# Exploring triangles

ES1 – A thinking mathematically targeted teaching opportunity exploring triangles and their different representations as well as defining their properties

## 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-2DS-01

## Collect resources

You will need:

• a snap lock bag, cling wrap or plastic bag

• paint or marker

• paint brush

• paper

• tissues.

## Watch

Watch Exploring triangles video (8:59). This video was created with Kelly from Keiraville PS.

Investigate features of collected triangles.

### Transcript of Exploring triangles video

[White text on a navy-blue background reads ‘Exploring triangles’. Small white text at the bottom reads ‘NSW Mathematics Strategy Professional Learning team (NSWMS PL team). In the bottom right corner, the NSW Government red ‘waratah’ logo.]

### Speaker

Let's explore triangles.

[A blue text on white header reads ‘You will need…’ Three bullet points below (as read by speaker). On the right, in a still colour image, sheets of white paper, tissues, purple, green and pink thick marker pens and a small Ziplock plastic bag.’ ]

### Speaker

For this activity, you will need paint, a paintbrush and paper, tissues and a snap-lock bag. Let's play!

[White text on a light blue background reads ‘Let’s play!’]

### Speaker

Hello, mathematicians! I hope you're ready for some more mathematical fun today because we are going to be exploring shapes together. In fact, today we are going to get our brains sweaty by playing with some triangles.

Now, I bet you know a lot of things about triangles and their features. And do you know what? I went on a hunt around my house and I've taken some photos of some triangles that I found.

[A person places a sheet of paper down on a white tabletop. On the paper is a colour image of a corn chip, a coat-hanger and a slice of watermelon.’]

### Speaker

Here they are. Can you believe that I found this triangle hiding in my wardrobe? Now I know that this coat hanger has a triangle inside of it because I can see 1, 2 and 3 sides. Let's trace that over and you can count with me and check.

[A blue marker pen is used to trace around the inside of the coat hanger image.]

### Speaker

1, 2, and 3. The feature that we've just described is the number of sides this triangle has. Let's write that down here. '3 sides.'

Now, do you know where else I found a triangle? Hiding in my pantry in the kitchen. Have a look at this corn chip. This corn chip also has the same number of sides. Let's count them together as I trace over them.

[A blue marker pen is used to trace around the outside of the corn chip.]

### Speaker

1, 2, 3. The corn chip also has 3 sides just like the triangle inside of my coat hanger. Oh, mathematicians! I've noticed something. I can count the number of sides like this. 1, 2, 3. Or I could start up here and count the number of sides. 1, 2, 3. Or I could even start over here and count the sides like this. 1, 2, 3. And guess what? It's the same number of sides each time. Let's record that down. ‘3 sides.'

Now, the last triangle that I found hiding was actually hiding in my fridge in this delicious piece of watermelon. But I'm noticing something that's a little bit different about a piece of watermelon when we compare it to the corn chip. Do you notice how the corn chip has 3 straight lines, but the watermelon has 1 straight line, 2 straight lines, and then it has a curved line down the bottom?

Now, because of that curved line, my piece of watermelon like this isn't a triangle. But do you know what? I've just had a thought. I'm going to cut this piece of the watermelon off because when we think about it, we don't actually eat that green part, do we?

[A pink-handled pair of scissors is used to cut through the bottom of the watermelon image.]

### Speaker

There we go. Now we'll be able to really count the sides of the watermelon that I would be eating. I'll trace and you count along with me. 1, 2, 3.

[A blue marker pen is used to trace around the outside of the watermelon image. ‘3 sides’ is also written alongside it.]

### Speaker

Oh, look at that. The piece of watermelon also has ‘3 sides’.

Now, mathematicians, are you noticing what I'm noticing? We have 3 different sized triangles, but they're all still triangles. I could describe the corn chip as a tall triangle. I could describe the coat hanger triangle as long and skinny. And I could describe the watermelon triangle as being smaller. But the feature that each of these shapes has in common is that they have the same number of sides. We've discovered that triangles...have 3 sides.

[A blue marker pen is used to write ‘Triangles have 3 sides’ on the sheet of paper. A blank sheet of white paper then replaces it on the desktop.]

### Speaker

I've got an idea. Now what I'm thinking, or what I'm wondering, really, is that if triangles have three sides like we just discovered, well, what happens if that triangle moves or changes its position? Let's explore that further. For this part, I'm using a lunch bag. Sometimes you might take your sandwich in one of these, or you might have a snack at school in one.

Now I'm using some paint, mine are in a pen, but you might have some paint at home. And I'm going to use what I know about triangles, that they have three sides and I'm going to paint on a triangle to my lunch bag like this. 1, 2, and 3.

[The thick purple marker pen is used to draw a triangle onto the Ziplock plastic bag. It is then coloured in.]

### Speaker

Make sure that my shape is closed. Now, if I colour this here, or paint it in really, I should say, like this, can you guess what my favourite colour is? That's right. It's purple. Then I can do something really cool. I'm going to print my triangle down like this. And rub, rub, rub, rub, rub.

[The Ziplock bag is turned over and pressed down onto a white sheet of paper. The bag is removed and a purple imprint of the triangle is left behind on the paper.]

### Speaker

And when I peel it off, look, I have a triangle. How cool is that? Now, let's check. Does our triangle have 3 sides? 1, 2, 3. We could go in the opposite direction. 1, 2, 3. Yes, our triangle has three sides.

[A blue marker pen is used to write ‘3 sides’ alongside the purple triangle.]

### Speaker

But what happens if we use this triangle and then we use our mathematical imagination? And let's imagine that this triangle has turned. Now, if we put some more paint on and we use our mathematical imagination and we imagine that our triangle is turning, and then look rub, rub, rub.

[The Ziplock bag is turned clockwise 90-degrees and a second purple triangle imprint is made on the sheet of white paper to the right of the first print.]

### Speaker

Like this, even though our triangle has changed position, is it still a triangle? We'll need to check. 1, 2, 3 sides. Yes, this is a triangle as well. Oh, let's imagine this time, Need to put some more paint on our triangle.

That's it, 1, 2… and there's my third side. Oops. I can see I'm colouring with my paint outside of the lines, oh my goodness!

Now let's imagine with our clever mathematician, mathematical imagination, and think about the triangle moving in a different direction. Our triangle started like this, then it rolled like this. Well, what happens if it keeps turning and ends up like this? Let's see.

[The Ziplock bag is rotated so the purple triangle is upside down compared to its original position.]

### Speaker

Place it down, rub it over…pull it off, oh, my goodness! Now, let's check if this one is a triangle. Oh, 1, 2, 3. It still has three sides!

Wow! Even though our triangle started in this position, we turned it into this position, and finished it in this position, we know that by using the number of sides, we can describe each of these triangles as triangles.

### Speaker

Let's look at what some of the mathematics is in this activity.

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

[A blue text header on a white background reads ‘What’s (some of) the mathematics?’ Two bullet points below (as read by speaker). On the right, two colour images of the corn chip, coat hanger and watermelon in one image and the rotated purple triangle imprints in the other.]

### Speaker

Triangles can look different and be described differently, but because they have the same features of 3 sides and 3 corners, we name them all as triangles. We noticed that when we printed the triangles in different orientations by turning them, we know they are still triangles because they still have 3 sides and 3 corners, even when they are upside down.

Now it's over to you mathematicians to see what triangles you can find around your home and explore what happens when you paint and turn them.

[White text on blue reads ‘Over to you!’]

[The NSW Government waratah logo turns briefly in the middle of various circles coloured blue, red, white and black. A copyright symbol and small blue text below it reads ‘State of New South Wales (Department of Education), 2021.’]

[End of transcript]

## Instructions

• Collect assorted triangles from around your house. Remember to ask permission before using natural materials.

• Trace around the triangles on a piece of paper, checking that they have three sides.

• Draw a small triangle like the ones you have traced around on the snap lock bag.

• Colour over the triangle using a marker or paint.

• Turn the snap lock bag over and make a print on your piece of paper by rubbing over the paint.

• Put some more paint on your triangle.

• Flip over the snap lock bag and turn your triangle so it is in different orientations and make another print.

• Keep printing your triangle in different orientations.

## Discuss/reflect

• Find some other shapes in your house to trace around and print.

• Describe to someone what the shapes look like when you print them in different orientations.