Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in this lesson from our unit on "Properties of 2D shapes and symmetry." I'm sure you've met lots of 2D shapes in the past, but we're going to remind ourselves about their names, the properties they have, and maybe introduce a few new ones.

And we're also going to be thinking about symmetry and how we know when a shape or a pattern is symmetrical.

So if you're ready to make a start, let's get going.

In this lesson, we're going to be sorting triangles in different ways based on their properties.

You may have been thinking about triangles recently, maybe you've learned some new names to describe triangles.

We're going to have a think about those, think about the properties of triangles, and we're going to do some sorting.

So if you're ready, let's make a start.

Ooh, lots of different names of triangles we've got in our keywords today, so I'm going to say them and then it'll be your turn.

Are you ready? My turn, equilateral triangle, your turn.

My turn, isosceles triangle, your turn.

My turn, scalene triangle, your turn.

My turn, right-angled triangle, your turn.

Fantastic, what a lot of different sorts of triangles there are.

Let's just check what each of those means, check their definitions because they're going to be really useful to us in our work today.

So an equilateral triangle has three equal sides and three equal angles, and we can show those equal sides using a little dash.

An isosceles triangle has two equal sides and two equal angles, and we can see that those angles are equal because of the little dash.

A scalene triangle has no equal sides and no equal angles, all the sides and angles are different.

And a right-angled triangle is any triangle that has one angle equal to 90 degrees.

We know 90 degrees is a right angle, and we can mark a right angle using a little square in the corner.

So we're gonna listen out for those keywords as we go through our lesson today.

So our lesson has two parts.

In the first part, we're going to be sorting triangles in different ways, and in the second part we're going to be drawing triangles based on their properties.

So let's make a start on part one, and we've got Laura and Jacob working with us today.

So Laura and Jacob are helping each other to remember what they've learned before about triangles.

Laura says, "I'm going to think about what is the same about these three triangles." And Jacob says, "I'm going to think about what is different about these three triangles." You might wanna have a look at that yourselves before Laura and Jacob share their thinking.

So Laura says, "Each triangle has three straight sides.

Each triangle has three vertices." The vertices are the points where the sides meet.

Jacob's looking at these again, he's trying to find out what's different.

He says, "The first triangle has three equal sides, the second triangle has two equal sides, and the third triangle has no equal sides." So the lengths of the sides are different related to each other in each triangle.

Jacob also says, "The third triangle has an obtuse angle," an angle greater than 90 degrees, "but the others only have acute angles." Laura says, "Can you remember the name for each type of triangle?" Can you remember? Jacob remembers the names for these three different types of triangles.

It's an equilateral triangle, an isosceles triangle, and a scalene triangle.

Can you remember what each of those means? The equilateral triangle has three equal sides and three equal angles.

The isosceles triangle has two equal sides and two equal angles.

And the scalene triangle has no equal sides and no equal angles.

Now Jacob and Laura sort these triangles into sets.

They're going to sort them into a set of scalene triangles and a set of isosceles triangles.

Remember to look for those little lines on the sides to show the sides that are equal in length.

So let's have a look and see how they get on.

Jun says, "I remember the scalene triangles have no equal sides." So one, two, three scalene triangles.

Laura says, "I remember the isosceles triangles have two equal sides." And we can see those marks on the remaining triangles so those all must be isosceles triangles, two equal sides and one side different.

Laura says, "What if I had an equilateral triangle to sort?" Where would that go? Ah, shapes that do not fit any of the criteria need to be placed outside of the sets.

So an equilateral triangle wouldn't fit into either of our sorting circles, so it would need to be outside the set.

Time to check your understanding.

Can you sort these triangles into sets? What types of triangles can you see, and how could you sort them so that each triangle fits into one of the sets? You need to name your sets as well here.

So pause the video, have a go.

When you're ready for some feedback, press play.

How did you get on? Well, did you spot that we had some equilateral triangles? There they are.

And we had some scalene triangles.

There they are.

We had no isosceles triangles this time, did we? Well done if you sorted those correctly.

Laura and Jacob cut out some more triangles to sort.

Laura says, "I've noticed something about the angles in these triangles." Jacob says, "These triangles have a right angle.

I'll mark them with a little square." So there we go, each of these triangles has a right angle in it.

Laura says, "I measured the length of each side and marked any equal sides with a line." Ah, so two of them have right angles and two equal sides.

Jacob says, "That means there are two isosceles triangles and two scalene triangles." Isosceles triangles have two sides the same and one different, two angles the same and one different as well.

And scalene triangles have no sides or angles the same.

So got two isosceles and two scalene triangles.

Laura says, "I think these triangles could be described in another way." And Jacob says, "Yes, these are all right-angled triangles." So a triangle that has one right angle can be described as a right-angled triangle.

Now Laura and Jacob sort these triangles into sets as well.

They're going to sort them into scalene triangles and right-angled triangles.

Laura says, "I think all of the triangles go into this set because they all have one right angle." They are all right-angled triangles.

Jacob says, "What about the scalene triangles? Should they go into this set as well?" 'Cause there are two scalene triangles in there as well, aren't there? Ah, so we could put the scalene triangles in there.

Laura says, "I think we need to overlap the sets so that there is a place for right-angled scalene triangles." Ha-ha, so now we've got the two sets overlapping.

So they're all right-angled triangles, but two of them are right-angled scalene triangles.

We could also have had an overlap for right-angled triangles and isosceles triangles, couldn't we? And the other two triangles would've been in the overlap that time.

I wonder what triangle might go in the empty part of the sorting diagram.

And Laura says, "I think you could draw any scalene triangle that does not have a right angle." So there's one and there's another.

So any scalene triangle with no right angle would go in the other side of that circle.

Jacob's done some sorting.

It's time to check your understanding, can you spot his mistake? He sorted his triangles into isosceles triangles and right-angled triangles.

So can you spot his mistake? Pause the video, have a go, and when you're ready for some feedback, press play.

Did you spot his mistake? Ah, that's right.

This triangle is an isosceles triangle and also a right-angled triangle, so it should be in the middle part of the sorting diagram.

There is an isosceles triangle with no right angle, so that's in the right place.

But the other two isosceles triangles also have a right angle, so they are right-angled isosceles triangles.

Time for you to do some practise.

Can you find three different ways to sort these triangles? Label the sets and write the letter of each triangle in the correct part of the sorting diagram each time.

And for question two, read each sentence carefully and decide if it is always true, sometimes true or never true.

And Laura says, "What triangles could you draw to give examples to support some of your answers?" So pause the video, have a go at questions one and two, and when you're ready for some feedback, press play.

How did you get on? So in question one, you were finding three different ways to sort the triangles.

I don't know what you chose, these are the ones we came up with.

So we've sorted into scalene triangles and right-angled triangles.

So F and G are scalene triangles but with no right angles.

A and C are scalene triangles that are also right-angled triangles.

And E is a right-angled triangle but it's not a scalene triangle.

So some of the triangles don't fit into this set.

B, D, H, and I don't fit into those sets.

We haven't got a place just for isosceles triangles or for equilateral triangles.

What about another way to sort? So we could have sorted into right-angled triangles and isosceles triangles.

So the right-angled triangles are A and C.

There's a right-angled isosceles triangle, E, which goes in the overlap.

And then the isosceles triangles are B and H.

So which triangles can we not fit into this sorting diagram? What about our poor old equilateral triangles? They don't have anywhere to go yet, do they? So G is just a scalene triangle, so that doesn't fit.

F is another scalene triangle, that doesn't fit.

And D and I are equilateral triangles and they still don't have anywhere to go in our sorting diagram.

I wonder if we can find them somewhere to go in the last way we sort.

Ah yes, let's sort into equilateral triangles and scalene triangles.

So finally our equilateral triangles, D and I, get to be in a sorting circle.

And what about scalene triangles? Well, A, C, F, and G are all scalene triangles.

We haven't got anything in the middle.

E, B, and H are all isosceles triangles, so they don't fit into this sorting diagram.

Did you find any sorting rules where the middle part was empty? There are no equilateral triangles that are also scalene triangles.

That can't be right, can it? Because we can't have a shape that has all sides the same lengths and all sides different lengths, so there can't ever be anything in the middle there.

So there's no possible shapes for the middle of that final sorting diagram.

I wonder if you came across any of those as well.

And for B, you were deciding whether these statements were always, sometimes, or never true.

So A, "A scalene triangle has a right angle." Well, that's sometimes true.

We can have scalene triangle with a right angle, but we can also have scalene triangles with no right angles.

"An isosceles triangle has a right angle," this is B.

Well, that's also sometimes true.

We can have an isosceles triangle with a right angle, but also we can have isosceles triangles with no right angles.

C, "An equilateral triangle has a right angle." That's never true.

You'll learn more about the angles in triangles later, I'm sure, but try and draw a triangle with three right angles.

I don't think you'll be able to draw a triangle with three right angles.

So for D, "An equilateral has three equal sides." Yes, that's always true.

That is the property of an equilateral triangle, it has three equal sides.

E, "A scalene triangle has two equal angles." That's never true.

The properties of scalene triangle is that they have three unequal sides and three unequal angles, so that's never true.

F, "An isosceles triangle has two equal sides." Yep, that's always true, that's a property of isosceles triangles.

Two of its sides are the same length.

And in G, "A scalene triangle has three acute angles." Well, that's sometimes true.

You can draw a scalene triangle with three acute angles, but you can draw a scalene triangle that has an obtuse angle or a right angle as well.

So that statement is sometimes true.

I hope you enjoyed exploring those and drawing some triangles to justify your decisions.

And on into part two of our lesson, we're going to be drawing triangles based on their properties.

So Jacob and Laura want to practise drawing triangles and they're going to use these pegboards to help them.

You might have some of these pegboards around that are actual pegboards and then you can put elastic bands around them, which is really good fun.

Sometimes you can find those to have a go at on the computer as well, but we are going to draw onto our pegboards on paper.

Laura says, "I can draw an isosceles triangle." And there we go, we can see that two sides are the same because she's skipped one peg and then she's got one side that's longer, that's different.

Jacob says, "I can draw an equilateral triangle and a scalene triangle." There's his equilateral triangle.

We know those sides are equal because he's missed out two dots between his vertices.

And this is a scalene triangle.

There's different numbers of dots between all of those vertices.

Laura and Jacob explore different pegboards.

"What triangles could we draw if we used a square board instead?" says Laura.

Jacob says, "We could use the edges of the squares to create some right-angled triangles." So there's a right-angled triangle, and another one.

And what about that triangle, is that right-angled? Laura says, "We've drawn one scalene triangle and two isosceles triangles." So our first right-angled triangle is a scalene triangle, our second right-angled triangle is isosceles, and we've drawn another isosceles triangle here but it doesn't have a right angle.

Jacob says, "We cannot draw an equilateral triangle using this pegboard." I don't think we can, can we? We can't draw a triangle where all three sides are going to be the same length.

The pegs just aren't positioned in the right way for us to be able to do that.

Time to check your understanding.

Laura and Jacob are going to draw triangles on another pegboard.

Who do you agree with here? Laura says, "It's not possible to draw a right-angled triangle using this pegboard." And Jacob says, "It is possible to draw a right-angled triangle using this pegboard." Who do you agree with? Pause the video, have a think, and when you're ready for some feedback, press play.

So Jacob was right, it is possible to draw a right-angled triangle using this pegboard.

There are lots of points you could connect to create a right angle.

So if we oriented that so that we could see the horizontal and the vertical, that vertex at the top is a right angle.

That one's easier to see, isn't it? We can see the horizontal and the vertical perpendicular lines.

And another one.

So lots of different ways that we could show that Jacob is correct.

We can create right-angled triangles on this pegboard.

Laura has a challenge for Jacob.

She's used matchsticks to make the first side of a triangle.

Jacob's shapes that he makes will not be true triangles because there'll be gaps between the matchsticks and we need straight lines, don't we, with no gaps in them to make a true triangle.

But we're making a representation of a triangle here so they'll be close to a triangle as possible.

Laura's challenge says, "Can you use more matchsticks to create three different types of triangle?" Jacob's going to try and make an equilateral triangle first.

Can you think how many more sticks he's going to need? How many will he need for each side? Now he says, "I know that an equilateral triangle has three equal sides and three equal angles." So he's going to use one, two, three matchsticks to make the second side, and another three matchsticks to make the third side.

So he knows that that is an equilateral triangle.

If the three sides are the same length, the three angles will be the same size as well.

Now he's going to try and make an isosceles triangle.

Can you remember the properties of an isosceles triangle? Jacob says, "I know that an isosceles triangle has two equal sides and two equal angles." So he's removed two of the sticks to make two equal sides of two and then he can sort of bend them in.

Very well done, Jacob.

So he's made an isosceles triangle.

Two sides are the same, one is different, two angles are the same and one is different.

Now Jacob will try to make a scalene triangle.

Can you remember the properties of a scalene triangle? That's right, Jacob says, "If I make all three sides a different length, I will have made a scalene triangle." So he's got rid of one matchstick from one side, so he's got one side that's three matchsticks that Laura gave him, one side that's two, and another side that's only one.

Next, Jacob made this right-angled triangle with the matchsticks.

Time to check your understanding.

Is this a scalene or an isosceles triangle? Think carefully about the properties.

Pause the video and when you're ready for some feedback, press play.

What did you think? Yes, it's an isosceles triangle, isn't it? Because two sides are equal in length and the third side is different.

Two of the sides are made from three matchsticks and the other side is made from four matchsticks.

Well done if you got that right.

And time for you to do some practise.

So we've got some pegboards here.

Can you see that A and B are slightly different? How many different triangles can you draw using these pegboards, and how could you describe each triangle? For question two, one side of a triangle has been drawn.

Use matchsticks or cut-up straws to make the other two sides of a triangle that matches each sentence.

So you're going to make a right-angled scalene triangle, a scalene triangle with no right angle, an equilateral triangle, a right-angled isosceles triangle, and an isosceles triangle with no right angle.

So pause the video, have a go at creating your triangles and thinking hard about their properties, and when you're ready for some feedback, press play.

How did you get on? So here are some of the triangles that you could have drawn on the eight-pin pegboards.

You could have drawn an isosceles triangle, a scalene triangle, a scalene triangle with a right angle, an isosceles triangle with a right angle, an isosceles triangle with no right angle.

The last pegboard is blank because all other triangles drawn will be the same as the five shown but they may be in a different orientation or a different position.

Have a look.

If you managed to draw six, can you find the one that you've repeated? And for B, these are some of the triangles you could have drawn on the seven-pin pegboards.

So we've got an isosceles triangle, a scalene triangle, another isosceles triangle, and another isosceles triangle, any more? Now this time the last two pegboards are blank because all other triangles drawn will be the same as the four shown but maybe in different orientations or positions.

So you couldn't draw as many different triangles on the seven-pin pegboard.

So for question two you're going to construct some triangles from one side given.

So A was a right-angled scalene triangle, so this triangle needs to have three sides that are different lengths but one angle must be a right angle.

So can you see the right angle and can you see that our sides are different lengths? B is a scalene triangle with no right angle.

So we've just moved things a bit, so we've got an obtuse angle this time, so we definitely haven't got a right angle.

An equilateral triangle.

Well, this time we just need to make sure that our other two sides are exactly the same as the side that's been given.

A right-angled isosceles triangle.

Now isosceles triangles have two sides the same and one different, and two angles the same and one different.

If it's a right-angled isosceles triangle, the right angle has to be the one that's different.

I challenge you to draw me a triangle with more than one right angle.

And finally, an isosceles triangle with no right angle.

So there we go, we've made the two sides a little bit shorter so our one different angle is actually an obtuse angle now.

We could have made the two sides longer so that that angle became more acute than a right angle as well.

Your triangles may have looked different but hopefully you had all the right properties.

Well done for exploring those triangles.

And we've come to the end of our lesson where we indeed were exploring, sorting, and classifying triangles.

So what have we learned? You can sort triangles in different ways based on their properties.

Here we've got a sort of some triangles into scalene triangles, right-angled triangles, with our equilateral triangles outside the set because they don't fit into being either scalene or right-angled.

And in the middle you can see we've got some scalene triangles that are also right-angled triangles.

And we've learned in particular that right-angled triangles can be scalene or isosceles.

A right-angled triangle just has to have one angle that is a right angle.

Thank you for all your hard work and your mathematical thinking in this lesson.

I hope I get to work again with you soon, bye-bye.