Lesson video

Hello, and welcome to today's lesson with me, Ms. on rotation symmetry.

For today's lesson, you'll be needing a paper and a pencil or something you could write on and with.

If you need to pause this video now to just get ready, get yourself into the right head space and get the equipment then please press pause, and when you're sorted, press play to begin the lesson.

Okay.

In today's lesson, you'll be able to define and identify order of rotation of symmetry given shape.

So your first task is for you to try this task.

The first is saying all triangles will look the same when I rotate them three times.

Our second student is saying, not always some triangles don't look the same when you rotate them three times.

Which student do you agree with? And I also want you to explain your choice.

So pause the video now and attempt this task.

Once you're done, press, play to begin again.

Okay.

Two questions I want you to be thinking of as we go through this slide.

First question.

What's his rotational symmetry.

Second question.

What is an order of rotational symmetry? As I play this video, I want you to think about this questions.

I will be talking over the video.

It is very fiddly.

So you do need to pay close attention to what is happening in the video for you to be able to answer these two questions on your screen right now.

So let's press play and watch the video together.

This black dot here is the start of my triangle.

How many times can I rotate the shape before I go back to the start of my triangle and the shape would have exactly the same shape as what I started with.

Okay.

So starting here, that's the black dot and I'm rotating it around.

So at this point, wait for it.

At this point here would be one because I have rotated from here to here once, and I still have the same shape as what I started with.

So that's one.

That will be two.

And that would be three.

That would be two.

And that back to the start would be three.

So I had one, two and back to the start three.

So I've rotated my shape three times.

My shape still kept the exact triangle I started with before I got to the end of my triangle.

So my second shape is a square.

How many orders.

How many times can I rotate the shape and it would still maintain its shape of a square, by the time I get back to the start of my shape? That would be one.

That would be two at the bottom there.

That would be three just on that corner over there, and just making a that would be four.

So right back at where I started from.

So I went through the first corner, second corner, third corner, fourth corner to where I started from.

So my shape took four rotations before I could get back to the start, still keeping the exact shape.

So this is a pentagon, as I mentioned before, the video is very fiddly, so please do pay attention and try not to miss anything.

So now we're looking at how many rotations will this pentagon going through from the start to the end, keeping the same shape.

So we're starting again.

Sorry about that.

So that's the first one.

Second one, third one, fourth and fifth.

Now, having watched that.

What do I mean, or how would you describe rotational symmetry? This is my definition, it could differ from yours.

I've said rotational symmetry is when an object is rotated around the centre point and it appears the same.

So I rotated around the centre point here to a certain number of degrees and it was the same here, it the same here, it was the same here and it was the same here.

Now, what do I mean by order of rotation symmetry? I've said that the number of times a shape can fit exactly onto itself in a complete turn, is called the order of rotation symmetry.

So for this pentagon, how many times did this pentagon fit exactly onto itself in a complete turn? It was five.

Yeah.

Okay.

We said we were going to come back to re-try this task.

So there were two students saying, one student was saying all triangles when rotated, would give me an order of rotational symmetry of three.

And another student was saying, no, I don't think they do it.

So having looked at that simulation on the previous slide, who would you agree with? Do you agree with the student that says, if I rotate any triangle, I would get my original shape three times by the time I returned to my starting point.

Or do you agree with the other student that says not all triangle would give me an order of rotational symmetry of three.

Yes.

It should have been this student, not always some triangles don't.

And I want you to think about which triangles will actually give you or an order of rotational symmetry of one.

Because only equal lateral triangles, give you an order of rotation of three.

But look at this one.

I've got to circle here.

Now we know that a circle has no end and start.

So how many order will be the order of rotational symmetry for a circle.

It's going to be infinity because I don't know where it starts, I don't know where it ends and his circle always fits onto itself exactly.

So it just keeps going on and on and on and on so infinity.

For this one, what is the order of rotational symmetry? I am going to show you a video to illustrate this one.

This right here is what is known as improvisation.

I do not have a tracing paper at my house.

However, I did have a clear sheet So I want to find the order of rotational symmetry for this shape.

And I have just shaded in where I want my starting point to be.

So I am going to be starting from this point here, and I want to work up the order of rotation as symmetry.

So how many times can I turn this, pretend it's a tracing paper.

How many times can I turn this so that it would give me the shape I started with before I get back to my original position? So if I turn it once, that does not give me the shape.

So that not an order of rotational symmetry.

If I turn it twice, that does give me the shape of I started with, so that is one order of rotation, a symmetry.

If I turn it the third time, that doesn't give me the shape I started with, and if I turn it one more time, that does give me the shape I started with.

And we are back to our original position.

You now have your independent task.

So please pause the video now to complete your task.

And once you're done press play so that we can go for the answers together.

Okay.

Let's go for our answers for the first one, write down the order of rotational symmetry for each of the following shapes.

Hopefully you've gotten everything correctly.

If you haven't make sure you correct your work so you can pause the videos to correct your work, if you've made a mistake or carry on playing the video.

Okay.

How many ways can you shade compete squares to create a shape that has rotational symmetry order two? And the answer is 12.

I can't show you everything, but I've just given you one example.

So if I shade in this square and this square, I would get an order of rotational symmetry two.

And b what is the maximum number of squares you can shade so that the shape created has rotational symmetry order two? And that is seven.

That means you can shade in seven squares so that the shape you've created from your shaded in has a rotational order symmetry of two.

And the minimum number of squares you can shade that would give you a rotation order symmetry of two is two.

If we're drawing a four by four square grid, mine isn't perfect, but this is mine.

What is the.

How many ways can you shade complete squares to create a shape that has an orientation order symmetric of two? There are so many ways.

There's no maximum.

There's so many ways you can shade the shape.

You can shade the four by four squares to get a shape that has a rotation order symmetry of two.

And for b what is the maximum number of squares you can shade so that the shape has a rotational symmetry order two 14 and the minimum you can shade is two.

Okay, let's go to your explore task.

For this task, it would probably help if you sketch this dodecagon out on a sheet of paper.

Just so that you can explore with it.

And you explore task is asking you to shade in regions of this regular dodecagon and regular dodecagon has 12 sides to create a pattern with a different order of rotational symmetry.

And the question on the bottom is which of the following orders are possible? So if I shade in a.

If I create a pattern here, would I be able with that pattern to have an order of rotation as mutual five? Any pattern I create, would I be able to have an order of rotational symmetry of five? Would I be able to have an order of rotational symmetry three? What of 11? So your task is to try different method, try different patterns through shaded in and see if you can create an order of rotational symmetry of these number here.

So pause the screen now, and I want you to attempt the task.

If you are struggling with it, then carry on playing this video where I can provide you with more help and support.

Okay.

You, okay.

So I have shaded this bit in one, two, three, four.

Just a random pattern that I've created.

And from this pattern, I want to see the order of rotational assymetry that I can get.

Would I be able to get one, two, three, four, five, six, seven, eight, nine, 10, 11, 12.

What order of rotational symmetry would I be able to get from this shape? Now I did this earlier on and I found that I was able to get an order of rotational symmetry of three.

So your job now is through trial and error, shade in different patterns on this regular dodecagon and see how many order of rotational symmetry you can get, what possible orders of rotational symmetry you can get from shaded in and created a pattern.

Okay.

Hopefully for exploration, you've seen that the only possibilities are orders of one, two, three, four, six, and 12, and these are the factors of 12.

So on a regular dodecagon, you can only get through creating a pattern for shaded in to create a pattern, you can only create patterns that would give you order of rotational symmetry that are factors of 12.

You have not reached the end of today's lesson.

We're done for stay in right through to the end.

This can be quite a challenging topic.

So if there are things you don't quite get, please go back into the video and watch again and do some more practise as well.

And I will see you at the next lesson.