# Sponge art transformations – Stage 3

This is a thinking mathematically targeted teaching opportunity focussed on exploring and comparing the properties of shapes used to create a sponge painting.

## 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
• MA3-GM-02
• MA3-GM-03
• MA3-2DS-03

## Collect resources

You will need:

• scissors​

• sponges to cut up​

• 2 different coloured paints

• 2 bowls (or containers to put the paint in)

• 2 sheets of paper per sponge

• a ruler​

• a snap lock bag.

## Watch

Watch Sponge art transformations Stage 3 part 1 video (8:25).

Compare angles created by sponge shapes.

### Transcript of Sponge art transformations Stage 3 part 1 video

[Text over a navy-blue background: Sponge art transformations. Smaller text in brackets beneath reads: (Stage 3). Beneath this, text reads: From youcubed. Small font text in the bottom left-hand corner reads: NSW Mathematics Strategy Professional Learning (NSWMS PL team). In the lower right-hand corner is the red waratah of the NSW Government logo. ]

### Speaker

Hi, mathematicians. Today we're going to create some sponge art transformations from youcubed.

[Text on a white background reads: You will need…

• Scissors
• Sponges to cut up
• 2 different coloured paints
• 2 bowls (or containers to put the pain in)
• 2 sheets of paper for each design
• A ruler
• A snap lock bag.

To the right of the text is an image of 2 vertical pieces of paper placed beside each-other, with a pair of orange handled scissors on the right, and a clear ruler above. To the left of the pieces of paper are 2 bowls, they are orange and yellow. The orange bowl has a dollop of blue paint in it and the yellow bowl has a dollop of mustard paint in it. Above these bowls are a green sponge cut in the shape of an arrow, a yellow sponge cut in the shape of a square, and a green post-it note.]

You will need scissors, sponges to cut up, two different coloured paints, two bowls or containers to put the paint in, two sheets of paper for each design you make, a ruler, and a snap-lock bag.

[Text on a blue background reads: Let’s create!]

Let's create.

[On a table there are 2 vertical pieces of paper placed beside each-other, with a pair of orange handled scissors on the right, and a clear ruler above. To the left of the pieces of paper are 2 bowls, they are orange and yellow. The orange bowl has a dollop of blue paint in it and the yellow bowl has a dollop of mustard paint in it. The speakers hands are hovering over the pieces of paper. In her left hand she is holding the small yellow square of sponge, and in the right she is holding the green shape.]

### Speaker

Hey, mathematicians, I've cut up some sponges today that I thought we could use to make some wrapping paper for a friend's birthday that's coming up. Now I'm having a look at my sponges, and I'm wondering what shape they might print when I dip them in paint.

[The speaker toys with the yellow sponge and gestures at the paint with it, then to the paper.]

Let's have a play around with this one first.

[The speaker puts away the green s and holds the yellow square sponge.]

Now, I've picked my two colours here. I've got a nice mustard colour and a purple. I thought they might make a really nice contrast, but I think I'm going to do the... orange one. I might stick with mustard, actually. And squidge it down.

[The speaker dips the yellow sponge in the mustard paint.]

Now, I need to make sure I don't have too much paint. And I'm going to print it right in the middle of my page. I think I might even still have a bit too much paint on the edges there.

[The speaker presses the sponge into the middle of the left-hand piece of paper.]

I'm gonna print it right in the middle of my page. I'll give it a squidge down and lift it up.

[The speaker lifts the sponge, revealing a mustard coloured square.]

### Speaker

Now, what shape do you think you'll see when we lift it up? There we go. So I'm looking at this shape and I'm thinking about what I know about shapes. So I know a polygon is regular, if all the sides are equal in length and all the angles need to be equal too, they all need to be right angles.

[The speaker points to the square she has printed.]

So I'm looking at this shape that I've just printed on my piece of paper, and I'm starting to wonder if all the angles are the same. And if all the sides are the same. So let's first see if my shape is a regular polygon. Now I'm going to use my ruler. I'm going to have to be careful not to dip it in the paint. But let's see if we can find out.

[The speaker takes the ruler and places it against the top edge of the square.]

This side is three centimetres.

[The speaker places the ruler against the right-hand edge of the square.]

This side is three centimetres.

[The speaker measures the remaining two sides of the square.]

Yep. So all sides are three centimetres. So I know all the sides are the same length. And that makes me think that it's a square. But we know we need to check one more thing with a square. We need to have a think about the angles.

[The speaker grabs the green post-it note from above the bowls.]

So for my square... for it to be a square, my angles need to be the same as well. So I have my post-it note here and it's going to help me check my angles.

[The speaker holds up the post-it note and outlines its corners.]

### Speaker

I've got four corners here and each of these intersect at 90 degrees, which I know is a right angle.

[The speaker aligns the bottom left-hand corner of the post-it note with the bottom left-hand corner of the square, covering the square.]

I was thinking when I laid it over the top, it was tricky for me to see whether I had right angles or not.

[The speaker aligns the post-it with the top left-hand corner of the square.]

I can't quite line it up because I can't see what's underneath.

[The speaker puts the post-it back above the bowls.]

And I was wondering what I could use to check to see if I had right angles. And I thought I could use this snap-lock bag.

[The speaker holds up a clear snap-lock bag.]

Because like my post-it note or a piece of paper, I can see where the lines meet. And we can see that it's a 90-degree angle. So let's see if my shape has a 90-degree angle.

[The picks up the post-it note and aligns it with the corner of the snap-lock bag.]

And I was even thinking I could just lay it on top and be careful not to smudge the paint.

[The speaker aligns a corner of the snap-lock bag with the top left-hand corner of the square.]

### Speaker

And I'm looking at this corner here and line it up and I can see that this angle here is a 90-degree angle just like it is on my snap-lock bag.

[A close-up view of the snap-lock bag over the mustard square appears in conjunction with the original view. A blue curved line appears traveling from the lower left-hand corner of the square to the top right-hand corner, with the curve closest to the lower right-hand corner. The speaker outlines the top left-hand corner of the square. In the close-up view two more lines appear along the top and left-hand edge of the square and traveling past it’s parameters. The lines end in arrows. Red lines outline the bottom and right-hand side of the square. All of the lines disappear and the view returns to normal.]

[The speaker aligns the corner of the snap-lock bag with the top right-hand corner of the square. A zoomed up view appears in conjunction with the original view.]

Yeah. And I can see that this angle here is also a right angle.

[The speaker outlines the edge in the original view with her finger. Two blue lines ending in arrows appear along the top and right-hand edge of the square and pass it’s parameters. A red line appears along the bottom and left-hand edge of the square.]

So that's two right angles. Three right angles.

[The speaker repeats the same process involving the close-up view with the lower right-hand corner of the square.]

### Speaker

I'm gonna check one more right angle. Yeah. And I can lay that down. And there's my fourth right angle there.

[The speaker repeats the same process involving the close-up view with the lower left-hand corner of the square.]

So now I know with this shape, it has four equal sides. They were all three centimetres and it has four right angles. I'm wondering what other words I could use to describe my shape.

[The speaker points to the shape.]

And I was thinking I could also say it's a parallelogram. And it's a parallelogram because this line here and this line here are parallel and they'll never meet up.

[Using her finger, the speaker outlines the top and bottom edge of the square.]

And these two lines down here are as well.

[Using her fingers, the speaker outlines the left and right edge of the square.]

So I'm thinking about my shape here. I know it's a parallelogram. I know it's a square, but I think that there's another word I can use to describe it. I'm thinking of a word that describes shapes that has all sides the same length, and all angles equal.

[Using her finger, the speaker outlines each edge of the square. She then points to each corner.]

Can you think of what the word is? Yeah, it's a polygon. And I know that this shape is a regular polygon because regular polygons have sides that are the same length and angles that are equal.

Now, I'm gonna have a look at the other sponge that I cut out. I'm wondering if this sponge will print a polygon on my piece of paper too

[The speakers grabs the green sponge cut in the shape of an arrow.]

### Speaker

So let's have a look.

[The speakers dips the green sponge in the blue paint.]

So I'm going to pop it up here on top of my square.

[The speaker presses the sponge into the paper above the square, with the arrow pointing away from the square.]

And I know that it's facing vertically because it's pointing straight up.

[The speaker gestures up and down along the piece of paper with her finger.]

I'm gonna take it off. Ooh, didn't come up with a very good point at the top. So I'm gonna squidge it back down a little bit. Might have had a little bit too much paint.

[The speaker removes the sponge, revealing a blue arrow shape without it’s tip. The speaker presses the sponge in more firmly and removes it, revealing the arrow with it’s tip.]

Whoa, there we go. Look at that. So I'm having a look at this shape now.

[The speaker points to the blue shape.]

And I'm not... I know it's not a square. It's got too many sides to be a square and too many angles. If I had to describe this shape, what words could I use? Well, let's start with how many sides it has.

[The speaker outlines the shape with her finger.]

It's got one, two, three, four, five, six, seven sides. And I know that a seven-sided shape is called a heptagon. But let's have a think now about this shape's features. Can it be a polygon too? Well, let's think back to what we know about polygons. We said that a polygon is a shape that has more than three angles and more than three sides.

So my arrow does have more than three angles and it does have more than three sides. But can it be a regular polygon?

[The speaker outlines the tip of the arrow.]

No, it's definitely not a regular polygon, because I can see that there's these angles up here in the top of the arrow that I don't think are right angles. So let's get my snap-lock bag angle checker and let's just take a little bit of a look. So I'm going to use the other corner of my snap-lock bag. I'm going to have a look at, first of all, this bottom corner down here.

[The speaker aligns the corner of the snap-lock bag with the lower left-hand corner of the stem of the arrow.]

### Speaker

Now, I'm looking at that one and that is a right angle down the bottom there. But they're not the ones that I'm worried about. I think that these three angles up here. They don't look like right angles to me.

[The speaker outlines the triangular tip of the arrow with her finger.]

When we lay our snap-lock bag down... on the arrow, what I can see is all this space here that's not filled in.

[The speaker aligns the corner of the snap-lock bag with the lower left-hand tip of the triangle. She uses a light-blue texter to colour the blank area between the edge of the snap-lock bag and the edge of the triangle.]

And that tells me that this angle is not a right angle. And I know that an angle less than a right angle is an acute angle.

[Using her finger the speaker outlines the lower left-hand tip of the triangle.]

So the tip of the arrow over here, definitely not a right angle.

So, now that I know it's not a right angle, I know that this can't be a regular polygon. What is the word to describe a shape that's not a regular polygon? Yeah, that's right. It's an irregular polygon. Or we could even call it an irregular heptagon because we know that it's got seven sides.

[Text on a blue background reads: Over to you to cut up some sponges using the features of regular and irregular polygons. How many sides and angles will your shape have when it’s printed?]

Over to you to cut up some sponges using the features of regular and irregular polygons. How many sides and angles will your shape have when it's printed?

[ 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]

## Watch

Watch Sponge art transformations Stage 3 part 2 video (9:24).

Create a sponge print by rotating, reflecting and translating.

### Transcript of Sponge art transformations Stage 3 part 2 video

[Text on a blue background reads: Let’s create! In the top left hand corner, smaller text reads: NSW Department of Education.]

#### Speaker

Are you ready to get creative, mathematicians?

[Two pieces of paper sit next to each other arranged vertically. In the middle of the left-hand piece of paper a square painted is painted in mustard paint, with a blue arrow above it, painting upwards. To the left are a yellow bowl with mustard paint and a small, square, yellow sponge in it, and an orange bowl with blue paint and a green sponge cut in the shape of an arrow in it.]

How can I make a really interesting design using my arrow? So, I'm gonna get some more paint on my arrow.

[The speaker aligns the green, arrow-shaped sponge with the arrow printed on the paper.]

Now, I started with my arrow up the top here. But what I think I'm gonna do today is I'm going to rotate my arrow a quarter turn and I'm going to print it down here.

[The speaker moves the sponge so it is now pointing out from the right-hand edge of the square. She presses the sponge into the paper and removes it, revealing a blue arrow.]

Now, I think there's another word I can use to describe my quarter turn, and a word that I can use to describe that is I can say that I rotated my shape 90 degrees. Now, I wondered if I could use my a little bit messy snap lock bag here to see whether I have rotated my arrow 90 degrees.

[The speaker holds up a clear snap-lock bag with traces of paint smudged on it.]

#### Speaker

So, I'm just gonna take it off. Oh, here we go. And when I put it in, looking at the tips of my arrows, I can see my right angle there.

[The speaker arranges the snap-lock bag so that the left-hand edge passes through the centre of the upper triangle and the lower edge passes through the middle of the arrow on the right.]

And that means that I rotated my arrow 90 degrees to the right.

[The speaker discards the snap-lock bag.]

Now, look what happens when we rotate our arrow 90 degrees. It actually changes the way that the arrow is represented.

[The speaker points to the arrow on the right.]

So, the arrow was vertical here.

[The speaker draws a line through the top arrow with her finger.]

But now that I've rotated my arrow 90 degrees, it's now a horizontal arrow.

Let's try again down below. So, let's get a bit of paint. Not too much here. And I'm going to rotate my arrow another 90 degrees, or another quarter turn, and place it down.

[The speaker dips the sponge in the blue paint and hovers it over the arrow on the right. She then moves it around the square to face downwards. She presses the sponge in and removes it, revealing a blue arrow.]

And look, now my arrow's facing straight down. So, I know that my top and bottom arrow are facing in a vertical direction straight up and down.

[Using her finger the speaker gestures in a line between the arrows facing upwards and downwards.]

#### Speaker

So, what do you think's going to happen when I turn my arrow another quarter turn?

[The speaker dips the sponge in the blue paint and hovers it over the arrow facing downwards. She then moves it around the square to face the left. She presses the sponge in and removes it, revealing a blue arrow.]

Let's try. Oh, there we go. Another quarter turn. What was that word we used to describe the way the arrow is now laying? Yeah. It's now on the horizontal line.

[Using her finger the speaker gestures in a line between the arrows facing left and right.]

Look at that. So, by rotating my arrow at 90 degrees, I went from vertical to horizontal, horizontal to vertical, and then back to horizontal again.

[The speaker points to the upwards facing arrow, the right-hand facing arrow, the downward facing arrow, and the left-hand facing arrow.]

I was thinking to myself though, as I moved my arrow around, does it change the properties of the shape? Does my shape still have seven sides? Does it still have seven angles? Well, let's check.

[The view moves closer to the shapes printed on the paper.]

My arrow, I can still see seven sides. I say three down the bottom, two across the middle, and two at the tip.

[The speaker outlines the arrow on the right-hand side with her finger. A red line appears where she has traced, outlining the arrow.]

#### Speaker

I can also see my right angle down the bottom here.

[The speaker holds the edge of the snap-lock bag in line with the base of the arrow. Two adjacent red lines appear within the red outline of the triangle, aligning with the base of the arrow to create two small squares.]

And I can also see my acute angle that I found at the top using my snap lock bag.

[The speaker aligns the side of the snap-lock bag with the base of the head of the arrow. Red curves appear between each of the angles created by the head of the arrow, one between each tip of the triangle, and two around the angles created by the adjacent lines joining the base of the arrow and the triangular head. The pattern disappears and re-appears on the upwards facing arrow.]

So, I know that even though I've rotated my arrow from a vertical to a horizontal arrow, I can keep rotating it but the properties will still stay the same.

[The red arrow shape with the lines representing the angles within it moves around and aligns itself with the arrow on the right. The red disappears and the view reverts back to normal.]

#### Speaker

Let's see what happens when we reflect our arrow.

The red I wonder if it will change from a vertical to horizontal line then. I think I'm gonna do... I might even put a square in the middle because that's kind of the design I've been going with.

[The speaker dips the square sponge in yellow paint and presses it into the page beneath the downward facing arow. She removes it, revealing a yellow square.]

Alright. So, let's have a look at what happened. So, I'm gonna place my arrow down here and I'm gonna start with it being on the horizontal line.

[The speaker dips the arrow-shaped sponge in the blue paint and presses it into the paper facing out from the right-hand edge of the newly painted square.]

So, what do you think is going to happen when I reflect my arrow? Just make sure I've got paint on both sides for the reflecting part. Do another print because I didn't make that print enough.

[The speaker re-dips the sponge in the blue paint and presses it down in the same place, filling in the arrow shape.]

So, what do you think will happen when I reflect my arrow? Can you predict? Let's have a look. Lift it up and reflect it over.

[The speaker lifts the sponge and presses it into the paper facing outwards from the left edge of the square.]

Can you tell what line my arrow is going to end up on?

[The speaker lifts the sponge, revealing a blue arrow.]

Yeah, look at that. A reflection makes my arrow just face in the other direction on that same horizontal line. I'm gonna repeat that same movement up here.

[The speaker prints a yellow square above the upward facing arrow near the top of the page.]

Keep my wrapping paper design happening. But this time, I'm gonna try it the other way. So, I'm gonna press down my arrow over here, and I am going to reflect.

[The speaker prints a blue arrow facing outwards from the left edge of the square. She then prints an arrow facing outwards from the right-hand edge of the square.]

Whoopsie, over the top. And there we see it again, my arrow, oops, my arrow is staying on that horizontal line.

[Using her finger the speaker gestures in a line between the arrows facing left and right.]

#### Speaker

What if I reflected my arrow going along the vertical line? Where would it end up then? Let's see. Put that there. Print it down.

[Using the yellow sponge, the speaker prints a yellow square at the tip of the arrow facing outwards from the left edge of the yellow square in the middle of the page.]

Alright, make sure I've got paint on both sides of my arrow for my reflection.

[Above the square, the speaker prints a blue arrow facing upwards.]

Print my arrow, lift it up, reflect it over. Oh, when I reflect my arrow from this position, it ends up on the same vertical line.

[The speaker lifts the sponge and prints an arrow facing the opposite direction on the opposite side of the square.]

So, when I rotated my arrow using a 90-degree turn, the arrow changes direction from vertical to horizontal.

[The speaker gestures to the upwards facing arrow and then the right-hand facing arrow surround the central yellow square.]

But when I reflect my arrow, it stays on the same line, so it stays either vertically represented or horizontally.

[The speaker gestures In a straight line with her finger between the left and right-hand facing arrows around the central square and then the upward and downward facing arrows around the square on the left of the page.]

I wonder what would happen if I translate my arrow.

So, let's try translating our arrow this time. Push it down.

[The speaker prints a yellow square in the lower left-hand corner of the blank page on the right-hand side.]

Use the square first as my starting point, because that just helps me see.

[The speaker prints a blue arrow facing upwards from the upper edge of the square.]

#### Speaker

Alright, so there's my arrow, and I'm gonna pick it up and translate it along my vertical line and look what happens.

[The speaker prints another arrow above the previous arrow.]

It stays the same when I translate it. I can fit one more in, look at that. The arrow's pointing straight up my vertical line.

[The speaker prints two more arrows in the same line, coming to the top of the page.]

Wonder what happens when we use the horizontal line. Let's start over here.

[The speaker prints a yellow square on the right-hand edge of the page a few centimetres below the top of the page.]

Do you think the same thing will happen? So, I put my arrow down and let's translate it along.

[The speaker prints a blue arrow facing outwards from the left-hand edge of the square. She then prints another along the same line.]

Look at that.

[The speaker gestures with her finger in a line across the page from left to right.]

When I translate my arrow in this direction, it stays on the horizontal line. So, I look at that, mathematicians.

[The speaker gestures with her hand to the first group of shapes she printed. She points to the upwards facing arrow, then the arrow facing to the right.]

#### Speaker

When I started with my vertical arrow and turned it 90 degrees, it actually ended up being a horizontal arrow. And then when I turned it another 90 degrees as well, it went back to that vertical line.

[The speaker gestures with her finger in a line up and down the middle of the page.]

Then when I reflected my arrow, it stayed as a horizontal arrow, just facing the other direction.

[The speaker points to both of the arrows facing left and right on either side of the yellow square at the bottom of the page on the left.]

It happened here with my vertical arrows, too.

[The speaker points to the arrows facing up and down on either side of the yellow square printed on the left side of the page.]

I've got one pointing upwards and the other pointing in the opposite direction. But they're still on that vertical line. Then we played around with the translation of the arrow.

[The speaker uses her finger to draw a line through the line of upwards facing arrows on the page on the right.]

They all ended up staying in the same direction, following the vertical or horizontal lines.

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

What's some of the mathematics?

[Text on a white background reads: When we rotated our vertical arrow 90 degrees, we noticed that it changed from being a vertical arrow to a horizontal arrow. We also found that when we rotated the arrow it didn’t change the properties of the shape it was still an irregular heptagon, just facing a different direction.

Beneath this text is an image of the original yellow square in the centre of the page, with four blue arrows facing out from each of it’s edges.]

#### Speaker

When we rotated our vertical arrow 90 degrees, we noticed that it changed from being a vertical arrow to a horizontal arrow. We also found that when we rotated the arrow, it didn't change properties of the shape. It was still an irregular heptagon, just facing a different direction.

[Text on a white background reads: We also noticed that when we reflected the arrow it ended up facing the opposite direction, on the same horizontal or vertical line.

Beneath this text is an image of a printed yellow square with a printed blue arrow facing outwards from it’s left and right edges.

Beneath this, more text reads: But when we translated the arrow it stayed facing the same direction.

Beneath this text is an image of the piece of paper on the right, with a yellow square printed in the bottom left-hand corner and 4 arrows in a line pointing outwards from it’s top, and two arrows facing outwards from the left side of a yellow square printed on the right-hand edge of the page near the top.]

We also noticed that when we reflected the arrow, it ended up facing the opposite direction on the same horizontal or vertical line. But when we translated the arrow, it stayed facing the same direction.

[Text on a blue background reads: Over to you to investigate what’s the same and different as you rotate, reflect and translate your sponges.]

Over to you to investigate what's the same and different as you rotate, reflect, and translate your sponges. Have fun getting creative as you design your own wrapping paper.

[ 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

• Ask an adult for some help to cut up some sponges using the features of regular and irregular polygons. Also get them to help you put some different coloured paints in bowls.

• Let's make some wrapping paper!

• Use 2 sponges to print shapes on your paper.

• How many sides does your shape have when it's printed and how many angles?

## Let's investigate

What's the same and different as you rotate, reflect and translate your sponge to create prints?