# Which one doesn't belong? (reasoning with numbers)

Stage 1 and 2 – A thinking mathematically targeted teaching opportunity, focussed on using reasoning to explore common features and differences between representations of quantities

## Syllabus

Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2023

• MAO-WM-01
• MA1-RWN-01
• MA1-RWN-02
• MA1-CSQ-01

• MAO-WM-01
• MA2-RN-01
• MA2-AR-01
• MA2-MR-01

## Collect resources

You will need:

• a collection of objects

• pencils or markers

## Watch

Watch Which one doesn't belong? video (4:56).

Explore how each domino is different using reasoning.

### Transcript of Which one doesn't belong? video

[A title over a navy-blue background: Which one doesn’t belong? 1. 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. Have you got your eyeballs ready? Great. What do you notice?

[on a white background, 4 dominoes are in each section of a cross. In the top left corner is a 4: 4 piece; in the top right is a 6:5 piece; in the bottom left is a 3: blank and in the bottom right is a 2:3 piece.]

Mmm. OK, so you can see four dominoes.

[A yellow round shape appears over the 4:4 domino in the top left section. Then the shape moves across to the 6:5 domino in the top right, then over the 2:3 domino below, and then across to the 3:0 on the left.]

Look, one, two, three, four. And yes, I see this too. They each have a different number of dots.

[The yellow round shape appears over the 4:4 domino.]

Look, this one has eight.

[The yellow round shape appears over the 6:5 domino.]

This one has 11.

[The yellow round shape appears over the 2:3 domino.]

Yes, this one has five.

[The yellow round shape appears over the 3: 0 domino.]

And this one? Has three, mm-hmm. So if you had to make an argument or case for why each domino doesn't belong, who would you argue for does not belong?

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

Mmm, what are you thinking? Mmm, so, this would be a good time to get out your paper and pencil and see if you could write down an idea for why each one of those dominoes you think...sorry, why one of those dominoes doesn't belong. And then...yes, I know.

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

### Speaker

We're gonna ask this question. Can you make a case for why each domino doesn't belong? Oh, yes. Some are trickier than others, aren't they? Shall we have a look together? OK.

[The starburst and textbox disappear.

The yellow round shape appears over 3:0.]

So what about this one? What's one reason why this one doesn't belong? OK. Yes, it's... Oh, I almost said it's the only domino with three on it, but it's not actually.

But what I do notice is it's the only domino that shows zero and some more.

[A speech bubble out of the yellow shape appears that reads: It’s the only one that shows zero and some more.]

Did you think about that too? Oh, you had a different reason for why that one. That's really cool. Keep a hold of that. You'll need it later. What about this one?

[The yellow round shape appears over 4:4.]

What's the reason why this domino doesn't belong? Ah, yes, I had noticed the same thing that some of you noticed…

[A speech bubble out of the yellow shape appears that reads: This one shows a doubles fact. It’s the only one to show a double.]

…and that it's the only one that shows a doubles fact. Yes, so it shows a double. Double four is eight. Mm-hmm. Ah! There's more reasons. Hold on to them. We will come back. OK, what about... This one, yes.

[The yellow round shape appears over 2:3.

A speech bubble out of the yellow shape appears that reads: This one shows a near double… double 2 and 1 more is 5.]

### Speaker

Look, this one shows a near double, double two and one more is five. Ah, yes, you're right.

[Another yellow round shape appears over 6:5

A speech bubble out of the yellow shape appears that reads: Oh… this one is a near double too… double 5 is 10, then 1 more is 11.]

But this one is a near double too. Double five is ten. Then one more is 11.

[A speech bubble out of the yellow shape over 2:3 appears that reads: Ok, so this one doesn’t work. Why else might 5 not belong?

The yellow round shape disappears from 6:5]

OK, so this one doesn't work. Why else might five not belong? What are you thinking? Ah, OK. Yes, lots of different answers. But some of you are thinking this as well.

[A speech bubble below the yellow shape appears that reads: It’s the only one that’s half of ten!]

It's the only one that's half of ten. Three is less than half of ten. Eight is more than half of ten, and, well, 11 is more than ten in total. Oh, OK.

[The yellow round shape appears over 4:4.

A speech bubble out of the yellow shape appears that reads: This one is also the only even number… all of the others are odd!]

You wanna come back to eight to talk about this? Yes, it's the only one that shows an even number because all of the other numbers are odd.

Yeah, three is an odd number because if I halve it, I'd have one left over. 11 is an odd number because if I halved it, there would be one left over. And five is an odd number because if I halved it there'd be one left over. Mm-hmm.

[The yellow round shape appears over 6:5.]

### Speaker

OK, so what about 11 then? Well, we worked out that it's odd, but so is three and five. They're both odd. What's a reason... Aha! I hear you.

[A speech bubble out of the yellow shape appears that reads: It’s the only 2-digit number!]

It's the only two-digit number.

[The yellow round shape disappears. A blue text box appears at the top centre with text: Can you make a case for why each one doesn’t belong?]

Oh, that's really nice. So, can I make a case now for why each one doesn't belong? Yes, we did that.

[A title over a navy-blue background: Well done, mathematicians!

Below is text that reads: There might be some other reasons we could have used, so it's back to you to see if you can come up with some other reasons.

Below is more text: Then, ask your family, friends or your classmates about the next diagram…see if you can work together to come up with a reason for each collection.]

So, well done, mathematicians. And there might be some other reasons we could have used. So it's back to you to see if you can come up with some other reasons. Then, ask your family or your friends or your classmates about the next diagram and see if you can work together to come up with a reason why each collection or image is the one that doesn't belong.

[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.]

### Speaker

(NOISE) I know. It's gonna make your brain sweat.

[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?]

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]

## Reflection

• Which one doesn’t belong?