Lesson video

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Hello everybody.

My name is Mr Kelsall and welcome to today's lesson about angles on a straight line and angles around a point.

Now, before we start, you'll need a pen on a piece of paper.

You'll also need a quiet place, somewhere you're not going to be disturbed and don't forget to remove any sort of distractions, perhaps put your mobile phone on silent or move it away completely.

Now, if you'd like to pause the video and then when you're ready, let's press play and let's begin.

So today's lesson is about calculating angles on the line or angles around a point.

We're going to start by looking what angles on a straight line add up to.

When then going to use this information to understand that angles around a point add up to 360 degrees, we're going to look at angles which are vertically opposite to each other.

And at the end, as always, we'll take our quiz.

For today, you will need a pencil and a piece of graph paper.

Our words for today, we're going to recap on right angle, acute, obtuse and reflex angles.

We'll talk about a protractor, baselines, Crosshairs.

We'll talk about the vertex or vertices which are a corner or corners of a shape.

We will look at angles around a point and then we will look of the vertically opposite angles.

Quick recap.

You know that angle is where two lines meet, a turn, refers to a rotation around a point, you can have a full turn 360 degrees, a half turn 180 degrees, or a quarter turn 90 degrees.

Acute angles are less than 90, right angle is 90, obtuse angle is between 90 and 180, straight line is 180 and a reflex angle is between 180 and 360 degrees.

The shapes we'll be talking about are quadrilaterals, pentagons and hexagons, which are four or five and six sided shapes.

So bit of fluency to begin with.

Can you say out loud the following times tables, I'm going to count to five to give you time to do this.

You should have said 90, 180, 270, 360, 450, 540 and so on.

If you didn't say them very fast, go back and practise it, pause the video and take this opportunity to think of your nine times tables and how they help the 90 times tables.

Next one.

Now that you've set these times tables, pause the video and can you think of how these times tables might link to the picture shown? Okay.

I'm hoping that you spotted that 90 is a right angle.

So knowing your 90 times tables is relatively useful.

Your 45 times tables is useful because half of a right angle is 45 degrees.

But where do the 30 and the 15 times tables, I know through 30 times 3 is 90, so I'm thinking is this to do with a third of a right angle? I don't know.

And the 15 times table, if 30 degrees is a third of a right angle, 15 degrees is a sixth of a right angle.

Let's see what happens in the coming slides.

Okay.

Our new learning for today, feel free to stand up and do this if you want, start by turning 90 degrees clockwise, then turn another 90 degrees and another 90 degrees and another 90 degrees.

And can you say how far you've turned or what you've turned? You should have turned a full 360 degrees or a full turn.

Let's use this information.

Ask yourself how many degrees are around a clock? I start here and I go all the way around, I should have turned 360 degrees.

I can check that because that's a right angle, that's a right angle, that's a right angle and that's a right angle.

And if I say my 90 times tables, I say 90, 180, 270, 360.

Okay.

So the question asks us how, how many degrees does the hour hand turn between midday and three o'clock.

Let's imagine if midday is there and three o'clock is there, how many degrees does this turn? Well, we've already worked out that this is a right angle.

And we know that that is 90 degrees.

By the way, is anyone else thinking about how far turn is one o'clock and two o'clock and so on? Well, it's funny you should say that because our next question asks just that.

How many degrees does the hour hand turn between midday and 1:00 p.

m.

? Let's see.

Well, midday is here and 1:00 p.

m.

is here.

Well, I know that this angle here was 90 degrees and how many sections I've got one jump, two jump, three jumps.

So I'm thinking, if I know that this whole is 90 degrees and it splits into three jumps, how much is each one of these jumps? I know that's 90 divided by 3, each jump is 30 degrees.

So I know from between midday and 1:00 p.

m.

it is 30 degrees.

My next question asks us, how many degrees does the hour hand turn between midday and 7:00 p.

m.

? Pause the video and when you're ready, press play to continue.

Okay.

So I'm going to draw on midday, draw on 7:00 p.

m.

and I can count on my 30 times tables, that's a good job we started this to begin with isn't it? 30.

Can you do it with me please? 30, 60, 90, 120, 150, 180, that's a straight line, 210.

So I know this turn from midday to 7:00 p.

m.

is 210 degrees.

So what can you say about the angles made by the hands? Can you find an acute angle and can you find an obtuse angle? Can you find any other angles? Pause the video and when you're ready, press play to continue.

Okay.

So I know here I have an angle greater than right angle.

So I know that this is going to be an obtuse angle.

I also know it's going to be 30, 60, 90, 120 degrees.

If I look at this angle here, I know this is a reflex angle, and I know this is going to be 30, 60, 90, 120, 150, 180, 210, 240 degrees.

So I found an obtuse angle and I found a reflex angle, but I haven't found an acute angle.

So let's apply this same information in a slightly different context.

This time let's have a look in our clock, let's have a look at a compass.

On a compass you've got North, East, South and West.

How many degrees is in each division? We know that that is 90 degrees.

It's a quarter turn, it's a right angle.

So how many degrees are in the next ones, 90, 90, 90.

Okay.

If I stand at East and I turn clockwise to West, how many degrees have I turned? Five seconds.

You should have turned 180 degrees, cause you're going 90 degrees, 180 degrees.

Shall we prove that first bit quite quickly, because this is the next stage of compasses.

When you talk about a turn somewhere between North and East, you call it Northeast.

And the same goes for the other compass points, you use North and South as your starting point and then West and East as your next starting point.

So if I'm looking for an angle or a measurement or turn somewhere between West and South, I would say South West, I wouldn't say West South because I always North and South are the priorities and the second priority is West and East.

So I'd say South West.

Okay.

Question for you.

If I turn from North to Northeast, how many degrees have I turned? Pause the video, have a look through the questions and see if you can answer some of these questions.

When you're ready, press play to continue.

Okay.

Well, I need to use some reasoning here and I know from North to East is a 90 degree turn.

So if my whole thing is 90 degrees and I've got one jump, two jumps, I'm splitting this 90 degrees into two.

So each parts must be 45 degrees.

Cause 45 add 45 makes 90 degrees.

Okay.

So if I stand at Southeast, let's mark Southeast, and I turn clockwise to Southwest, how many degrees have I turned.

Five seconds.

Okay.

Oh, there's two ways to look at this.

I can either measure from here to here and recognise that it's a right angle or I can count in jumps at 45 and I can say 45, 90.

And I got to say 90 degrees a right angle.

Okay.

Let's introduce some language here.

We'll use a stem sentence, I'll demonstrate it and then I'd like you to repeat it.

If I stand at Northeast and turn clockwise to South, how many degrees have I turned? And then I need to find the answer.

Well this time we're going to count in 45s.

45, 90, add on 10 that gives me 100 and there's another 35.

So 135.

So I know if I stand at Northeast and I turn clockwise to South, I have turned 135 degrees.

How many more degrees must I rotate to complete a full turn? Can you count with me, 45, 90, remember that one from before 135, 180.

Now I've got 235, 190, 200, 210, 215.

So 215.

So I know I need to complete a further 215 degrees, for a full turn, okay.

I would like you to pause the video, and I'd like to practise some of the stem sentences on your own.

Say them out loud, make sure you're saying them and then check them afterwards, pause the video and when you're ready, press play to continue.

And the final part of this task, we're going to continue with this stem sentence, but we're going to change to turning an amount of degrees.

So if I stand at Northwest, and turn 90 degrees anticlockwise, where will I be? I know I've got 45, 90 degrees.

And remember this way is anticlockwise.

So I've turned 45 degrees, 90 degrees.

So I'm going to end up at the Southwest.

Okay.

Pause the video, have a go yourself.

So we're now at the develop learning stage of our lesson.

Bit of an investigation for you.

You need to use three facts.

You need to use the fact that a full turn is 360 degrees.

A half turn is 180 degrees.

And a quarter turn is 90 degrees.

Use these facts to find out other facts, try and link them to these angles on the page.

What do you know about these angles? Pause the video and when you're ready, press play to continue.

Well the first angle shows us all that we need to know.

We've got a right angle, which is 90 degrees and another right angle, which adds up to 180 degrees.

And we've got two more right angles there, which add up to 360 degrees.

This angle is exactly the same, apart from it's just rotated around a little bit.

However, angle number three is slightly different because it's split.

Well, I still know that that angle is 180 degrees and that angle is 180 degrees.

Angle number four is similar.

That's still 180 degrees and that's still 180 degrees.

These two angles have just been rotated around.

Now angle number five looks a little bit different than the other angles on the page.

So I know that that angle is 180 degrees, but I've got no idea what this is.

What do you think it is? Well, actually I know that it's still a straight line.

So I know both them angles added together add up to 180 degrees, but at the moment, I don't know either of these angles, but I do know that they add together to give me 180 degrees.

I could use this information.

For example, if I said this angle is 80 degrees, this angle must be 100 degrees because 80 and 100 adds up to 180 degrees.

Similar, if I said this was 70 degrees, what would this angle be? It would be 110 degrees.

And what if that is 60 degrees, this would be 120 degrees.

Fantastic.

Now we come to the final angle here.

Actually, if I look very closely, I've still a straight line there, and I've still got a straight line there.

So I know this adds up to 180 degrees and I can use the same ideas here, here.

Actually I've just noticed as well, that's a straight line too.

Oh, and that's a straight line too.

We're going to learn a little bit more about these angles later on.

They're called vertically opposite angles, but we can find out a lot of information about them just by knowing some facts.

Okay.

Let's extend these ideas a little bit more.

Do we need to mention these angles or can I use some known facts? Let's use the stem sentence.

If I know angles on a straight line, add up to 180 degrees, then I know 120 add on 60 equals 180 degrees.

So I know this missing angle is 60 degrees.

Can you say that? Pause the video press play when you're ready.

Okay.

Let's take that learning a little bit further.

What is this angle here, which is missing? I hope when you saw it's 90 degrees, because I know 90 degrees add on 90 degrees adds up to 180 degrees.

I can use this same information, as long as I recognise that that is a straight line.

So I can think, well, what are these angles add up to? Let's use that stem sentence again.

If I know angles on a straight line, add up to 180 degrees, then I know 135 degrees add on, I need to add 5 to get to 140 and 40 to get to 180.

I need, then I know 45 degrees is the size of the missing angle.

Using this same stem sentence and if you need do calculations, see if you can work out the missing angles.

When you're ready, press play to continue.

Okay.

So if I start with this angle here, this time I've got three angles.

I know two of them, add up to 110 degrees, so the other one must add up to 70 degrees, because 110 add 70 makes 180.

For this angle here, I know 100, if I know 140 add 40 makes 180, then I know my missing angle is 40 degrees.

And finally I can use the same information here.

Remember I am adding a five, so I've got to add on five.

Takes me to 120, 130, 140, 150, 160, 170, 180.

So I can add on a further 65 degrees.

Okay.

Here's some questions for you to have a go at.

Pause the video, and when you're ready, press play to continue.

Okay.

Now we're going to expand this learning.

This time, I'm going to use the fact that angles around a point add up to 360 degrees.

So if I look at my first angle, all these angles add up to 360 degrees.

While these two angles add up to 270 degrees.

Which means I need to add a further 90 degrees to get to 360 degrees.

My angles here, 50 add 150 is 200.

Which means I need to add another 160 to get to 360 degrees.

This angle here, I need to add 90 add 135, that is 225.

And i need to count it up to 360.

So 225 add five is 230.

Another 100 is 330 add 30 is 360.

So I've got my 5, my 100 and my 30.

So it's 135 degrees.

Pause the video and see if you can do the last question on your own.

You should have worked out that the angles add up to 305 degrees.

Which means the missing angle is 55 degrees.

And the final part of our developing learning is to do with vertically opposite angles.

Now, I can either tell you that this is 50 degrees and you can believe me.

Or I can prove it to you.

Because I know that these two angles create a straight line.

So 50, add 130, makes 180 degrees.

I also know these two angles sit on a straight line.

So 130 add 50 makes 180.

I know these two lines sit on a straight line.

Use this information, to see if you can answer the other two questions on the page.

You should have worked out that this angle is 100 degrees and this angle is 80 degrees.

And this angle is also 80 degrees.

This angle is 75 degrees.

Which means that this angle is 105 and 105.

This time I'd like you to create questions, using the pictures.

You've seen all of these pictures in the lesson so far.

Pause the video, and try and create some of your own questions.

See if you can test them on somebody, and see if you can find the answers for yourself.

Pause the video, and now when you're ready, press play to continue.

And before we go, please complete the quiz.

So, that brings us to the end of today's lesson on angles on a straight line and angles around a point.

A really big well done for all the fantastic learning that you've achieved.

Now, before you finish, perhaps you'd quickly like to review your notes and identify the most important part of your learning from today.

Well, other than that, all that I have to say is thank you.

Take care.

And enjoy the rest of your learning for today.