� Supporting children to learn multiplication facts:�Effective strategies for rehearsal and recall

Learning the facts

Developing multiplication fact knowledge and recall:

The process

Learning to drive analogy

The learning to drive analogy

When learning, novice drivers need…

•expert instruction

•plenty of time dedicated to hands-on experience and discussion

•support to make connections to prior knowledge and skills.

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What is a multiplication table?

Multiplication table

A list of multiples of a particular number, typically from 1 to 12.

1 x 3 = 3

2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

6 x 3 = 18

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Can you see that when there are 4 groups of 3, there are 12? So 4 x 3 = 12

Making room for the teaching and learning

National Curriculum expectations

• Year 2:
• ●count in steps of 2, 3, 5 and 10
• ●recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables
• Year 3:
• ●count from 0 in multiples of 4, 8, 50 and 100
• ●recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
• Year 4:
• ●count in multiples of 6, 7, 9, 25 and 1000
• ●recall multiplication and division facts for multiplication tables up to 12 ×12

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Sequences within ESSENTIALmaths

• Y2 –2LS22 -Times Tables –2s, 5s and 10s. Patterns and Strategy (counting in 3s)
• Y2 –2LS23 -Multiplication –Multiples and Repeated Addition
• Y2 –2LS24 Multiplication –Number of Groups, Group Size, Product
• Y3 –3LS16 –Multiplication –3, 4 and 8 Times Tables including Counting
• Y3 –3LS17 –Division –1, 2, 3, 5, 4 and 8 Times Tables
• Y3 –3LS18 –Multiplication –Strategy, Associative and Distributive Laws
• Y4 –4LS5 –Counting in Multiples of 6, 7, 9, 25 and 1000
• Y4 –4LS6 –Multiplication and Division Facts (Times Tables)

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Essential Maths

Working to systematically learn a multiplication table

Children are likely to need:

•an understanding of what a multiplication table is

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A list of multiples of a particular number, typically from 1 to 12.

•the opportunity to ‘build’ the facts and talk about them, e.g. using cubes or a beadstring

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•time to create a list which matches the facts they have built

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•opportunities to rehearse the facts until they develop recall

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1 x 3 = 3

2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

6 x 3 = 18

Learning the facts –cubes and cards

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Start with 1 x __

•Make the array

•Clarify 0 x __ = 0

•Write the list, building the array

•Check it

Games with the cards

On their own, in a pair, with an adult…

•In order first, with the list still visible

•In order, without the list

•Starting with the product, give the fact

•Out of order –choose ‘easiest’ first

•Out of order –less choice of order

•Speed round

front back

0 x 4

0

1 x 4

4

2 x 4

8

3 x 4

12

4 x 4

16

4LS6 – Step 2

How many

facts do I need

to learn?

169 facts?

Once you understand commutativity...

91 facts

If you know your 10 x table = 45 facts?

Once you understand 1 x

• 66 Facts?

If you know your doubles up to double 12

• 55 facts?

Which facts do you think are hardest to learn? Why?

• X 7

Some believe that the 7 times table is the hardest to learn because 7 is a prime number and the numeric pattern isn’t quite as obvious as for other numbers. There are no obvious patterns or quick tricks like for the 9 times table.

Commutative law –2LS24 -

Reference to ‘commutative’ in Y2

of the National Curriculum

Distributive law –3LS18

Part 1: Rehearse

Developing varied opportunities for rehearsal

• Once you have been taught the basics, it is time to…

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•rehearse the different elements

•build up stamina

•go back to ‘learn’ if needed

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Counting expectations

Year 1:

• count in multiples of twos, fives and tens

Year 2:

• count in steps of 2, 3, 5 and 10
• (non-statutory)count in fractions up to 10, starting from any number and using the 1/2 and 2/4 equivalence on the number line (for example, 11/4, 12/4 (or 11/2), 13/4, 2)

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Year 3:

• count from 0 in multiples of 4, 8, 50 and 100
• count up and down in tenths

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Year 4:

• count in multiples of 6, 7, 9, 25 and 1000
• count backwards through zero to include negative numbers
• count up and down in hundredths

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Year 5:

• count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000
• count forwards and backwards with positive and negative whole numbers, including through zero
• (non-statutory)extend counting from year 4, using decimals and fractions including bridging zero, for example on a number line.

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Rhythmic counting / count all

Counting to a regular beat:

e.g. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,…

Count all

Hybrid

Skip Count

Fact Recall

Skip counting

Counting in multiples:

e.g. 0, 3, 6, 9, 12,…

Count all

Hybrid

Skip Count

Fact Recall

Hybrid counting

A combination of rhythmic and skip counting:

e.g. 0, 3, 6, 9, 12,(13, 14), 15(16, 17), 18

Count all

Hybrid

Skip Count

Fact Recall

Counting stick ideas

0, 4, 8, 12, 16, (hic!), 12, 16, 20, 24, (hic!), 20, 24, 28, 32, (hic!), 28…

Spot the swap stick

Hiccup stick

Counting stick ideas

Sneezing stick

Boomerang stick

Counting stick ideas

Sneezing stick

Spot the swap stick

Hiccup Stick

Boomerang stick

Building understanding of the array

Hide the Grid

• How to play:
• Each player picks a coloured pencil to use for the game.
• On your turn, roll the two dice, these will be your factors.
• Outline and colour a rectangle on the grid to match your two factors. E.g if you roll a 3 and a 4, you colour in any 3 x 4 or 4 x 3 rectangle on the grid
• Write the product of your two factors inside the rectangle
• If there is not enough space to draw the rectangle to match your factors, you miss ago
• When no more play is possible, add up all your products.
• The winner is the player with the greatest total product

Hide the grid

9 x 5 = 45

7 X 7 = 49

9 x 4 = 36

12 x 3 = 36

Part 2: Recall

..

Opportunities to retrieve facts

Once you have had varied rehearsal

• Recall how to perform a range of manoeuvres.
• Recall manoeuvres in increasingly complex situations
• Return to the ‘learn’ or ‘rehearse’ stage if needed

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Three in a row

In your pair, decide which multiplication table you are using.

You each need a different coloured pencil and a dice.

Three in a row

Write the answer in the correct square.

The winner is the person who gets 3 in a row first

Example with 5 times table

Three in a row - adaptations

Example with 5 times table

Moggle (Boggle with maths)

• You will need:

16 cards out of a deck of playing cards.

A handful of counters

Moggle

What you need:

• A standard pack of playing cards
• A handful of counters

How to play:

1. Remove all 10s, jacks and quees from the pack.
2. Decide how many kings to include in the game. These will be ‘wild cards’ and can represent any digit you need them to be during play.
3. Shuffle the cards.
4. Layout a 4 x 4 array, with all cards face up.
5. Take it in turns to spot correct calculations on the array.

Ace is worth one.

The numbers must touch – diagonally is allowed

The numbers must be in the correct order.

Kings (wild cards) can be any digit you need for that calculation

6. Track the calculation with a counter on each card involved – bank the counters you have used. The longer the calculation the more counters you win.

Next person has a go.

The winner is the player with the most counters at the end of the game

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6 x 1 = 6 (3 counters)

6 x 4 = 8 x 3 (4 counters)

Moggle Adaptations

Supporting Pupils

• Strategically select the base cards
• More wild cards
• Multiplication square
• Initial paired guidance (e.g. lay down counters to make ‘54’ and they have to find the factors)
• Relax the adjacent rule

• Adding Challenge
• Banning A x B = C format – must be more complex

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• Fewer wild cards

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• Only allowed to use a card once and aim to fill the board

Gaming Index

Videos to support learning