Multiplication tables

Although schools traditionally taught pupils the TWOs MULTIPLICATION TABLE, then the THREEs MULTIPLICATION TABLE, etc., it is recommended that the tables are taught in the order shown below.  This can help children to build confidence and progress more quickly.

NOTE.  The National Numeracy Strategy (UK) suggests that pupils should know multiplication tables as follows:

YEAR 2 = 2 and 10      YEAR 3 = 2 and 10 and 5      YEAR 4 = 2 and 10 and 5 and 4      YEAR 5 = ALL (up to 10)

It also helps to teach children about commutativity at this point - though they do not need to know what it is called!

10

Be careful NOT to talk about "adding a nought on the end"!  Mathematically speaking, this is NOT what you are doing - and it is best if children use mathematical language correctly from the outset.

The best way to illustrate what is happening mathematically is to repeatedly jump 10 spaces on a number line.

9

Use a number line to discover and record: One jump of nine spaces, two jumps of nine spaces, three jumps...etc.

Encourage children to notice the pattern of the results.  "The number of tens increases each time ... and the number of units decreases by one."  They may also notice that the sum of the digits is always 9.

Encourage children to speculate why this is happening.  "Because when we jump on 9 spaces it is like jumping forward 10 and then stepping back one."

Use the finger-based method to reinforce the number facts of the 9 multiplication table.  This easy-to-learn method can do wonders to build children's confidence.

1 x 9 = 09

2 x 9 = 18

3 x 9 = 27

4 x 9 = 36

5 x 9 = 45

6 x 9 = 54

7 x 9 = 63

8 x 9 = 72

9 x 9 = 81

10 x 9 = 90

5

Children generally find it easy to learn FIVEs MULTIPLICATION TABLE, largely because of the rhythmic pattern of the numbers.  The easiest approach is to recite "5, 10, 15, 20, ..." whilst pointing out the positions on a number line and keeping track on fingers.  Practice and repetition soon cement these number facts.

2

Establish the principle of commutation.  Once children recognise that "seven twos" is the same as "two sevens", it is relatively easy to work out how to "double up" - by using a "counting on" method.

4

Once children are familiar with TWOs, it is a fairly simple step to working out FOURs - which are merely "doubled up" again.

TWO groups of SEVEN            FOUR groups of SEVEN

8

Once children are familiar with FOURs, it is a fairly simple step to working out EIGHTs - which are "doubled up" yet again.

3

Teach children a simple three-beat rhythm - such as "LEFT - RIGHT - CLAP - LEFT - RIGHT - CLAP - etc."  to which they snap fingers with left and right fingers then clap hands together.  (Alternatively, beat lightly on desk, or knees, with left and right hands then clap hands together.)

Once children are familiar with the rhythm, they can perform it at a steady pace whilst counting.  "one - two - THREE - four - five - SIX - etc." with each third number (on the clap) said louder than the others.  This helps to familiarise children with multiples of three.

The next stage is for children to count the rhythm - whilst the teacher adds in the framework of the table.

 Teacher one times three is - THREE two times three is - SIX three...etc Children one two four five seven

6

Once children are familiar with THREEs, it is a fairly simple step to working out SIXes - which are merely "doubled up" again.

THREE groups of SIX                SIX groups of SIX

7

By the time you get around to SEVENs, the task will become so much easier if children have a secure knowledge of all the preceding tables.  They simply apply the law of commutation.

There is some disagreement about whether to teach children ELEVENs and TWELVEs MULTIPLICATION TABLES.  Those in favour tend to overlook the fact that the reason why these tables were traditionally taught in schools had more to do with pre-decimal currency (12 pennies in a shilling) than it did with mathematical expediency.  The sensible approach, I believe, is to limit each table to TEN numbers.

There is no reason why children should not learn ELEVENs - and preferably early on - because the first nine numbers in the sequence are so memorable, as is the tenth.  Able children could also be encouraged to learn TWELVEs.  Of more practical value (for reasons associated with computer programming, etc.) is a knowledge of SIXTEENs ... up to 16 x 16 ... but I would not normally advocate teaching these other than to well-motivated, more-able children