• MAO-WM-01
• MA1-DATA-01
• MA1-2DS-01

[A title over a navy-blue background: Making Mandalas. Below the title is text in slightly smaller font: MathXplosion – Go Fly a Kite! Small font text in the lower left-hand corner reads: NSW Mathematics Strategy Professional Learning team (NSWMS PL team). In the lower left-hand corner is the red waratah of the NSW Government logo.]

Speaker

I think this time I'm going to try to flip the peg along the bottom edge.

[She points to the space below the centre peg.]

Aha! Like this.

[She holds the top part of top peg, keeping its bottom part against the centre peg’s bottom part. She lays it down on the sheet. It ends up upside down below the ribbon.]

Now, the top half of my design is the mirror image of the bottom half. That's great.

[She removes the ribbon and joins the bottom parts of each peg.]

I can keep building my design now.

[She picks up some leaves.]

I found these lovely leaves in my garden. Beautiful stripes on one side…

[She flips the leaves.]

…and then they have a purple colour on the back.

[She flips the leaves.]

Now, this is something that I'll really need to think about to make sure that my design stays symmetrical.

[She places the leaves down and picks up the ribbon.]

Speaker

This time, I'm going to be thinking about the line of symmetry that will run…

[She places the ribbon over the 2 pegs.]

…from top to bottom of my design, which means that this half…

[She points to the right side of the ribbon.]

…of my design, needs to match this half…

[She points to the left side of the ribbon.]

…and be that mirror image.

[She picks up a leaf.]

If I place the first leaf down like this…

[She places the leaf diagonally on the right side of the ribbon.]

…on a bit of a diagonal. What I'm noticing is that I have the point…

[She points to the leaf’s outer point.]

…of my leaf facing outwards and I have the stem part…

[She points to the leaf’s other end.]

…of the leaf closest to the yellow pegs.

[She picks up the other leaf.]

This is something that I'm going to need to consider as I place this next leaf, making sure that the stem part…

[She points to the leaf’s stem.]

…of the leaf and the point…

[She points to the leaf’s point.]

…are in the right position.

[She places the leaf over the leaf on the sheet.]

Speaker

I can overlay this leaf to help me think about how to move it. If I flip the leaf along this edge here…

[She points to the left side of the leaves.]

…let's see what happens.

[She turns the leaf over and it ends up on the purple side.]

Oh, that's not quite right, is it? Now I have one side that has a stripy leaf…

[She points to the leaf on the right.]

…and my other side has a purple leaf.

[She points to the leaf on the left.]

It's not quite right. I'll need to think of something different.

[She picks up the leaf on the left and holds it over the other leaf.]

I could try to slide the second leaf.

[She moves the leaf she is holding diagonally down to the left, and places it down over the other side of the ribbon.]

But look what happens now. Even though both sides have that stripy leaf, the point of my leaf is not facing out and the stem part of my leaf is not closest to the yellow pegs. That doesn't work either.

[She picks up the leaf.]

I'll need to think of a different strategy.

[She holds it over the other leaf.]

Speaker

I think this time I'm going to try to turn my leaf in an anti-clockwise direction like this.

[She turns the leaf anti-clockwise until it is diagonally pointing to the top left.]

Oh, great. And look, the pointy part of my leaf is facing out…

[She points to the leaf’s point.]

…and the stem part of my leaf is closest to the yellow peg.

[She points to the leaf’s stem.]

That helped my leaf pop into the right position.

Now, I wonder if you're thinking what I am, this part of my design is starting to make me think of a butterfly. I love butterfly wings because they are symmetrical.

[She picks up more leaves.]

Let's see if I can use these other two leaves to create some butterfly wings in my design.

[She places a leaf diagonally on the right side of the ribbon, below the other leaf.]

I think I'll start by placing this leaf down here on the opposite diagonal. Again, I've got the point of my leaf…

[She points to the leaf’s point.]

…facing out and the stem part of my leaf…

[She points to the leaf’s stem.]

…is facing inward closest to the yellow pegs. Now, I've noticed something about my design.

[She holds a leaf over the leaf she just put down.]

I'll be able to use the same strategy of turning this leaf, but this time I'm going to turn it in a clockwise direction…

[She turns the leaf clockwise until it is diagonally pointing to the bottom left.]

…just like that, until it's in the right space. If I move that…

[She removes the ribbon.]

…out of the way, da da, it looks like I've got a bit of a butterfly mandala design. Now, the next thing I think I'm going to add to my design is some Lego.

[She picks up a brown Lego block.]

Speaker

I've got these little Lego bricks that I found in my drawer. Do you notice how one face of the Lego…

[She points to the round bumps on the Lego.]

…has these circles, these bumps? And if I turn my Lego brick over…

[She turns the Lego over.]

…this side is much more smooth and flat

[She rubs the Lego.]

…and it's just got the four circles.

Again, this is something I'll really need to think about to ensure that my mandala design stays symmetrical.

[She places the Lego on the right side, in between the two leaves.]

I think I'm going to place the Lego brick down here like this. Let's just put it there. That's great. Now, I'll need to be careful…

[She picks up a Lego.]

…and really think about how I can make sure that this same bumpy face is showing upwards over here…

[She points to the space in between the leaves on the left.]

…in this design. Let's see, if I put the brick like this…

[She places the Lego over the other Lego.]

…let's try flipping first.

[She picks up the Lego on top. She points to its short-edge on the left.]

Speaker

If I flip the brick along this edge here.

[She flips the Lego and places it down on the sheet. It ends up with the smooth side up.]

Doesn't look quite right, does it? Are you noticing what I'm noticing?

[She points to the Lego on the right side of the pegs.]

This side, the brick has the bumpy circles.

[She points to the Lego on the left side of the pegs.]

But over on this side of my design, it's not the same. They don't match.

[She picks up the left Lego.]

This part only has the flat circles. So if I was to leave my Lego piece like this…

[She puts the Lego down in between the leaves.]

…my design wouldn't have that line of symmetry…

[She places the ribbon over the 2 pegs.]

…running top to bottom, because this side…

[She points to the left side of the ribbon.]

…is not a mirror image of this side.

[She points to the right side of the ribbon.]

Speaker

I'll need to have another think.

[She places the Lego on the left over the Lego on the right.]

I place the brick back here. I've just had another idea. I can slide it across.

[She picks up the Lego on top and places it directly across over the ribbon.]

Speaker

That way, I know that both sides of my design now have the bumpy part of the Lego piece facing up.

So now my design is symmetrical again. I think I'm almost done…

[She removes the ribbon.]

…but I've found some really cool golden beads in my drawer that I'd like to use.

[She picks up a couple of golden beads.]

Now, something else about symmetry, is that when you add one in…

[She places a golden bead at the end of the leaf in the bottom right.]

…I'll be able to know that my design stays symmetrical…

[She places a golden bead at the end of the leaf in the top right.]

…if each of the points of the leaves for example, if they have a bead just like this. So I have one here…

[She points to the bead on the bottom.]

…one here…

[She points to the bead on the top.]

[She places a white bead at the end of the leaf in the top left.]

…one on this side and one down here.

[She places a golden bead at the end of the leaf in the bottom left.]

That's great. What are you thinking? Oh, I've noticed that as well, something's not quite right. If I use our blue ribbon…

[She places the ribbon over the 2 pegs.]

…and we think about our mathematical imagination, I can see the same thing you can. This side…

[She points to the beads on the right side.]

…I have my gold beads, but on this side…

[She points to the beads on the left side.]

…I have one white bead.

[She points to the bead on the top left.]

Speaker

So they're not the mirror image of each other. I'll need to fix it by using another gold bead like this.

[She replaces the white bead with a gold one.]

Now, this side of my design…

[She points to the right side of the ribbon.]

…is a mirror image of this side.

[She points to the left side of the ribbon.]

And if I use our blue ribbon again…

[She removes the ribbon and places over the 2 Legos.]

…and I change it this way, the top part of my design is a mirror image of the bottom. That's great.

[She removes the ribbon.

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

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

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

· We can use our mathematical imagination to help us explore lines of symmetry.

· We can make symmetrical designs by sliding, flipping and turning materials.

· Mathematicians can describe two-dimensional designs as symmetrical when they have one or more lines of symmetry, which means one side of the design is a mirror image of the other side.

Next to the points is an image of the mandala with 2 leaves, and a dotted line running down over the ribbon. Below this image is another image of the mandala with 4 leaves, a dotted line running down over the pegs and another dotted line running across over the Legos.]

Speaker

We can use our mathematical imagination to help us explore lines of symmetry. We can make symmetrical designs by sliding, flipping and turning materials. Mathematicians can describe two-dimensional designs as symmetrical when they have one or more lines of symmetry, which means one side of the design is a mirror image of the other side.

Now it's over to you to create your own mandalas. I wonder how many lines of symmetry you'll be able to find in your design, or if you can create a design that doesn't have any lines of symmetry. It's time to explore.

[Text over a blue background: Over to you!

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]