Which one doesn't belong?

Ok, mathematicians, what do you notice?

Yeah, I've got the numbers 9, 16, 43 and 25. And what I'm interested in is this idea 'Which one doesn't belong?' Can you think of a reason for which number you think doesn't belong?

Mmmmm and there's lots of really interesting answers. In fact, some people think it's 9. Some people think it's 43. Some people think it's 16 and some people think it's 25. Yes, so now my questions changed a little bit. What I'm interested in is, can you make a case, a reason for why each one doesn't belong?

It just got a lot trickier. Are you thinking? Write down some of your ideas in your notebook.

Ok, let's have a look. We'll share some ideas together so some of you were thinking about 9 because it's pretty evident. In some cases a reason for 9 in that it's the only one digit number. Yes, and some of you also think and rightly argued, that it's also the only one that's divisible by three. Yeah, and some of you are also thinking,. maybe thinking it's also an odd number.

Uh-huh yes, I hear you, but what about 25 and 43? They are also odd numbers so that argument for why 9 doesn't belong doesn't work. Yes, but since we've highlighted 25 something we've noticed about it is it's a square number look. If we arrange 25, we can make a perfect square. 25 is 5 fives or 5 x 5, and that means there is the same number of arrays rows and columns in the array, so 25 is definitely a square number, but... Yes, I can hear you too. What about other numbers like 9 and 16?

Let's have a look. Yep. They are both square numbers too. Look you can make a square array using nine things and you can make a square array using 16 things where they have equal number of rows and an equal number of columns. So that one also doesn't work. They are both square numbers. But what that does tell us though is something about 43.

Yes, so by the process of elimination we now know that 43 is not a square number. Yes and some of you have picked up on this idea, it's a prime number.

Yeah, so let's have a look. We've got some reasons for 9, some reasons for 43, what about 16? Can you think of a reason why 16 is the one that doesn't belong in this collection of numbers? Ah, so a few different ways of thinking. We thought about this one too. It's the only one that's divisible by 2, which means it's the only even number. Ok, so that means we have a reason for 9, 16 and 43. Let's try for 25. What's something that you can see about 25 that we could make an argument for a case for it being the one that doesn't belong.

Oh, we thought about that also. It's divisible by 5. Oh yes, and let's go back to 9 because some of you noticed this. Nine is the only one where the digits don't add to 7. Look with 1 and 6, if I combine those digits, it's 7. 2 and 5 combines to make 7 and 4 and 3 combine yes to make 7. So that's another reason why 9 is the one that doesn't belong.

Oh, Ok, and I'll come back to 43 because someone else is saying 43 is is the only one that has an even number of factors. Oh, I hear you pondering about this and thinking, 'Are you sure about that?' So our challenge mathematicians was to think of one reason for why each number doesn't belong, but I'm going to send this back your way now.

First I want to say, well done mathematicians, but that you might have realised that there might be some other reasons that we could have used. So since we came up with three reasons why 9 is the number that doesn't belong, see if you can come up with three reasons for 25, 16 and 43.

And we might have found the third one for 43, but you'll need to check. We said is the only number with an even number of factors, so you'll need to check that before you can say you've got three reasons.

Then you could ask your family and friends or classmates about the next diagram and see if you can work together to come up with at least one reason for each collection. Ready? Here it is.

Oh, it's nice, isn't it? Yes, so 'Which one doesn't belong?' and can you make a case for why each one doesn't belong?

Over to you mathematicians.