### Video Transcript

Mason spilled ink over his division
homework. What number is the arrow pointing
at?

We can see if we look quickly at
Mason’s division homework here, he hasn’t just had to do one thing to find out the
answer. He’s had to complete several
steps. But unfortunately, because he
spilled ink over his homework, the final answer and some of the other numbers he
uses in his working out have been covered up. Interestingly, our question doesn’t
ask us to find a final answer. We need to find the number that the
arrows pointed at. This is one of the numbers that
Mason uses along the way. Possibly the best way of finding
out this missing number is to think as if we were Mason. We could go through the whole
calculation step by step as if we were him and find all the missing numbers. Then we can understand what he was
trying to do.

To begin with, we can see the
division that Mason is trying to work out is 42 divided by three. And underneath the number 42, he’s
drawn a part–whole model. And we can imagine the sorts of
thoughts that would have gone through his head as he did this. He must have thought to himself,
“Well, 42 is quite a large two-digit number.” Perhaps he only knew his three
times tables facts up to 10 threes are 30. And so he’s clearly thought to
himself, “I need to split up the number 42 into easier parts, parts that I can still
divide by three.” Now although one of the parts has
been covered over when Mason spilled his ink, we can see that the first part is
30.

And what number goes together with
30 to make 42? 30 and 12 make 42, don’t they? And we know that both 30 and 12 are
numbers in the three times table. They’re multiples of three. And they’re a bit easier to divide
by three than 42. And Mason knows that if he divides
both parts by three and then adds his answers together, he’s going to find the
overall answer. In other words, 30 divided by three
plus the answer to — Oh dear. Here’s another ink splotch. Can you see what this missing
number is? It’s the same as the first one,
isn’t it? It’s talking about our second part
and dividing it by three. That’s better.

To find his answer, Mason needs to
divide 30 by three, 12 by three, and then add the two together. And in the next step, this is what
we can see he starts to do. We know that there are 10 threes in
30. That’s where the number 10 comes
from here. And now we’ve got another ink
splotch. This is going to be the answer that
we get when we divide 12 by three. Three, six, nine, 12. There are four threes in 12. So 12 divided by three equals
four. Now we found out the answer to this
particular question because we found the missing number. But it would be a shame not to
complete the calculation, wouldn’t it? 10 plus four equals 14.

So Mason has found out the answer
to 42 divided by three by breaking apart 42 into two easier numbers. What made them easier to work with
is that they’re both smaller than 42 and they’re both multiples of three. So Mason could just use
multiplication facts he already knew to help him. By going through the problems step
by step, we knew that the missing number was going to be the answer to one of our
parts divided by three. And that part was 12, and because
12 divided by three equals four, we know that’s the number that the arrow is
pointing at. The answer is four.