Video: Dividing by Using Number Bonds to Create a Sum of Simpler Quotients

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

03:53

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.

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