Here is a diagram for sorting numbers. Write one number in each box. One is done for you.
This type of diagram is known as a Carroll diagram. And it’s a bit like a table. Each row and each column stands for something different. For example, all the numbers in this column will be multiples of five. Then the next column along is always an opposite statement. So instead of a multiple of five, everything in the last column is not a multiple of five. And there are two rows. The first row contains numbers that we can see are multiples of three. And then, again, the second row contains numbers that don’t fit this rule, numbers that are not a multiple of three.
We can see how the Carroll diagram works because we’ve been given one number already. The number 30 is in the multiple-of-five column. Five, 10, 15, 20, 25, 30. We know that 30 is a multiple of five. We also know that it’s a multiple of three. And that’s why it’s in the top row. Three, six, nine, 12, 15, 18, 21, 24, 27, 30.
The question asks us to write one number in each box. But there are a lot more than one number that we can choose from. Let’s remind ourselves of the multiples of five to start with. These are all the multiples up to 10 times five, which is 50. Of course, we could write numbers larger than that. The question doesn’t limit us. But we’ll stop there for now. And here are the multiples of three up to 10 times three, which is 30.
Let’s consider the box to the right of the number 30. This is in the column for numbers that are not a multiple of five. So we need to make sure that our number doesn’t end in a five or a zero. And it’s in the same row as multiples of three. So we’re looking for a number that is a multiple of three but is not a multiple of five. Perhaps the quickest way to find this answer is to find multiples of three that are multiples of five and then just don’t write those.
The number 15 is also a multiple of five, and the number 30 is also a multiple of five. But we can choose any one of those other numbers to put in that box. Let’s write the number 18. That’s a multiple of three but not a multiple of five.
Now let’s look at the square underneath the number 30. This is in the column labelled multiple of five. So we’re looking for a number that ends in a five or a zero. And it’s in the same row as the label “Not a multiple of three.” So we can’t allow any numbers that are multiples of three.
There are lots of possibilities. So again, let’s find the numbers that are multiples of three. And we just won’t use those. We can see that they’re the same numbers as before: 15, 30. And because our five times table goes a little bit higher, 45 is also a multiple of three. So we can’t use that.
But we can write any of the other numbers that are multiples of five. Let’s choose the number 25. 25 is a multiple of five. But it’s not a multiple of three. On to the last box, this time we’re looking for a number that’s not a multiple of five — so we can’t write any numbers that end in five or zero — but also not a multiple of three. We need a number that’s in neither times table. In other words, if we can’t see the number on the screen, we can write it in this box.
What about the number 17? It’s not in the three times table, and it’s not a multiple of five either. Let’s go with the number 17 then. This is an interesting question to make a video for because there are so many possible answers. For example, in this bottom box, we could’ve written any of the numbers, one, two. Can’t write three cause it’s a multiple of three, four. Couldn’t write five cause it’s a multiple of five. Can’t write six cause it’s a multiple of three, seven, eight. Can’t write nine cause it’s a multiple of three. Can’t write 10 cause it’s a multiple of five, and so on. We won’t carry on going through them.
And so as we go through the answer now, we’re going to describe each box in terms of the type of number that you should’ve written in the box rather than the actual number. In the top right-hand box, we could’ve written any number that’s a multiple of three but doesn’t end in five or zero. We chose the number 18.
In this box here, we could write any number that ends in a five or a zero but is not a multiple of three. We chose the number 25. And in the final box, we could write down any number that’s not a multiple of three or five. We chose the number 17.
So although there are lots and lots of possible answers, if you follow these rules, you can check whether your particular answer is correct.