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Learning multiplication facts? Take a look at the products

Monday, 6 November 2017
Many hours are spent in primary classrooms on activities to help children learn multiplication facts, with varying degrees of success. I’ve seen (and used) chanting, counting patterns, songs, games, trio cards, bingo, round the class cards, tables tests… and many more strategies to try to get it to stick. So here’s another strategy to add to the mix – focus on the products.

A multiplication sentence such as 3 x 4 = 12 is made up of two factors: the multiplicand (3) and the multiplier (4) and the product or multiple (12).

We often focus on the two factors of a multiplication sentence, however it is interesting to identify and focus on the products. If children begin to remember some of the key numbers that are products, then it will help to recall multiplication facts. We do it as adults without realising it.   

Finding products of multiplication facts 

products

1. List all the multiples of 10 in a column up to 10x10 = 100.

These are usually easy for children to learn, so just check, ‘we know all these don’t we?’ Obviously sort out any difficulties children have with these numbers, but if there are I would suggest the activity may be a challenge at this stage.

2. How many products are there in the 90s? 80s? 70s?

Find all the products of the times tables up to 10x10 starting with those in the 90s. It has more impact when starting with big numbers. 
There are none in the 90s, one in the 80s: 9x9=81 and one in the 70s too: 8x9=72 

P1
PP1
3. Which products of multiplication facts appear in the 60s, then in the 50s?

There are two products in the 60s: 63 and 64, and amazingly there are also only two products in the 50s: 54 and 56.
PP2
There are only six products to remember that are greater than 50.
 
54, 56, 63, 64, 72 and 81

So if we focus on the products of the times tables up to 10x10 (and ignore multiples of 10), there are only six key numbers for children to remember.

62 isn’t there, or 58… and many other numbers that shouldn’t enter our heads when we’re trying to quickly recall our tables facts. 


4. Continue finding products in the 40s, then 30s and 20s.

If we carry on through the tens, the numbers increase:
Four products in the 40s: 42, 45, 48 and 49
Three products in the 30s: 32, 35 and 36.
Five products in the 20s: 21, 24, 25, 27 and 28.

5. Find products in the teen numbers.

There are five more numbers between 10 and 20: 12, 14, 15, 16 and 18

The numbers missing are just as interesting: 11, 13, 17 and 19 are all prime numbers.

PP4
PP5

If we look at all those products on a 100 square you realise how few numbers there are to learn.

There are some other interesting features too, the pattern of the multiples of 9 and the products, such as 24 and 36, that have several multiplication facts.

P9

I’ve used this as an activity with Y3-6 children and it really makes them think about these key numbers. Some of them have taken the numbers on the 100 square and circled one at a time to learn the facts associated with that product. It’s just a different and alternative way in to the quest to become quick recallers of our tables facts.

What about the 11 and 12 times tables?

True, these aren’t included, but in the ‘numbers to 100’ rule the 12 times table only adds two more numbers: 84 and 96. The multiples of 11 do add to the list, but the pattern is as easy as the multiples of 10 and is a nice tables pattern to learn.
 
A good way of learning the 12x table is to use the power of partitioning. Break it up into x10 and x2, which seems slow, but is actually a pretty quick way of recalling correctly (rapid speed isn’t everything!). For example, 7 x 12 = (7 x 10) + (7 x 2) = 84
 
The process is ‘7 times 10 then add double 7’ – which isn’t a bad way of playing with the numbers to develop number sense and fluency.

P10
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