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Mason spilled ink over his division homework.
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What number is the arrow pointing at?
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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.
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He’s had to complete several steps.
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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.
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Interestingly, our question doesn’t ask us to find a final answer.
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We need to find the number that the arrows pointed at.
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This is one of the numbers that Mason uses along the way.
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Possibly the best way of finding out this missing number is to think as if we were Mason.
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We could go through the whole calculation step by step as if we were him and find all the missing numbers.
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Then we can understand what he was trying to do.
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To begin with, we can see the division that Mason is trying to work out is 42 divided by three.
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And underneath the number 42, he’s drawn a part–whole model.
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And we can imagine the sorts of thoughts that would have gone through his head as he did this.
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He must have thought to himself, “Well, 42 is quite a large two-digit number.”
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Perhaps he only knew his three times tables facts up to 10 threes are 30.
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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.”
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Now although one of the parts has been covered over when Mason spilled his ink, we can see that the first part is 30.
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And what number goes together with 30 to make 42?
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30 and 12 make 42, don’t they?
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And we know that both 30 and 12 are numbers in the three times table.
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They’re multiples of three.
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And they’re a bit easier to divide by three than 42.
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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.
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In other words, 30 divided by three plus the answer to — Oh dear.
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Here’s another ink splotch.
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Can you see what this missing number is?
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It’s the same as the first one, isn’t it?
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It’s talking about our second part and dividing it by three.
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That’s better.
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To find his answer, Mason needs to divide 30 by three, 12 by three, and then add the two together.
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And in the next step, this is what we can see he starts to do.
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We know that there are 10 threes in 30.
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That’s where the number 10 comes from here.
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And now we’ve got another ink splotch.
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This is going to be the answer that we get when we divide 12 by three.
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Three, six, nine, 12.
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There are four threes in 12.
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So 12 divided by three equals four.
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Now we found out the answer to this particular question because we found the missing number.
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But it would be a shame not to complete the calculation, wouldn’t it?
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10 plus four equals 14.
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So Mason has found out the answer to 42 divided by three by breaking apart 42 into two easier numbers.
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What made them easier to work with is that they’re both smaller than 42 and they’re both multiples of three.
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So Mason could just use multiplication facts he already knew to help him.
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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.
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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.
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The answer is four.