2 truths 1 lie (2D shapes)

This is a thinking mathematically targeted teaching opportunity to explore and reason about the features of some 2D shapes.

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

Outcomes

  • MAO-WM-01
  • MAE-2DS-01
  • MAE-2DS-02
  • MAO-WM-01
  • MA1-2DS-01
  • MA1-2DS-02

Collect resources

You will need:

  • paper
  • pencils or markers
  • a small sticky square to investigate.


Watch

Watch 2 truths 1 lie (2D shapes) part 1 video (2:15).

Prove which statements are true using mathematical reasoning.

[Text over a navy-blue background: 2 truths. 1 lie. 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

Two truths, one lie…

[A title on a white background reads: You will need…
Bullet points below read:

  • eyeballs and brains
  • something to write on and write with
  • a small sticky square to investigate.

Next to the last bullet point are 2 red squares. The square on the right has its corner turned up so it looks like a diamond.]

Speaker

..for this task, you will need your eyeballs and brains, something to write on and write with and if you have a small sticky square to investigate.

[Text over a navy-blue background: Let’s explore!]

Speaker

Let's explore.

[A large white sheet divided into 3 columns. The first column has a blue shape with text below that reads squares have 4 equal sides. The second column has a yellow shape with text below that reads diamond. The last column has a pink shape with text below that reads triangle.]

Speaker

Hello, mathematicians, I've got a challenge for you today. It's called two truths, one lie, I've got three statements here, two of them are true and one is a lie. Let's have a look at them, my first statement is squares have four equal sides…

[The speaker points to the text in the first column.]

Speaker

..my second statement is this shape here…

[She traces the yellow shape in the middle column.]

Speaker

..is a diamond and my third statement is…

[She points to the pink shape in the last column.]

Speaker

..this is a triangle. Now, have a look at those three statements, which one do you think is the lie?

And well, let's work through the first statement. Squares are four equal sides, the first part of that is that squares have four sides. So, let's say squares have four equal size, I want to start here…

[She places a finger just outside the left side of the blue shape in the first column.]

Speaker

..and I'll place my finger here, so I remember where I started…

[She points to the left side of the shape, then the top side, then the right and bottom.]

Speaker

..one, two, three, four.

[She takes her hands away.]

Speaker

Now, you maybe already knew that squares have four sides but are they equal? I’ve got some cubes here…

[She places two red cubes near the top right corner of the shape.]

Speaker

..they called unifix, and I'm going to use these to measure the size of this square.

[She lays some unifix across the top of the shape, snapping them together as she goes.]

Speaker

OK, let's see, one, two, three, four.

[She leaves the assembled unifix against the top of the shape.]

Speaker

So, the length of the top side is four unifix. Let's see what the length of the bottom is…

[She picks up the unifix.]

Speaker

..is it four unit fixed?

[She places the unifix against the bottom of the shape.]

Speaker

Yes.

[She picks up the unifix and places it against the right side of the shape.]

Speaker

The length of the right is four unifix…

[She picks up the unifix and places it against the left side of the shape.]

Speaker

..and the length of the left is also four unifix. So I've just proven that squares have four equal sides.

[Text over a navy-blue background: Over to you! Which statement is true and which is a lie?

Below the text is an image of a section of the sheet. The first column shows a yellow shape with text below that reads diamond. The second column shows a pink shape with text below that reads triangle.]

Speaker

Now over to you. Which statement is true and which is a lie? Is the yellow shape a diamond? Is the pink shape a triangle? Which is true and which is the lie?

[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

Can you help Barbara figure out which of the statements are true and which one is a lie?

  • Squares have 4 equal sides.

  • This shape is a diamond.

  • This shape is a triangle.

Image: Which statement is true?

Watch

Watch 2 truths 1 lie (2D shapes) part 2 video (2:50).

Explore solutions to statements using mathematical reasoning.

[A large white sheet of paper divided into 3 columns. The first column has a blue square with text below that reads squares have 4 equal sides. The second column has a yellow shape with text below that reads diamond. The last column has a pink shape, with text below that reads triangle.]

Speaker

How did you go? Now, we've proven that the first statement is true, so I'm just going to write true here

[The speaker writes ‘true’ in the first column, under the text.]

Speaker

Which means that one of these must be a lie.

[She points to the middle and last columns.]

Speaker

Do you think that this is the lie…

[She points to the yellow shape in the middle column.]

Speaker

..that that is in fact not a diamond? Or do you think that this is the lie…

[She points to the pink shape in the last column.]

Speaker

..that that is not actually a triangle? OK, so, I want to show you something that I think might make you change your mind if you think that this is true. Remember how we said that squares have four equal sides, and I use my unifix here to measure them.

[She places an assembled unifix of 4 cubes next the right side of the square in the first column.]

Speaker

Each side was four unifix long.

[She places the unifix against the top of the square.]

Speaker

That's right.

[She places the unifix against the left side of the square, then the bottom.]

Speaker

Now looking at this shape, it also looks like there might be four equal sides. Let's test that out.

[She places the unifix against the bottom right side of the shape.]

Speaker

One, yep, that side is four unifix long…

[She places the unifix against the top right side of the shape.]

Speaker

..this side is four unifix long…

[She places the unifix against the top left side of the shape.]

Speaker

..this side is four unifix long.

[She places the unifix against the bottom left side of the shape.]

Speaker

And this side is four unifix long. So it looks like that shape here also has four equal sides. Now I'm gonna show you something amazing, are you ready?

[She picks up the yellow shape in the middle column and turns it slightly to the right.]

Speaker

Ta da. Yeah, it's a square. It was just on its point and we're used to seeing squares resting on their sides, but it's still a square.

[She picks up the yellow shape in the middle column and turns it slightly to the left, three times.]

Speaker

So this is a square, this is a square, and this is a square. In fact, they're the same sized square.

[She picks up the yellow square and places it on top of the blue square in the first column.]

Speaker

OK, so that means that this statement here, that this is a diamond…

[She points to the middle column.]

Speaker

..is a lie.

[She writes ‘lie’ in the middle column under the text.]

Speaker

Now let's go to the last statement. That is a triangle. Now, we are very used to seeing triangles like this.

[She picks up the pink shape in the last column and turns it slightly to the left.]

Speaker

Also on their side. Sometimes they might look like this…

[She picks up the pink shape in the last column and turns it slightly to the right.]

Speaker

..but that's the way that we're used to seeing triangles.

[She picks up the pink shape in the last column and turns it slightly to the right, with its point facing down.]

Speaker

But in the same way that this is a square that just happens to be on its point, this is a triangle and this is a triangle…

[She picks up the triangle and turns it slightly to the left with its point facing right and its left side completely straight.]

Speaker

..and even diagonally.

[She turns the triangle so that its right point faces the top right corner of the sheet.]

Speaker

So this statement here is true.

[She writes ‘true’ in the third column under the text.

Text over a navy-blue background: What's (some of) the mathematics?

A title on a white background reads: What's (some of) the mathematics?
A bullet point below reads:

· The orientation of a shape does not change it. For example, a square on its point is still a square.

Below the point are 2 red squares. The square on the right has its corner turned up so it looks like a diamond.]

Speaker

What's some of the mathematics? The orientation of a shape does not change it. For example, a square on its point is still a square. We're used to seeing squares resting on their side, but changing the orientation, rotating the shape, doesn't change what it is.

[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]


Discuss

  • Create your own '2 truths. 1 lie.' problem and challenge a friend, family member or classmate to solve it!

Return to top of page Back to top