# The three bears – Stage 1

A thinking mathematically targeted teaching opportunity, focussed on comparing and the volume of food containers using an informal unit of measure

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
• MA1-3DS-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
• something to measure with such as a spoon or small scoop.

## Watch

Watch The three bears Stage 1 part 1 video (7:15).

Investigate which containers hold the most and least using comparison.

### Transcript of The three bears Stage 1 part 1 video

[A title over a navy-blue background: The three bears. Below the title is text in slightly smaller font: (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 logo.]

### Speaker

The Three Bears, Stage One, 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
• something to measure with such as a spoon or a small scoop.

Below the points is a row of images of the items listed above.]

### 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, something to write with, and something to measure with such as a spoon or a small scoop.

[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 Vaishnavi and we're at the Three Bears house. Vaishnavi, here's…

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

…Father Bear... and here's...

[The speaker lifts the medium blue bear.]

Mother Bear. And here is...

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

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, Vaishnavi, which bowl do you think belongs to Father Bear?

[The speaker points to the yellow bear.]

### Speaker

This big one.

[The speaker points to the large red bowl.]

Why do you think this holds the most? Because it's more bigger. OK, it looks big. Now, I wonder if we can check which bowl holds the most... This, of course. This one? Thank you. 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 bowl. I'm just gonna level it like this, Vaishnavi, so I make sure that it's full of beans right up to the top. I'm going to take the purple bowl, full of beans, and pour it into the red bowl.

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

OK? Oh... That doesn't hold the most. This purple bowl... Holds only a 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…

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

…at the bottom of the big, red bowl. And, wow, look how much space there is still. OK, well, I'm gonna put these beans away.

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

### Speaker

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?

[The speaker pours beans into the green bowl.]

Here, I'll fill it up for you. Ooh, up to the top there, just a little more. Do you want to level it, see if it's filled up now?

[The speaker places their hand over the bowl.]

Yeah, it is. 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.]

Woah!

[The speaker shakes the red bowl.]

### Speaker

Wow! I see that the beans from the green bowl will 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.]

Daddy Bear! Daddy Bear, Father Bear. OK, do you wanna give Father Bear this bowl?

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

Set the table. There we go.

[The speaker places the green bowl below the purple bear.]

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.]

…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…

[The speaker points to the green bowl.]

…and this looks small.

[The speaker points to the purple bowl.]

### Speaker

So, you think the green one holds more than the purple one? OK, I wonder how we can find out.

[The speaker holds up the tray of bean.]

Oh, why don't we put some of these beans in this purple bowl, fill it up and see?

[The speaker pours beans into the purple bowl.]

We could! Let's flatten it.

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

Yeah, make it level. OK, terrific. Why don't you pour the beans from the purple bowl into the green bowl? Yep, on it.

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

Oh, hey. What did you notice? It still holds a lot of space. Yeah, there's still space in this green bowl for more beans.

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

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 that purple bowl but a little bit less than that red bowl, doesn't it? Here you go, you set the table.

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

### Speaker

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! OK, 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.]

It holds the least. OK, is that why you gave it to Baby Bear? Yup.

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

Why did you give it to Baby Bear? Because Baby Bear doesn't want a lot of food, right? Right. So, it holds... The least. ...the least, and he is the littlest of all the bears, isn't it? Holds the least beans... and who does this green bowl belong to?

[The speaker points to the green bowl.]

### Speaker

It belongs to Mother Bear. Well, how do you know that this one belongs to Mother Bear? Because it's like the middle size of both of these.

So, this green bowl will 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. Hey, Vaishnavi, we 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 one's for 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.]

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?

[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?

## Watch

Watch The three bears Stage 1 part 2 video (6:23)

Measure the spoons or scoopfuls needed to fill containers.

### Transcript of The three bears Stage 1 part 2 video

[In the middle of a butcher’s paper are bowls in a row: a red one, a green one and a purple one. Above the bowls are three bears: a large yellow one, a medium blue one and small purple one. Below the red bowl is text: The red bowl holds the most beans. Below the green bowl is text: The green bowl holds more than the purple bowl and less than the red bowl. Below the purple bowl is text: The purple bowl holds the least beans.]

### Speaker

There's another way that we can work out which bowls holds the most, which bowl holds the least and order them. I've got some rice here.

[The speakers brings a tray of rice below the bowls.]

Yeah.

### Speaker

OK, and I found some different size containers in my house.

[The speaker places 2 cups and a spoon on the tray.]

Look, there's this one, this one and this one. And we could use spoonfuls…

[She takes a spoonful of rice.]

### Speaker

…or cupfuls…

[She takes a cupful of rice.]

…to work out which bowls can hold the most. Look, if I put the spoonful in that bowl…

[She places 3 spoonfuls of rice into the red bowl.]

…that's one spoonful. Two, three, do you think it's gonna take a long time?

Yeah.

### Speaker

(LAUGHS) We might not use that one. That will take a long time.

[The speaker pours rice from the red bowl into the tray. She picks up the large cup and places the other cup aside.]

I think we might use this one. OK, watch this.

[She takes a cupful of rice.]

I'm going to fill my cup full of rice like you did before. Level it.

Yeah.

### Speaker

And I'm going to see how many cups it takes to fill this green bowl. You ready?

[The speaker pours rice into the green bowl.]

One cup of rice.

[She takes a cupful of rice and pours it into the green bowl.]

Two cups of rice. Gonna fill this to the top.

[She takes a cupful of rice and pours it into the green bowl.]

Three cups of rice. So that green bowl takes up three cups of rice. Let's record that so that we remember. So this green bowl takes three cups.

[Below the green bowl, she writes: 3 cups of rice.]

I'm going to pour this rice back.

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

Now, this green bowl can hold three cups of rice. How many cups of rice do you think the big bowl is gonna hold, (UNKNOWN)?

Maybe five.

### Speaker

Why did you choose five?

### Child

Because it's the biggest. This will take three so this, well, I thought it was gonna be like two, but it's actually three. So this should have like more than this one.

### Speaker

OK, so you think that the red bowl should have more cups of rice than the green one? OK, let's find out. OK, you do the counting. So tell me, how many cups?

[She takes a cupful of rice and pours it into the red bowl.]

One.

### Speaker

One cup.

[She takes a cupful of rice and pours it into the red bowl 4 more times.]

### Child

Two cups. Three cups. Four cups. I don't know.

Four cups.

### Child

Five cups. What? It's (INAUDIBLE).

### Speaker

There's no more space, isn't it? Wanna change your mind? How many cups do you think we'll do?

Seven.

### Speaker

Seven. Alright, that's fine. I'm just gonna fill this one up a bit more. So five cups and then...

[She takes a cupful of rice and pours it into the red bowl.]

### Child

Six cups.

[She takes a cupful of rice and pours it into the red bowl.]

Seven cups. It taked up seven.

### Speaker

It did. It took up seven cups. Wow, that's...

[The child places his hand over the bowl.]

### Child

It almost finished up all the rice we have.

### Speaker

It did, didn't it?

[Below the green bowl, she writes: 7 cups of rice.]

So this red bowl takes up seven cups of rice. OK, you alright, (UNKNOWN)?

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

Let's find out how many cups the purple bowl takes up. Alright, how many do you think? Alright, you count the cups.

[She takes a cupful of rice and pours it into the purple bowl.]

One.

### Speaker

One cup and?

[She takes a cupful of rice and pours it into the purple bowl.]

### Child

Oh. OK.

[She places her hand over the bowl.

[Below the purple bowl, she writes: 1 cup and a little bit of rice.]

### Speaker

So this purple bowl holds one cup and a little bit of rice. So which one holds the least? The purple one?

[The child points to the purple bowl.]

Yeah.

### Speaker

And which one holds the most?

[The child points to the red bowl.]

The red bowl?

Mmm hmm.

### Speaker

Why do you say that?

### Child

Because seven is the biggest number here.

### Speaker

And which one is the medium bowl?

Three.

### Speaker

Yeah, the green bowl with three cups.

[The speaker points to the green bowl.]

Nice.

[Text over a blue background: Let’s create!

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

Over to you mathematicians.

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

· Use your measuring container such as a spoon or scoop and filling material like sand or pasta, to work out how many spoonfuls or scoopfuls each cup holds.

• How many scoopfuls does Father Bear's cup hold?
• How many scoopfuls does Mother Bear's cup hold?
• How many scoopfuls does Baby Bear's cup hold?

Below the points are 2 images: on the left is an image of the 3 bowls and rice being poured into the green bowl; on the right is an image of 3 cups of different sizes.]

### Speaker

Use your measuring container such as a spoon or scoop and filling material like sand or pasta, to work out how many spoonfuls or scoopfuls each cup holds. How many scoopfuls does Father Bear's cup hold? How many scoopfuls does Mother Bear's cup hold? How many scoopfuls does Baby Bear's cup hold?

[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 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.

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

• We can use informal units to work out how much a bowl can hold.
• We can compare the bowls by finding out how much they hold.

Below the points is a row of 3 images: on the left is an image of the red bowl with text below that reads: 7 cups of rice; in the middle is an image of the green bowl with text below that reads: 3 cups of rice; on the right is an image of the purple bowl with text below that reads: 1 cup and a bit.]

We can use informal units to work out how much a bowl can hold. I used a scoop of rice to work out how much a bowl could hold. The green bowl could hold three cups of rice. We can compare the bowls by finding out how much they hold. So the red bowl could hold the most. It could hold seven cups of rice. The purple bowl could hold the least.

It held one cup and a bit of rice, and the green bowl could hold less than the red bowl, but more than the purple bowl, it could hold three cups of rice.

[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 your measuring container such as a spoon or scoop and filling material like sand or pasta work out how many spoonfuls or scoopfuls each cup holds.

## Discuss/Reflect

• How many scoopfuls does Father Bear’s cup hold?
• How many scoopfuls does Mother Bear’s cup hold?
• How many scoopfuls does Baby Bear’s cup hold?