Lesson video

Hello there.

My name is Mr. Goldie and welcome to today's maths lesson.

And here is the learning outcome for today's lesson.

I can recognise right angles and describe what happens when they are joined at a point.

And here are the keywords, for today's lesson.

I'm going to say the keywords, can you repeat them back? So the keywords are, at a point.

Let's take a look at what that means.

A point is an exact location.

It has no size, only position.

And here's our lesson outline.

So in the first part of the lesson, we're going to be joining right angles, and in the second part we're going to be completing shapes by joining right angles.

Let's get started.

In this lesson you will meet Aisha and Laura who are going to be helping you with your maths and introducing you to some tricky puzzles as well.

Aisha is investigating shapes with right angles.

A square has four right angles, two squares can be joined at the point, Aisha draws a point on one of the right angles of that square and she joins two squares together, at that point.

"The two right angles connect together to make a straight line," says Laura.

"Four right angles join together perfectly.

They make one full turn." So here's another square joined at the same point and here's another square, also joined together at the same point.

Can you see there, a full turn is equal to four right angles.

"The four smaller squares fit together to make a larger square," says Laura.

So the four smaller squares create a larger square.

Aisha chooses a different rectangle next.

So this time she's chosen a rectangle that isn't a square.

"Any rectangle has four right angles.

I can join together any of them around a point." There are the four right angles on the rectangle and there is the point on one of the right angles.

Aisha is going to join four rectangles together around that point.

So here it's another rectangle, here is another one and here's another one.

So each rectangle is joined around the point using one of its right angles.

Four right angles joined together perfectly to make one full turn.

A full turn is equal to four right angles.

Now you can try that for yourself.

You can stand up and turn four right angles.

So start by facing in one direction, turn a right angle, turn another right angle, turn another right angle, and then turn one more right angle.

And you should end up facing in the same direction as when you started.

"The four smaller rectangles fit together to make a larger rectangle," says Laura.

So we've got four smaller rectangles and in this case they fit together to make one larger rectangle.

What other patterns could the rectangles make? How else could you join them together around the point using one right angle from each rectangle.

"Join together four of the right angles around a point." You could have a go at trying to draw four rectangles or actually take four rectangles and join them together at their right angles and see what different shapes you can make.

Pause the video and see what you can come up with.

And welcome back.

Now here are some possible answers.

You may have joined the rectangles together in a very similar way to these.

So you could have joined them up like this.

Here's one rectangle, here's another, here's another, and here's another.

So you could have actually made this shape here.

Instead, you could have joined 'em up this way.

So well done if you came up with either of those or a different pattern of your own.

Well done.

Aisha investigates a triangle next.

"This triangle has a right angle," says Aisha.

So here is the right angle on the triangle.

It is a right angle triangle.

"I'm going to add more triangles by joining them together by their right angles around a point." Now only one vertex on this triangle is a right angle.

Aisha has to make sure she joins 'em at the point using the right angle on the triangle.

Here is the point.

So Aisha starts with this triangle.

She adds another triangle.

Another triangle, and one more to complete the shape.

"Four right angles join together to make a full turn," says Laura.

"The four triangles fit together to make a square." Now it doesn't matter what shape the polygon is, if you join four right angles around a point, you only need four shapes, for one complete turn.

Aisha investigates a different triangle.

This triangle also has a right angle.

I'm going to fit four triangles together around a point.

You can see the point marked already.

So here is another triangle.

Here is another triangle.

Here is another triangle.

"Oh no!" says Aisha.

"It didn't work.

I've been left with a gap" There's a gap here between these two triangles here.

Why has Aisha been left with a gap in her pattern? Can you work out why Aisha's four triangles do not fit together exactly? Why have they left a gap? Pause the video, see if you can mark out the answer.

And welcome back.

Did you manage to find an answer? Wow, Laura says, "Sorry Aisha, but you didn't join the right angle on the last triangle to complete the pattern." So Aisha did not use the right angle on the triangle to complete the pattern.

She actually joined a different vertex at the point and that vertex was not a right angle, so that's why she's been left with a gap.

Aisha did not join together four right angles.

Now you'll have a chance to investigate with this shape in your task.

And here is task A.

So you're going to choose one of the shapes each time, "Find the right angle or angles within the shape." Now some of the shapes might have just one right angle, some of them might have more than one.

"Join four right angles together.

What new shapes and patterns can you make?" So here are the shapes to cut out, to make patterns.

So choose one of those shapes, work out where one of the right angles is and then put four of those shapes together using the right angles to make one complete turn and see what shapes and patterns you can come up with.

Pause the video and have a go at task A.

And welcome back.

How did you get on? Did you investigate all four shapes? Very well done if you did.

Let's take a look at some of the answers you may have come up with.

So here are some possible answers.

Now if you were looking at shape A, you may have come up with something very, very similar to this because this shape only has one right angle.

If you'll look here at shape B, you may have come up with something like this or something quite different.

And remember where four right angles meet, there is a full turn and no gaps between the shapes.

So if you're joining the shapes by their right angles, you should have one full turn.

Let's take a look at shape C and shape D.

So these are the patterns you may have come up with on those two shapes as well.

And shape C only had one right angle, so you may have come up with something very similar to that.

And Shape D only has one right angle as well.

So your shape should have looked the same as that.

Very well done for having a go at task A and I hope you came up with some really interesting shapes and patterns.

And let's move on to part two of the lesson.

So completing shapes by joining right angles.

Aisha and Laura are using these four shapes.

"Rectangles have four rectangles," says Aisha.

This rectangle here has right angles.

And this rectangle here, which is a square also has four right angles.

"Each triangle has one right angle," says Laura.

So this is a right angle triangle and this is also a right angle triangle and you may have spotted a difference between the two right angle triangles.

One of them has two sides of the same length, the other one does not.

Aisha creates a challenge for Laura, I joined four right angles together around a point," says Aisha.

"Four smaller shapes made this shape, which four shapes did I use?" Aisha has chosen four of those shapes and she's put them together joining right angles around a point and come up with this shape.

She just gives an outline of the four shapes she put together, which four shapes did she use? Laura says, "I need to work out which shapes Aisha used.

I'll start with a square." So Laura's thinking maybe Aisha used a square, first of all.

So Laura puts a square in the shape, then she adds a rectangle.

"Next I've added a rectangle.

This can't be correct as the shapes aren't joined together at right angles." So the two right angles, the shapes here are not meeting.

So Laura has not started that one correctly.

Laura starts again.

This is a really good technique called trial and improvement.

You have a go at trying something.

If it doesn't work, just try again.

And in fact you've learned something from the mistakes you have made.

So "This time," says Laura, "I'll start with a rectangle and add a triangle joining up the rectangles around a point." So here's Laura's rectangle she's used first of all.

She's going to join all the shapes together around this point here.

Start with a triangle next.

Next I'll add another triangle and a rectangle.

Here's a triangle and a rectangle.

Joining the right angles around the point.

So you can see that all four right angles are being joined together around that point.

"Well done, Laura.

Those are the four shapes I joined at right angles." Laura has joined four shapes of right angles and she has completed that shape.

Those four shapes fill up that shape exactly.

Very well done, Laura.

Aisha creates another challenge for Laura.

"I joined four right angles together around a point.

Which four shapes did I use this time?" So Aisha has joined four right angles around a point.

She joined four those shapes together using their right angles.

And this shape here is the shape that she's created using those four shapes.

"The whole shape is not a rectangle.

So I know you didn't only use rectangles," says Laura.

So she may have used rectangles as well, but she definitely just hasn't used rectangles.

"I think you the shape using two of each triangle," says Laura, I'm going to start with the smaller triangle and join the shapes at the point.

So here's one triangle that Laura has put into the shape.

She's going to join them together around this point here.

So all four right angles joined together.

She's going to use one of the larger triangles next and another one of those and then another smaller triangle at the bottom.

So you can see there that Laura has completed that shape.

She's filled that shape using four triangles and each of the triangle joins at its right angle.

"Fantastic! You found the answer quickly," says Aisha.

Aisha has created a challenge for you next.

Here's the outlined shape that she has created using four of those smaller shapes.

Aisha has made this shape.

"I joined four right angles together around a point," says Aisha, "Which four shapes did I use this time?" You may be able to work it out by looking at the problem, might give you a clue as to what shapes Aisha has used or you might have a go trying to draw out the shape and trying to work it out that way.

But pause the video and see if you can work out what four shapes Aisha has used and how she's joined the right angles together to create that whole shape.

And welcome back.

How did you get on? Did you manage to answer that problem? Let's take a look, see whether you got it right.

So Laura says, "Here is the solution to Aisha's challenge." I wonder if you got it right.

There's a square and another square and then one of the larger triangles and another larger triangle.

And you can see there that Aisha has joined those four shapes together around their right angles.

There's a point right in the middle where the four right angles are joined together to create one full turn.

Very well done if you manage to find the solution to Aisha's problem.

Well done.

And let's move on to task B.

Use any four of the smaller shapes to complete the larger shape.

Join four right angles together around a point.

Aisha's giving you a bit of helpful advice here.

She's saying, "Look carefully at the larger shape.

Try out different possible answers until you get it right." So it'd be helpful to actually cut the four shapes out and then see if you can fit them into one of those larger shapes.

Thinking carefully about joining four right angles together around a point.

So here are the shapes you're going to cut out.

So you may wanna cut out lots and lots of different shapes.

Try different shapes out.

Remember the right angles need to fit together to make one full turn.

So pause the video and have a go at task B.

And welcome back.

How did you get on? Did you manage to make all the shapes? Let's take a look at those answers.

So here are the solutions.

You can see in each solution that four of the shapes fit together exactly into that larger shape and that each of them is joined together by one of its rectangles around a point.

Let's take a look at shape A.

To make A, you had to use smaller squares and rectangles.

So there was a larger rectangle you had to make.

So that might have given you a bit of a clue as to what shapes you had to use to make the shape.

Let's have a look at C.

So you can see there again, there's C, there are four right angles joined together at a point in the middle.

To make C, you had to use a mixture of squares and triangles.

The larger shape has some horizontal and diagonal lines, so it cannot be made from only rectangles or triangles.

So very well done, if you came up with some of those different solutions or if you came up with all of them, give yourselves a big pat on the back.

That's brilliant work today.

And hopefully you are feeling confident about joining four right angles together around a point.

And you know that those four right angles together make one full turn.

Very good work today.

Well done.

And let's move on to our lesson summary.

So where four right angles meet, there is a full turn and no gaps between the shapes.

Joining four right angles at a point will always make a full turn.

And a right angle is marked with a small square corner inside the angle.