# The three bears – Early Stage 1

A thinking mathematically targeted teaching opportunity, focussed on comparing the volume of food containers

From NZ Maths – Three Bears

## 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
• MAE-3DS-02

## Collect resources

You will need:

• 3 different sized cups or glasses

• one type of filling material such as beans, rice, pasta or sand

• paper or workbook

• pencils or markers.

## Watch

Watch The three bears Early Stage 1 video (7:42).

Investigate which containers hold the most and least using comparison.

### Transcript of The three bears video

[A title over a navy-blue background: The three bears. Below the title is text in slightly smaller font: (Early Stage 1). Below this is another text: From NZ maths. Small font text in the lower left-hand corner reads: NSW Mathematics Strategy Professional Learning team (NSWMS PL team). In the lower right-hand corner is the white waratah of the NSW Government log

### Speaker

The Three Bears, Early Stage 1, from New Zealand maths.

[A title on a white background reads: You will need…

• 3 different sized cups or glasses
• one type of filling material such as beans or rice or pasta or sand
• something to write on
• something to write with

In the lower right-hand section of the screen images of the items listed above set in 2 rows and 2 columns.]

### Speaker

You will need three different sized cups or glasses, one type of filling material such as beans or rice or pasta or sand, something to write on, and something to write with.

[Text over a blue background: Let’s investigate!]

Let's investigate.

[In the middle of a butcher’s paper are bowls in a row: a green one, a purple one and a large red one. Above the bowls are three bears: a large yellow one, a medium blue one and small purple one.]

Hello, mathematicians. I'm sitting here with my friend Bashadevi, and we're at the three bears' house. Bashanevi, here's Father Bear…

[The speaker moves the large yellow bear to the left.]

…and here's... Mother Bear.

[The speaker lifts the medium blue bear.]
And here's... Baby Bear.

[The speaker moves the small purple bear to the right.]

### Speaker

Baby Bear. Now, we have to set the table for dinner. There are three bowls here. We have to figure out which bowl is whose. Yeah, we do. We have to figure out which bowl belongs to who. Now, I'm wondering, Bashanevi, which bowl do you think belongs to Father Bear?

[The speaker points to the red bowl.]

This big one. Why do you think this holds the most? Because it's bigger. OK, it looks big. Now, hey, I wonder if we can check which bowl holds the most, I wonder...

[The speaker points to the red bowl.]

This, of course. This one? Yeah. OK. Well, let's find a way to check. I've got some beans here…

[The speaker brings a tray of beans below the bowls.]

…and I'm going to check.

Put them inside. Oh, we could.

[The speaker pours beans into the purple bowl.]

I'm going to pour the beans in. I'm going to pour the beans in the purple ball. I'm just going to level it like this, Bashanevi…

[The speaker places a hand over the purple bowl.]

…so I make sure that it's full of beans right up to the top. OK.

OK. I'm going to take the purple bowl full of beans and pour it into the red ball.

[The speaker pours beans from the purple bowl into the red bowl.]

### Speaker

Oh, OK. Oh!

That doesn't hold the most. This purple bowl... Holds only one little bit. Holds only a little bit. And look, I can tell because the beans from this purple bowl takes up a little bit of space at the bottom of the big red bowl. And wow, look how much space there is still.

[The speaker places her right hand into the bowl; thumb into the beans and forefinger on the top of the bowl.]

OK. Well, I'm going to put these beans away.

[The speaker pours beans from the purple bowl into the tray.]

So, you're right. This red bowl holds more than this purple bowl, doesn't it? Do you wanna check that the red bowl holds more than the green bowl? Why don't we do that? Here, I'll fill it up for you.

[The speaker pours beans into the green bowl.]

Ooh! Up to the top there. So, I'll put some more. Do you wanna level it see if it's filled up now?

[The speaker places a hand over the green bowl.]

### Speaker

(LAUGHS) Yeah, it is. It is. OK.

Alright. So, pour the beans from the green bowl into this red bowl and let's see what happens.

[The speaker pours beans from the green bowl into the red bowl.]

Whoa! Wow, I see that the beans from this green bowl take up half of this red bowl. But look at how much space there still is.

[The speaker places her right hand into the bowl; thumb into the beans and forefinger on the top of the bowl.]

Yeah, there's, like, still this space. Yeah, there's still this big space. So, yeah, I think you're right. I think this red bowl holds the most beans, and it definitely belongs to?

[The speaker pours beans from the red bowl into the tray.]

(YELLS) Daddy Bear. SPEAKER Daddy Bear, Father Bear. OK. Do you wanna give Father Bear this bowl, set the table?

[The speaker places the red bowl below the yellow bear.]

There we go. Oh. There's a bit of a problem. I don't know which bowl out of these two, the purple and the green, belong to Mother Bear or Baby Bear? I think this…

[The speaker points to the green bowl.]

### Speaker

…belongs to Mother Bear and this…

[The speaker points to the purple bowl.]

…belongs to Baby Bear. Why do you think that? This looks big and this looks small. So, you think the green one holds more than the purple one? Yep. OK, I wonder how we're going to find out. Why don't we put some of these beans in this purple bowl?

[The speaker pours beans into the purple bowl.]

Fill it up and see. Yes. You could.

Let's flatten it. Yep, make it level. OK. Terrific. Why don't you pour the beans from the purple bowl into the green bowl?

[The speaker pours beans from the purple bowl into the green bowl.]

Yep, on it. Oh! Hey... What did you notice? It still holds a lot of space. Yeah, there's still space in this…

[The speaker places her right hand into the bowl; thumb into the beans and forefinger on the top of the bowl.]

### Speaker

…green bowl for more beans. So, I think you were right, weren't you? You thought this purple bowl belongs to Baby Bear because it holds the least and this green bowl holds more than our purple bowl, but a little bit less than that red bowl does.

[The speaker pours beans from the green bowl into the tray.]

OK, here you go. You set the table. You give the bowls to the right bears.

[The speaker places the purple bowl below the purple bear and the green bowl below the blue bear. They take away the tray of beans.]

Now we can set the table. Yay! Lovely. Hey, let's write that down.

[A large yellow paper is below the bowls. The speaker holds a marker.

The speaker points to the red bowl.]

This bowl belongs to... Daddy Bear.

And it holds the most.

[Below the red bowl, the speaker writes: The red bowl holds the most beans.]

[The speaker points to the purple bowl.]

### Speaker

OK. Is that why you gave it to Baby Bear? Yep. Why did you give it to Baby Bear?

[Below the purple bowl, the speaker writes: The purple bowl holds the least beans.]

Because Baby Bear doesn't want a lot of food, right? Right. So, holds the least. And he is the littlest out of all the bears, wasn't it? Yeah. Holds the least beans.

And who does this green bowl belong to?

[The speaker points to the green bowl.]

Ah...it belongs to Mother Bear. Well, how do you know this one belongs to Mother Bear? Because it's like the middle size of both of these. Mmm. So this green bowl had more beans... could hold more beans than the purple one, but less beans than the red one. Alright, so this green bowl holds…

[Below the green bowl, the speaker writes: The green bowl holds more than the purple bowl and less than the red bowl.]

…more than... ..the purple bowl and holds less than... ..the red bowl. OK. Hey, Bashanevi, we've set the three different sized bowls for dinner. Now we have to find three different cups or glasses of different sizes to set for Father Bear, Mother Bear and Baby Bear. So, over to you, mathematicians. See if you can find three different sized cups and work out which ones were Father Bear, Baby Bear and Mother Bear.

[Text over a blue background: Over to you!]

Over to you.

[A title on a white background reads: Over to you, mathematicians…

• Find 3 cups or glasses you think are of different sizes.
• Use filling material like sand or pasta to check by pouring and filling the cups to see which holds the most and which holds the least.
• Which cup would you give to Father Bear?
• Which cup would you give to Mother Bear? Which cup would you give to Baby Bear?

In the bottom right section of the screen is an image of 3 cups of different sizes.]

### Speaker

Find three cups or glasses you think are of different sizes. Use filling material like sand or pasta to check by pouring and filling the cups to see which holds the most and which holds the least. Which cup would you give to Father Bear? Which cup would you give to Mother Bear?

Which cup would you give to Baby Bear?

[Text over a blue background: What’s (some of) the mathematics?]

What's some of the mathematics?

[A title on a white background reads: What’s (some of) the mathematics?

• We can use direct comparison to work out which container holds more.
• We know something is full when it is filled to the brim.
• We could compare how much the bowls hold by pouring them into each other. This helps us work out which bowl holds the most, less and least.

Below the points is a row of 3 images: on the left is an image of the 3 bowls with the purple bowl in the middle filled with beans; in the middle is an image of the beans from the purple bowl being poured into the red bowl; on the right is an image of the red bowl with beans.]

As mathematicians, we can use direct comparison to work out which container holds more. We know something is full when it is filled to the brim. We can compare how much the bowls hold by pouring them into each other. This helps us work out which bowl holds the most, less and least.

[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

• Find 3 cups or glasses you think are of different sizes.

• Use filling material like sand or pasta to check by pouring and filling the cups to see which holds the most and which holds the least.

## Discuss/reflect

• Which cup would you give to Father Bear?
• Which cup would you give to Mother Bear?
• Which cup would you give to Baby Bear?