### Video Transcript

Look at Ethan’s work. He used eight equals five plus
three to write eight times three as the sum of simpler products. Eight times three equals five times
three plus three times three. Find another sum of products that
is equal to eight times three. Two times six plus six times three,
three times three plus six times three, two times three plus six times three, or two
times two plus six times three.

One of the useful things about
multiplication is something called the distributive property. This means that if we’re like Ethan
and we come across a multiplication that perhaps we don’t know the answer to, we can
split it up into the sum of simpler products, in other words, two multiplication
facts that are a little bit easier that we can add together to find the fact that we
want to know.

Now we can see that the
multiplication fact that Ethan wants to find out is eight times three. But perhaps he’s not great with his
eight times table because he split up the eight part of eight times three into five
and three. And because five and three make
eight, instead of working out eight times three, he just needs to work out the
answer to five times three and three times three and then add the two together.

And this is what we can see in his
number sentence. Eight times three equals five times
three plus three times three. Here’s what eight times three might
look like as an array. And by splitting the number eight
into five plus three, we can see that Ethan split up the larger calculation into
smaller ones that are hopefully easier to work out.

Now, this question doesn’t ask us
to use Ethan’s method to find the answer to eight times three. In a way, we’re asked to use his
method but differently. We need to find another sum of
products that’s equal to eight times three. Now, the first thing we can say
about what Ethan’s done is he split up the number eight, but he’s kept the number
three in his calculation. Can you see he’s working out both
five times three and three times three? Both of these simpler products are
still multiplying by three, aren’t they? It’s only the eight that’s been
split up.

And if we look at our possible
answers, only two of them could be correct. Only this one here and this one
here show two products that involve multiplying by three both times. We’ve got three times three plus
six times three, and then we’ve got two times three plus six times three. The answer has got to be one of
these two. So, we need to ask ourselves,
“Ethan’s split up the number eight into five plus three. How else could we split this number
up?”

For example, eight is the same as
four plus four. Then, we get the calculation four
times three plus four times three. But that’s not one of our possible
answers. How else could we split up the
number eight? What about six and two? Then we could answer the question
by finding the sum of six times three and two times three. Now, if we look carefully at our
possible answers, we can see that one of them shows this addition. The multiplications may be the
other way around. But we know we can add two values
together in different orders and they’d still make the same answer. We know that eight equals two plus
six. And so, we also know that eight
times three can be solved by working out two times three plus six times three.