get adults to use counters to represent 2x 3
Use the arrays to represent
2 x 3 = 6

13. Phase 2 -Derived Facts Strategies
Adding /subtracting groups
Doubles/halving (4,8, 6,12)
Understanding inverse – division
Share progression sheets (bike examples

14. Phase 2: Derived fact strategies 1. Adding or subtracting a group
Use nearby 2, 5 and 10 facts
9 x 6 =
10 x 6 = 60
60 – 6 = 54
I don’t know 9 x 6, but I can use 10 x 6

15. Phase 2: Derived fact strategies 1. Adding or subtracting a group
Use nearby 2, 5 and 10 facts
6 x 7 =
5 x 7 = 35
= 42
It is also important for children to know their number bonds to support mental calculations
I don’t know 6 x 7, but I can use 5 x 7

16. Phase 2: Derived fact strategies 2. Halving and doubling
6 x 8 = 24
3 x 8 = 24
Double 24 = 48
I don’t know 6 x 8, but I can use 3 x 8 and double it

17. Phase 2: Derived fact strategies 2. Halving and doubling64
8 x 8 =
8 x 8 = 64
Half of 64 = 32
I don’t know 4 x 8, but I can use 8 x 8 and halve it

18. Phase 2: Derived fact strategies 3. Using a square product36
7 x 6 =
6 x 6 = 36
= 42
I don’t know 7 x 6, but I can use 6 x 6 and add one more 6

19. Activity 5 x 3 = 15 Can you create a story to match this calculation?
Context is very important.
There are 5 tricycle all with flats tyres in the playground. How many new tyres would I need to buy to fix them?
There are 5 chn at a party each child will get 3 sweets how many sweets do I need to buy?
Can you colour arrays to represent story?

20. Fill the grid 4 x
The aim is to fill as much of the grid as possible with arrays showing multiples of 4.
1. Each player has a 100 square sheet
2. Roll the die and multiply that number by 4.
Complete the array on the grid and say aloud what is shown, e.g. “the product of 3 and 4 is 12” or “three groups of 4 is 12”...etc. Record the array in the empty boxes below.
3. The player to fill most of their grid is the winner.

21. Fill In The Grid – Game

22. Moving to phase 3 – committing to memory
Dice game
Instructions:
Player 1 throws one die to generate a multiplication. Find the answer (using the taught strategies) and write the answer on their grid.
Player 2 checks their answer is correct.
Player 2 does the same and Player 1 checks their answer.
The first player to complete their grid wins.

23. Derived Strategies Gamex 1 2 3 4 5 6 7 8 9 10 11 12

24. Impact of the 3 phase approach
Children are finding it useful
More confident as they have a range of strategies to use when they are stuck.
I know 2 x 3 so I can work out 2 x 6 by doubling the answer
Enthusiastic
Eager to do these activities
Interesting in tracking their own progress – more confident to the recall

25. Key messages Practice little and often Range of activities
Keep it fun through games.
Use computer to practice fluency
years/multiplication-and-division

26. Evaluation form