# Sorting shoes

ES1 – A thinking mathematically targeted teaching opportunity focussed on sorting, organising and classifying collections of objects

## 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-RWN-01
• MAE-RWN-02
• MAE-DATA-01

## Collect resources

You will need:

• shoes

• paper

• markers or pencils.

## Watch

Watch Sorting shoes video (9:34).

Investigate ways to sort a collection of shoes.

### Transcript of Sorting shoes video

(Duration: 9 minutes and 34 seconds)

[Text over a blue background: Sorting shoes.

In the lower right-hand corner of the screen is the waratah of the NSW Government logo. Small font text in the lower left-hand corner of the screen reads: NSW Mathematics Strategy Professional Learning team (NSWMS PL team).]

### Speaker

Hi, mathematicians. Today we're going to use a task from reSolve where we're going to explore data by sorting shoes.

[Black text over a white background: You will need…

· shoes

· paper

· pencils or markers.

Beside the text is an image of different styles of shoes piled in a heap on some lawn.]

### Speaker

For this activity, you'll need some shoes. Make sure you ask an adult for some help collecting some shoes.

[White text over a blue background: Let’s explore!]

### Speaker

Let's explore.

[On the right side of the screen is the image of the pile of shoes. To the left is a small square sticky note on a blue background.]

### Speaker

Hey, mathematicians, we've been tidying at our house, and we found this bucket full of shoes. But it's really hard for me to see whose shoes are there. Do you think you can help me think of a way that we might be able to organise them? Hmm. I noticed that there's a pair of Ugg boots in there.

[The speaker writes “Ugg boots” on the sticky note.]

### Speaker

So, maybe that could be one of our categories. Let's write that down as an idea.

[The sticky note moves to the top of the screen. A blank sticky note appears at the bottom, on which the speaker writes the word ‘colours’.]

### Speaker

What else do you notice? We can see lots of different colours. Well, let's write that down as an idea too. Colours, we can see yellow and black and brown.

[The ‘colours’ sticky note moves to the middle of the screen. A blank sticky note appears at the bottom.]

### Speaker

I wonder what else we might be able to sort our shoes by. We've got Ugg boots and not Ugg boots, colours. Maybe we could think a little bit more about the Ugg boots. And use another word that might describe the shoes.

[The speaker counts the types of shoes on their fingers.]

### Speaker

Because I can see in there that because we have football boots, we have Ugg boots, we have... I think there might even be thongs in there.

[The speaker removes the “Ugg boots” sticky note from view and replaces it with a blank sticky note. They write the word ‘type’ on it.]

### Speaker

Maybe we could change Ugg boots to the type of shoe. So, now we've got the type of shoe, we've got the colours, what could be another way it could be sorted?

[The speaker writes the word ‘size’ on a blank sticky note.]

### Speaker

Oh, yeah, it could be based on size. Oh, maybe there might be some smaller shoes and some larger shoes.

[On a white paper background, an image of the shoes sorted into rows occupies half of the screen. From top to bottom, there are two pairs of Ugg boots, three pairs of thongs, five pairs of running shoes, one pair of gumboots, one pair of dress shoes, and two pairs of football boots.]

### Speaker

So, we've been doing some organising of our shoes. And we can now see the different types of shoes that we found in our bucket. Can you notice some types of shoes in here?

[Beside the image, the speaker writes “football boots”.]

### Speaker

I can see some football boots.

[The speaker writes “thongs” beside the row of thongs.]

### Speaker

I can also see some thongs.

[The speaker writes “gum boots” beside the row of gumboots.]

### Speaker

In the middle, I can also see some black gumboots. They're good for sloshing around in the mud.

[The speaker points to the row of Ugg boots, and writes “Ugg boots” beside them.]

### Speaker

We've also got up here some Ugg boots.

[The speaker points to the row of running shoes, and writes “runners” beside them.]

### Speaker

Big long line here. They look like good shoes for running in. So, I think I'm going to call them runners. You might call them joggers, or sand shoes, but we'll go with runners today.

[The speaker points to each row of shoes. They point to the row of gumboots, then to the row of dress shoes.]

### Speaker

So, let's have a look at our shoes now. And they're all organised in neat and tidy rows so we can easily see how many they are. I noticed that there's only one pair of gumboots and one pair of dress shoes, but have a look.

[The speaker points to the bottom row of football boots, indicating the space between each pair. They point to the top row of Ugg boots, which are spaced closer together.]

### Speaker

I wonder if you notice anything here, and here. Hmm. I can see two pairs of Ugg boots. But there's also two pairs of football boots.

[The speaker uses a finger to draw a line from the end of the row at the bottom, up to the top of the image.]

### Speaker

But if I lined them up using this line here, I would think that there's more football boots than Ugg boots.

[The speaker indicates the pairs of thongs in the second row.]

### Speaker

And when I look at the thongs, look how spread out they are.

[The speaker points to the row of running shoes, then to the row of thongs.]

### Speaker

Oh, that's not helpful. These ones are close together. These ones are stretched right out long. And it makes me think that there's more thongs than what there are. Hmm, I wonder what we could do to fix that. That's a good idea, mathematicians. Let's move them so they're all equally spaced out.

[A white piece of paper sits on top of a blue background. On the paper is an image of the shoes organised in rows, with each pair of shoes equally spaced out. From top to bottom, text beside each row reads: ugg boots, thongs, runners, gum boots, dress shoes, football boots.

In the top left corner is a sticky note with the word ‘type’ written in marker.]

### Speaker

OK, so let's take a look now. We've had another try at organising our shoes, so that we might be able to tell which shoes we have the most of, and which shoes we have the least of, and maybe if some of them are the same, just by looking and thinking. Now, when you look at our data display here, what are some things that you notice?

[The speaker writes “3 pairs of thongs” on a blank sticky note. They place it underneath the top sticky note.”

### Speaker

Yes. There are three pairs of thongs. Good noticing. What else do you notice?

[The image of the shoes and adjoining text fills the screen. The speaker points to the row of thongs, then to the row of Ugg boots above it. They indicate the blank space at the end of the row of Ugg boots.]

### Speaker

Well, look at that. If we look at thongs and we know there's three, and we look at the Ugg boots, we can see in this blank space here that there's one less pair of Ugg boots.

[The screen returns to the wider view showing the sticky notes on the blue background. On the middle sticky note, text appears, reading “1 less pair of ugg boots”. Below it appears “so there are 2”.]

### Speaker

So, if we know that there's three thongs, then we also know that there's two Ugg boots, because it's one less. So, we know there must be two.

[The screen changes to the closer view of the shoes and text. The speaker points to each row of shoes.]

### Speaker

I wonder if you can find any shoes that have the same amount as the Ugg boots. I'm looking across. I know it's not thongs, because I already know there's one more pair of thongs. Maybe if I bring my eye close and look really carefully, maybe if I draw a line down here, look at that.

[The screen changes to the wider view with the sticky notes. The speaker places a blank sticky note near the bottom of the screen and writes “football boots and ugg boots have the same amount”. They point to the row of Ugg boots, then to the row of football boots.]

### Speaker

Football boots and Ugg boots have the same amount. And I know they're the same because there's two here and two here. What else can you notice?

[The screen changes to the closer view of the shoes and text. The speaker places a blank sticky note in the top left corner. They write “Gumboots and dress shoes are the same. Both have 1.” They point to the row of dress shoes, then to the pair of gum boots.]

### Speaker

I can see some other ones that have the same, can you? The gumboots and the dress shoes both have the same amount. And we know they're the same because they both have one pair. You can see one pair of dress shoes, and one pair of gumboots.

[The screen changes to the wider view with the three original sticky notes.]

### Speaker

I wonder which shoes we have the most of in our house?

[The screen changes to the closer view of the shoes and text. The speaker places a blank sticky note below the top note. They point to the row of running shoes. On the sticky note they write, “Runners have the most.”]

### Speaker

Oh, can you see, mathematicians? I can see too. Have a look here. Such a big long line of runners. We must do lots of running in this house. So, runners have the most.

[The speaker points to the row of running shoes. They point to the row of thongs above, indicating the blank spaces at the end of the row.]

### Speaker

How many pairs runners do we have? I know already that there are three pairs of thongs and I can see here that there's one blank space here. And one blank space here. That's two empty spaces in the thongs row.

[On the sticky note, the speaker writes “2 more runners 5 pairs of runners.”]

### Speaker

So, there must be two more runners. So, I know I have five pairs of runners.

[White text on a blue background: Over to you… What shoes do you have that you can sort? How will you sort them? Draw a picture to show what you found.]

### Speaker

So, over to you, mathematicians. What shoes do you have that you can sort? How will you sort them? Draw a picture to show what you found.

[On a white background, an image of a column graph made up of drawings of different styles of shoes. From left to right, text under each column reads: ugg boots, thongs, runners, gym boots, dress shoes, football boots.]

### Speaker

[White text on a blue background: What’s (some of) the mathematics?

In the lower right-hand corner of the screen is a white speaker icon.]

### Speaker

What's some of the mathematics?

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

Text: The graph was a bit tricky to read. It was hard to see how many there were because there were big gaps in between the pairs of shoes.

· When we looked across from the football boots to the Ugg boots we thought there were more football boots because there was a big gap in between.

To the right of the text is an image of the shoes sorted into rows by style. The top row of football boots has a red highlight over the shoes. A vertical red line at the end of the row extends to the bottom row. The bottom row of Ugg boots also has a red highlight, with a blank space between the shoes and the vertical line.]

### Speaker

Our graph was a little bit tricky to read to start with. It was hard for us to tell how many shoes there were because of the big gaps in between the pairs of shoes. But when we drew our imaginary line from the football boots over to the Ugg boots, we thought that there were more football boots. But then we noticed that there was a big gap in between the football boots that made it hard for us to tell how many there were.

[Text: When the shoes were lined up neatly with not gaps and overlaps it was easier to see how many we had of each time of shoes.

· We saw there were the same amount of Ugg boots and football boots. They both had 2 pairs.

To the right of the text is the image of the shoes sorted into rows and equally spaced out. There is a red vertical line from the end of the top row of football boots down to the end of the bottom row of Ugg boots.]

### Speaker

When the shoes were lined up neatly with no gaps and overlaps, it was much easier for us to see how many we had of each type of shoe. We saw that there were the same amount of Ugg boots and football boots. They both had two pairs.

[Text: We used what we knew about numbers to decide if we had more or less. We could think about how many more and how many less.

· We noticed there were 3 pairs of thongs. We saw there were two empty spaces in the thongs row so there must be two more pairs of runners.

In the image of the shoes, a red vertical line extends from the third row of runners down to the bottom row of Ugg boots. The line begins after the second pair of runners, underneath which there are two red squares to indicate blank spaces in the row of thongs underneath.]

### Speaker

We used what we knew about numbers to decide if we had more or less. We could think about how many more and how many less. We noticed there were three pairs of thongs and we saw that there were two empty spaces in the thongs row. So, that meant there must be two more pairs of runners.

[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

• Decide how you want to sort them. You could sort them by the type of shoes like we did or maybe by colour or size.

• Organise your shoes into a data display, remember to line the up evenly in rows.

• Draw a picture showing how you organised your shoes, you could ask someone to help you to write down what you notice.

## Discuss/Reflect

• Can you see what you have the most or least of?

• Do you have any in your display that show the same amount.

• Can you think of other ways to sort your shoes?

• How does you data display change when you change how you sorted your shoes?

• How is the data you have collected on the different shoes helpful? Could it help you to make some decisions?