Lesson video

Check in that you've got your pencil, your ruler, and something to write on, and somewhere quiet with no distractions.

We're going to move on to our key learning and vocabulary moment, with a speedy times tables warm up.

Yay! Times tables! Then, we're going to recap on what we know about triangles and then focus in on equilateral and right angle triangles.

You've got a main activity, which will involve a bit of investigation and some drawing.

And then, a final knowledge quiz to see what you've remembered from our session.

Always excited when I know that we're going to be doing some uh, some speedy times tables.

So, our key learning today then is to identify and classify right angles and equilateral triangles.

And here are our key words: triangle, right angle, equal, equilateral, compare, and 90 degrees.

Wonder why I've put 90 degrees down as one of our bits of key vocabulary today? Well, if you spotted that 90 degrees is also a right angle, and we're also looking at right angle triangles, then, well done to you.

You've got it.

You understood why it's there.

Alright.

So, we are going to start with our speedy times tables challenge.

So, make sure that you are ready.

I know that you're going to be ready for this because I know how quick some of us are becoming with our times tables.

So, make sure you are ready to impress.

Do the ones you find tricky first if you want to challenge yourself.

If you want to get through it in the time, do the ones you know first.

Alright.

So, twos, fives, tens.

Look here, check the easier ones.

Give it a good go.

When you finish, see if you can write down the time it took you, and hopefully, you've been doing that over the last few weeks, and you are getting quicker.

So, your speedy times tables challenge, guys, is just about to start.

Best of luck.

Go! Very well done, everybody.

Hopefully, you got through that.

Would you believe me if I told you I managed it all in 9 seconds? Oh, of course you wouldn't.

It was worth a try.

Alright.

Take a look here at the answers coming up.

Give them a go.

Check through them, and if you made more mistakes, um, just make sure that you highlight that times table so you know to practise it for next time.

I'm sure you're making less and less mistakes every single time.

So, very, very well done to all of you.

Alright.

So, today's learning then.

What is a triangle? I mean I could show you pictures and you'd all go yeah that's a triangle.

I know that's a triangle, but what makes a triangle a triangle? What are the properties of a triangle? Well, a triangle is a polygon, that's a shape, with three edges or sides and three vertices.

Can you remember another word for vertices? I wonder if you can.

I'm going to give you a little clue.

Another word that means the same as vertices Yeah, corner or , um, points.

So, I know it's a triangle if it's got three sides and three vertices, three corners, three angles.

Okay? Now, What about different types of triangles? Remember when we talked about oblong and square and rectangle and how rectangle was the last name? Well, triangle is kind of like the last name of another family.

Triangle is the last name of the tree sided shape family, and there are different types.

Have a look at these ones on your screen now.

What do they have in common? Are they all the same? What's the same? What's different? Now, I'm going to draw your attention to a particular feature: one of the vertices.

I'm going to draw it in on this one.

It should give you a clue.

If I do it like that, what does that tell you about that corner? What do I, what information have I given you there? If you remember, when we mark off a corner or a vertices or an angle like that, it means it is 90 degrees.

And 90 degrees is a, yeah, a right angle.

So, look at these.

What do they all have in common? They all have a right angle in them.

Can you spot them? See if you can spot them before I get through them all.

Got two more.

Beat me! Well done.

They all have right angles in them, so that, therefore, means they are right angle triangles.

Can you believe that? A triangle, with a right angle in it is called a right angle triangle.

Boom, mind blown! That's crazy, right? I'm going to teach you another word that a lot of children don't learn until much later in school, in a few moments, that will help you impress people with your right angle triangle knowledge.

But yeah, a triangle with a right angle in it is a right angle triangle.

Have a look here, though.

These are all equilateral triangles.

Now, in a equilateral triangle, the key bit is the first part of the word.

It sounds like equal.

Equilateral just means that all sides are equal, all angles are equal.

So, if, for example, this was three centimetres long, then it would all be three centimetres long.

And each angle, each one of the vertices in a triangle, that is an equilateral triangle, will measure 60 degrees.

60 degrees, 60 degrees, 60 degrees cause the angles inside a triangle add up to 180.

So, these are all equilateral triangles, no matter which way up they go, which way down they go, if they're sideways.

As long as all the sides and all the vertices are equal, it's an equilateral triangle.

Now, these are all right angle trials triangles.

Now, I'll explain to you why.

If it has a right angle in it, then it is a right angle triangle.

Okay? And here's a really great word for you.

The side opposite the right angle, so this side or this side, has a special name.

The side opposite the right angle in a right angle triangle is called the hypotenuse.

Can you give it a go? Hypotenuse.

Well done.

Not a hippopotamus.

So, if you see a right angle in a triangle, you know it's a right angle triangle.

and then you can say, to someone to really impress them, put on your proper brain here, and you go hmm well I know that the angle that is here is a 90 degree angle that must mean it's a right angle, and the side opposite the right angle is the hypotenuse.

You use that piece of information and you're going to be impressing people left, right, and centre.

So, if all the sides are equal and all the vertices are equal, it's an equilateral triangle, but in this case, and for a right angle triangle, if one side is a right angle, then it is a right angle triangle.

If one angle is a right angle, it's a right angle triangle.

The longest side is always opposite the right angle, and the sides don't all have to be the same length.

So, moving on then.

Have a look here.

Some more dots.

I told you there were going to be more dots today so you are going to be going away dotty eyed again.

Sorry about that.

Now, if you look, you've got lots of dots within a shape.

It's a 6 sided shape.

So, what do you call a 6 sided shape? Yep, it's a hexagon, and it's right there on the page telling you.

And it's a regular hexagon because all the sides, remember, are the same.

All the vertices are the same.

If that's the case, then it is regular.

I wonder how many equilateral triangles you could make inside a regular hexagon.

How many can you fit into one? Now, by that, I don't mean just draw a little one on the inside.

You're going to want to do it with a ruler.

I don't mean that.

Can you do one using one of the sides as one of the sides of your triangle? Okay, so that could be one side.

Where would the others go? How many equilateral, and that's the important bit.

Equilateral, that means all sides are the same.

All sides and vertices are equal.

How many can you make inside one of those hexagons? And then you've managed to work your way through that.

Using now just, what I would suggest is you really visualise it first before you start committing to paper.

Okay.

Give it a go, and just think okay if this is one side where would the others go? I'll give you a clue.

You should end up with a regular kind of pattern.

Now, once you've done that, can you do the same by using right angle triangles? How many can you make inside your regular hexagon this time? Right angle triangles, don't forget, have to have one corner of 90 degrees.

One of the vertices is 90 degrees.

Give it a go.

Hi! Welcome back! Now I'm not going to lie to you, that was tricky.

It could've been quite a tricky task for some of you, and you know what? That's fine.

Don't worry because if you don't make mistakes, you've got nothing to learn from.

So, let me share with you then how could've done it.

Let's start then with the equilateral triangle.

How could you have created equilateral triangles inside your hexagon? Well this is how.

I'm literally just using my middle point and coming outwards to create one, two, three, four, five, six of them.

You could try other ways of doing, but I'm not sure if you manage.

You could've tried some smaller ones for example.

What a dreadful straight line.

There's one.

I could've overlapped and done another one there.

There's two.

Can you do it that way? How many could you fit around? So, one, two, hmm.

Could you try it again? So, if you haven't tried it that way, and you're going to use a ruler, I didn't, and look how awful that looks.

Give it a go, and see if you can do it that way.

For the right angle triangles, this one hurt my head.

Just looking at it hurt my head, but take a look.

You can see here I've started.

There's my right angle.

And there.

And there.

So I've got one, two, three, four, five, six, seven, eight.

Wonder where the rest will go.

There's nine, ten, eleven, and twelve.

So you've started in between some of the dots here.

That one was hard, and there may be another ways of doing that as well.

But I sat staring at this for quite a while thinking how can I do it? How can I do it? And then it just made sense.

All I had to do was split my equilateral triangles and you can see my equilateral with wobbly lines.

You can see my equilateral triangle is there and I just split it in half.

Okay, and that seems to work quite nicely.

Did it hurt your head? Is that tricky? I found that one quite tricky.

We're going to move on though now to our main activity.

So, with our main activity you're going to get two sets of slides to have a go at.

I'm only going to give answers to one of them.

Because the first set of slides, which I'm going to show you right now, is just about exploring.

See, you've got three grids.

On the first grid I'm going to ask you to draw an equilateral triangle with a perimeter of 6.

Now, I've not said 6 centimetres because you might not have anything to measure with, but you can still use the dots.

Okay? On an equilateral triangle what do you know about each side? It needs to be, yeah, the same.

Now, if the perimeter, and remember the perimeter is all the way around the outside If all the way around the outside measures 6, how can I work out what one side is worth? Then you're going to draw a right angle triangle with one side that measures 4 centimetres.

Okay, now the right angle triangles are easy.

Any of those sides can be four.

And then draw and equilateral triangle with a perimeter of 18.

Now, when you've done that, the next part of your activity is this.

Can you split the large pink equilateral triangle into 5 identical equilateral triangles? Is that possible? And then can you split that large equilateral triangle into 6 different triangles? And they don't have to be all equilateral this time.

So give it a go.

Come back when you're ready.

And welcome back! Now, the first one, like I said to you, I'm not going to give you the answers to those first three dotty grids.

That's just for you to explore with.

But let's take a look here shall we? Now, I've managed to split this into 4, but no the original 5 that it asked.

I wonder if you did.

And here I managed to split it into five different rec, uh, triangles.

Okay.

What did you manage? So I've got an equilateral, and I've got a right angle triangle here, a right angle triangle here, and two other types of triangle, which we will be talking about tomorrow.

Here I managed 4 identical equilateral triangles.

One, two, three, and four.

But I couldn't do the five that it originally asked for.

Remember? We wanted 5 here and 6 here.

I've failed, but I wonder if you didn't.

I'm sure you've done a great job and I bet some of you beat me on that one.

Now, very well done.

Last thing that I need to say to you then is you need to, first of all, give yourself a big ole pat on the back cause you've done a great job today.

But, until next time, that's it from me Mr. C.

Goodbye.