Multiplication Mayhem: It’s Base-ic Maths

Why all the fuss about multiplication testing?

Some teachers have been up in arms about the new Year 4 multiplication tests and for good reasons. What’s the point of telling teachers what they already know about their own classes?

But there are other considerations.

Here’s the other thing:  in Year 4, children are expected to learn “multiplication and division facts for multiplication tables up to 12×12”.

But wait, the content of the new statutory tests is all multiplication – what about poor old division? Why isn’t she invited to the party?

Division has been shunned, told it’s not welcome and left out of the equation.

This means that by not including the all-important related division facts some schools will teach to the test and not bother with them but just focus on ‘tables’.

Knowledge of division as the inverse operation of multiplication is as important as understanding the relationship between addition and subtraction. Without this crucial understanding children have to learn the division facts independently of the multiplication facts and that is a very tall order that many find hard to do.


I’m not convinced that the DfE understand the crucial distinction between the two types of multiplication table, e.g. the ‘table of 4s’ and the ‘4 times table’.

The table of 4s collects together sets that have a cardinality of 4, whereas the 3 times table is all about the total number in four sets. Lots of maths textbooks fail to make the difference between the two equivalent ideas and quite often confuse the two.

The multiplication tests are already starting to look like a bit of a mess.

There is a solution to all this: always read the question.

What do I mean? Let me explain. I’ll ask you a few questions:

4 x 5 =

4 x 6 =

4 x 12 =

This could come up in the new tests.

Now let’s mark the test as taken by Neil,

4 x 5 = 12

4 x 6 = 13

4 x 12 = 19

How did Neil do? Well, if the DfE were marking then he’d score zero.

If I were marking then I’d give him 3 out of 3.

You see, this is a ‘real-life’ incident.

Neil was a Y6 boy I taught some 25 years ago and the only maths ‘genius’ I have ever taught in that time. I’ve taught plenty of talented mathematicians but not of Neil’s calibre – he is one of life’s savants and a huge fan of Lewis Carroll.

When I told Neil he’d got 0/3 he challenged me and I ended up revising my marks in light of his comments.

He told me that the questions I asked didn’t specify which base to answer in so he answered according to the following logic:

4 x 5 = 12 on base 18

4 x 6 = 13 on base 21

4 x 12 = 19 on base 39

Come on, this is just base-ic maths.

Wow! Point taken!

And there’s the solution….if the new tests expect children to answer on a base 10 understanding then they’d better make that explicit at the top of the test: please answer in base 10.

If they don’t then they cannot make assumptions that children don’t know their times tables because they might be thinking (as Neil was) in completely different ways.

It’s all about the base….and the cost. The tests are going to cost around £5.2 million – imagine how else that money could be spent instead.

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