# Which one doesn't belong Stage 3

A thinking mathematically targeted teaching opportunity, focused on using reasoning to explore how each number in a set can be different.

## Syllabus

Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus (2022) © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2024.

## Outcomes

- MAO-WM-01
- MA3-RN-01
- MA3-AR-01
- MA3-MR-01

## Collect resources

You will need:

- a collection of objects
- pencils or markers
- your mathematics workbook.

## Which one doesn't belong?

Watch Which one doesn't belong? Stage 3 video (5:33).

[A title over a navy-blue background: Which one doesn’t belong? 2. Small font text in the upper left-hand corner reads: NSW Department of Education. In the lower left-hand corner is the white waratah of the NSW Government logo.

Text over a navy-blue background: Ok, mathematicians… what do you notice?]

### Speaker

OK, mathematicians. what do you notice?

[on a white background, 4 numbers are in each section of a cross. In the top left corner is 9; in the top right is 16; in the bottom left is 43 and in the bottom right is 25.

In the bottom right corner in smaller font is text: Task from: https://wodb.ca/numbers.html

A yellow round shape appears over 9, then 16, 43 and 25.]

Yeah. We've got the numbers nine, 16, 43 and 25.

[The shape disappears.]

And what I'm interested in is this idea, which one doesn't belong?

[A green starburst shape appears in the upper right corner. Inside is text: Which one doesn’t belong?]

Can you think of a reason for which number you think doesn't belong? Mm-hmm...and there's lots of really interesting answers. In fact, some people think it's nine. Some people think it's 43. Some people think it's 16, and some people think it's 25. Yeah. So, now my question's changed a little bit. What I'm interested in is…

[Below the starbust, a blue text box appears with text: Can you make a case for why each one doesn’t belong?]

…can you make a case, a reason, for why each one doesn't belong? Ugh. It just got a lot trickier. Ah, are you thinking? Write down some of your ideas on your notebook. OK.

[The starburst and textbox disappear.]

Let's have a look. We'll share some ideas together.

[The yellow round shape appears over 9.]

So, some of you were thinking about nine, mm-hmm, because it's pretty evident, in some cases, a reason for nine in that it's the only one digit number.

[A speech bubble out of the yellow shape appears that reads: It’s the only 1-digit number.]

Yes. And some of you also think and rightly argued that it's also the only one that's divisible by three.

[A speech bubble below the other speech bubble appears that reads: …and, it’s the only one that’s divisible by 3.]

Yeah. And some of you also are maybe thinking it's also an odd number.

[A speech bubble below the other speech bubble appears that reads: …It’s also an odd number.]

Aha! Yes, I hear you. But what about 25 and 43?

[A yellow round shape appears over 25 and 43.]

They're also odd numbers.

[A speech bubble below the other speech bubble appears that reads: …but 25 and 43 are also odd numbers so that one doesn’t work.]

So, that argument for why nine doesn't belong doesn't work.

[The speech bubbles:

· It’s also an odd number…

· …but 25 and 43 are also odd numbers so that one doesn’t work

turn blue.]

Yes. But since we've highlighted 25…

[A speech bubble out of the yellow shape appears that reads: 25 is a square number!]

…something we've noticed about it is it's a square number.

[On a white background are 5 columns of 5 red squares. Next to the shapes is text which reads: 25 is 5 fives and 25 = 5 x 5.]

Look, if we arrange 25, we can make a perfect square. 25 is 5 fives or five times five and that means…

[A speech bubble out of the squares appears that reads: That means there are the same number of rows and columns in the array.]

…there's the same number of arrays, rows and columns in the array.

[Back to the slide with the numbers.]

So, 25 is definitely a square number. But, mmm, yes, I can hear you too.

[A speech bubble below the other speech bubble appears that reads: What about the other numbers?]

What about other numbers like nine and 16?

[A yellow round shape appears over 9 and 16.]

Let's have a look.

[On the left side is 3 columns of 3 red squares. Under the tiles is text which read: 9 is 3 threes and 9 = 3 x 3.

On the right side is 4 columns of 4 red squares. Under the tiles is text which reads: 16 is 4 fours and 16 = 4 x 4.]

Yep, they're 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 equal number of columns.

[The speech bubbles:

· 25 is a square number!

· What about the other numbers?

turn blue.]

So, that one also doesn't work. They're both square numbers. But what that does tell us though is something about 43.

[A yellow round shape appears over 43, and the others disappear.]

Yes. So, by the process of elimination, we now know that 43 is not a square number.

[A speech bubble out of the yellow shape appears that reads: 43 is NOT a square number.]

Yes. And some of you have picked up on this idea: It's a prime number.

[A speech bubble below the other speech bubble appears that reads: It’s a prime number.]

Yeah. So, let's have a look. We've got some reasons for nine and some reasons for 43. What about 16?

[The yellow round shape appears over 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.

[A speech bubble out of the yellow shape appears that reads: It’s the only one that’s divisible by 2 (meaning, it’s the only even number.]

We thought about this one too. It's the only one that's divisible by two, which means it's the only even number. OK. So, that means we have a reason for nine, 16 and 43. Let's try for 25.

[The yellow round shape appears over 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.

[A speech bubble out of the yellow shape appears that reads: It’s divisible by 5!]

It's divisible by five. Oh, yes. And let's go back to nine…

[The yellow round shape appears over 9.]

…because some of you notice this.

[A speech bubble out of the yellow shape appears that reads: The digits DON’T add to 7.]

Nine is the only one where the digits don't add to seven. Look, with one and six, if I combine those digits, it's seven. Mm-hmm. Two and five combines to make seven, and four and three combine, yes, to make seven. So, that's another reason why nine is the one that doesn't belong. Oh, OK. And I'll come back to 43…

[The yellow round shape appears over 43.]

… 'cause someone else is saying 43 is the only one that has an even number of factors.

[A speech bubble above the other speech bubble appears that reads: Has an even number of factors.]

Oh, I hear you pondering about this and thinking, are you sure about that?

[A speech bubble above the other speech bubble appears that reads: 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 gonna send this back your way now.

[A title over a navy-blue background: Well done, mathematicians! Below are points that read

· There might be some other reasons we could have used, so, since we came up with 3 reasons why 9 is the number that doesn’t belong, see if you can come up with 3 reasons for 25,16 and 43.

o we might have found 3 for 43 but you’ll need to check… is it the only number with an even number of factors?

· Then, ask your family, friends or your classmates about the next diagram…see if you can work together to come up with at least 1 reason for each collection!]

First, I wanna say, well done, mathematicians, but 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 nine 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 it's 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 can 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.

[on a white background, 4 shapes consisting of triangles are in each section of a cross. In the top left corner: a purple triangle and a green triangle create a square, which is on top of another purple and green triangle forming a square.

In the top right corner: a purple triangle and a green triangle create a square, is next to a purple triangle. Below the purple triangle is a green triangle.

In the bottom right corner: 4 triangles are joined at the points form a big purple and green square.

In the bottom left corner: 4 triangles are joined alternating on their angled sides to form a parallelogram.]

Oh, it's nice, isn't it? Yes. So, which one doesn't belong?

[In the upper right corner of the screen, a green starburst appears with text: Which one doesn’t belong?

Below the starbust, is a blue text box with text: Can you make a case for why each one doesn’t belong?]

And can you make a case for why each one doesn't belong?

Over to you, mathematicians.

[Over a grey background, the red waratah of the NSW Government logo appears amongst red, white and blue circles. Text: Copyright State of New South Wales (Department of Education), 2021.]

[End of transcript]

### Instructions

- Which one doesn’t belong? What's your initial thinking?
- Can you make a case for why each domino doesn’t belong?
- Record 3 other reasons for why 25, 16 and 43 don’t belong? (We might have found 3 for 43 but you’ll need to check… is it the only number with an even number of factors?)

### Share/Submit

- Collaborate with your family, friends or classmates to discuss and record, which one doesn’t belong with this collection?
- Can you make a case for why each one doesn’t belong?