Which angle is smaller than a right angle?

Which angle that we have been looking at today is greater than a right angle?

This triangle contains an obtuse angle. True or false?

What type of angles are in this triangle?

To recognise obtuse and acute angles

Key Stage 2

Maths

Angles and shape

In order to indicate that an angle is a right angle, what shape can we draw on the angle?

﻿Hello, year three. Miss Brinkworth here, carrying on your angles work this week with Oak National Academy. So I'm going to share what I'm sure you'll all be interested in hearing, which is what Mickey Mouse had to say about maths. Now, Mickey Mouse had to say that being a good mathematician is about being able to count to 20 without taking your shoes off. I'm sure you've all got a bit further than him, year threes. Okay, let's look at today's learning. So I'm moving on from right angles yesterday and our new terms for today are acute and obtuse. So you're going to understand what those terms mean by the end of the lesson in relation to your other angles work. So let's have a look at what you need today. It's the same as in the previous lesson. So just something to write with, and something to write on, and then that right angle checker. So hopefully you've still got one from yesterday or grab another. It's just a nice sharp corner of a piece of paper or one that you've folded twice to make that corner there. And to check it, put it in the corner of a piece of paper, in the corner of a page of a book, and just check that it fits perfectly, and then you've got a perfect right angle checker. That's going to really help you today. So if you need to pause the video now and go and get those things, please do. And if you haven't had a chance already, pause the video and do the introductory quiz, which is some revision on yesterday's right angles. So that will really help you with today's lesson. Okay, let's start with a little bit of recapping then about right angles, our learning from yesterday. Have a look at this triangle. It's got three angles and one of them is a right angle. Pause the video if you need to. You probably don't need two minutes and have a think about which one of those angles is a right angle? Okay, so we know we talked yesterday about how triangles which have a right angle are called right-angled triangles. They only have one. And in that triangle, it is the largest angle. It is this one down in the bottom right. It is the largest angle. If I use my angle checker, my right angle checker, it would fit perfectly into that corner of the triangle. So, well done if you've got that right. That's the right angle on that right-angled triangle. Okay, let's have a look at our star words today. We haven't got too many today. So I'll say them and then if you could repeat them back, that'd be great. We've got right angle, greater, smaller, acute, obtuse. And those last two, acute and obtuse, are our main focus for today. Don't worry if you're not sure what those words mean yet, you will by the end of the lesson. Okay, so just a quick bit of revision here. An important bit of learning to remember about angles. Now, do right angles or any angles for that matter become bigger or smaller or change at all when they're moved or rotated? Think about your right angle checker. Does that stop being a right angle if it gets bigger? Does it stop being a right angle if it gets smaller? Does it stop being a right angle if I rotate it? No, it doesn't. It carries on being a right angle. The angle has not changed. Remember that the angle is the distance between two lines that intersect at the same point. Just because I make that bigger, or I make it smaller, or I twist it doesn't change that angle. Okay, so that picture that makes that really clear. We had that picture yesterday. Those are all right angles, just at different orientations. So it's a really important thing to remember when you're looking at the angles today, that it's not the orientation of the angle, that means it's not how the angle is positioned, that tells us what it is. It's the distance between the two lines. So just a key bit of learning to bear in mind today, as we move on through our angles work. So having a look at these angles then. We've got three here. So they are either greater than, which means bigger, smaller than, or equal to right angles. So having a look at these three, pause the video here. Decide, is it greater than, smaller than, or equal to right angles? Come back together. Let's have a look. Now, remember when we're measuring angles, that it's the distance between two lines. And when we talked about right angles yesterday, remember our angle arms. The right angle, straight up and straight out is a right angle. So anything smaller than that, can you see one which is smaller than a right angle? Hopefully, you can see that this first angle here on the left is smaller than a right angle. The two lines are closer together than a quarter turn. That one in the middle, hopefully, you can see it's actually greater than a right angle. The lines are further apart from each other. They're wider than a quarter turn. That one is greater than a right angle. And the one on the far right there. Hopefully, you can see. Use your angle checker, it would fit perfectly. Your right angle checker would fit perfectly into that angle, and that's because it is equal to a right angle. It is a right angle. So let me just leave those there for you to have a moment and look at for a moment, 'cause this is our learning for today. We're looking at angles which are smaller than right angles and angles which are greater than right angles. Okay, so let's get on with some vocabulary then. If angles are smaller than right angles, we call them acute. These are our acute angles. So I know an angle is acute because it's smaller than a right angle. And if you can see those three angles down there, they are all acute. If we use our angle arms, right angle straight up and straight out. Acute, closer together, okay. So to make your acute angle, you can either move one arm closer to the other or I can move both my arms close together. So any angle smaller than a right angle is called an acute angle. And here we have some more pictures here to show you. Yeah, if you use your right angle measurer, your right angle checker, it would go over the top of an acute angle. It would be bigger than it. So you can see from that picture there, if I put my right angle checker over an acute angle, it would cover one of the lines. So just take a moment to have a look at that. Because it's smaller than a right angle. Again, there's a right angle with your angle arms. Ones that are smaller than a right angle might look like this. That's our acute angle, smaller than a right angle. Okay, have a look at this picture then. There are two acute angles on this shape. Can you find them? Which two angles are acute? How did you get on? Which two do you think are acute? Which are smaller than right angles? It's this one and this one. These are both smaller than right angles. Okay, so let me move on to these other angles, the ones which are greater than right angles, and we call them obtuse. Angles which are greater than right angles are obtuse. So if you think about our angle arms, if we go back to our right angle again. We would make them bigger. We would take our arms further away from each other. The gap between the two lines would be bigger. So again, we might just move one arm further away, or the other arm further away, or we might move them both further away, and we'd make an angle which is bigger than a right angle. Now just have a look at those three angles at the bottom there. There they are all obtuse. Now right angles are a quarter turn and obtuse sit between a quarter and a half, a quarter and two quarter turns if you're thinking about a clock, okay. After that, so if we think about a right angle as a quarter like this and obtuse we can go all the way down to two quarter turns. Anything further than that is called, anything bigger than that, is called something else. But you only need to know obtuse for now. So between a quarter and two quarters or a quarter and a half, we know that those two are equivalent from last week, is called obtuse. And so for today's lesson, when angles are bigger than a right angle, greater than a right angle, they are obtuse. Okay and if we were to use our right angle checker on obtuse angles, the right angle checker would sit in between them because obtuse angles are bigger than right angles. So an obtuse angle would sit over a right angle because they're bigger. Just having a look at that there. Okay, and finally, if we just compare that with our angle arms here. Hopefully, this is a bit clearer for you. You've got your right angle there with your angle arms. And then these ones here are obtuse angles where the lines of the angle are further apart than a right angle, further apart. The angle is wider. Have a look at that. Okay, so here's a shape. Can you find those two obtuse angles in this shape? Those two angles which are greater than a right angle. Have a go. Which two angles are greater than a right angle on that one? Pause the video if you need to. We've got one here at the top and we've got one here at the top. Hopefully, you can see those other two angles on that shape are smaller than right angles. The two lines at those angles are closer together, but the ones at the top are wider apart. They are obtuse angles. Okay, your turn then here. Have a go at these questions where you need to decide are they smaller than a right angle, so acute? Larger than a right angle, obtuse? Or are they equal to a right angle? Okay, be careful of a few of them where they're very, very close to right angles, b in particular and a, you might want to use your angle checker. You could put it against the screen if you need to. And just think carefully about those angles which are close, close to right angles, if not right angles. So pause the video here and have a go. Which ones do you think are smaller than right angles, which ones are greater than right angles, and which ones are equal to right angles? Okay, so if we come back together, looking at these angles. Like I say, a is quite tricky. If I just look at it, I think it does look quite a lot like a right angle, but I think if I use my angle checker, I can see that a is actually acute. It's clear to see with e that e is an acute angle, smaller than a right angle. But with a, it's a bit harder. So I definitely want to make sure I used my right angle checker on a. Okay, again with question b, which ones are obtuse. It's a bit tricky to see that, although it's clear that d is obtuse I think, wider, the lines are further apart than a right angle. With B, it's a bit trickier to see. So I'd want to use my right angle checker, because b is larger, greater than a right angle. And then that leaves us with those two, the c and f, which are right angles. They're equal to right angles. Now, sometimes we saw in yesterday's lesson that you're given a little box in the corner of a right angle, a square or a box to tell you that it's a right angle. You're not always given that though, so be careful. Okay, we've got the main activity here and it is time for you to pause the video and have a go on your own. Although, I will go through the first question with you. So Part A, it's very similar to the question we just looked at. Which of these is, are they acute, obtuse, or right angle? And it's up to you which order you want to do those in. You might just want to start with question A. You might want to do A, which is A? Or you might want to look at the one that you think are the easiest, one you feel most confident with. I think I'd start with A, and I'd want to get my angle checker out I think, 'cause that one looks quite close to a right angle. But if I do put my angle checker against it, my right angle checker, I'll see that actually it's smaller than a right angle, so that one is acute. So pause the video here and have a go at that main activity on your own, please. Okay, coming back together. Let's have a look at these then. So we talked about A is acute. I think it is quite clear to see that B is acute. It's quite a tight angle. The lines of that angle are quite close together. So I think it's clear to see that B is acute. C, that looks like quite a broad angle, doesn't it? I might want to put my angle checker next to it, but I think I can see that C is obtuse. And D, if I used my angle checker carefully, I can see that is a right angle. Well done if you got those ones right. Out of the angles at the bottom, again, using your angle checker would definitely help here. Which one is obtuse, which one is the largest? Sometimes it's quite easy to see when angles are next to each other and you're being asked to see which one is the largest. It's quite easy to compare when they're next to each other. And hopefully, you could see that that middle one there is the largest, is the obtuse angle, so the lines are furthest apart. Okay, moving on to Part B then. Look at these shapes and decide which different angles they have. So each of the angles on these shapes, what are they? How did you get on? Let's have a look here. So looking at that first shape, we've got all of the angles are the same. They're all identical angles on that shape. And the only angles it has are obtuse. They're all bigger than a right angle, so well done if you worked that out on that shape. That shape has six sides and six corners. It's a hexagon. Looking at the next shape then. This is a bit different. It's got, what's it got? It's got two obtuse angles there in pink, but it's also got an acute angle there down at the bottom, a much tighter angle. You can see that that one where the lines are much closer together. And then at the top of the shape, it's got a right angle. That's a kite, that shape. And then looking at the shape over there, the final shape. It looks a bit like a rectangle, but it's not. It's actually a parallelogram and a parallelogram has those two obtuse angles. Those two larger angles where the lines are further apart and it has, there are two obtuse angles, and it has two acute angles as well. And you can see that on a parallelogram, the opposite angles are equal. Well done. How about this challenge question then? How did you get on? Drawing a shape that has an acute angle, an obtuse angle, and a right angle? Quite a tricky question. Hopefully, you had a go doing some doodles. Having a go at answering that question. Maybe you came up with a shape that looks like this. It's a good idea to sort of start with your right angle. Draw like the corner of a square and then carry on from there. See if you can draw a bigger angle and a tighter angle to get in those obtuse and acute angles. Your shape doesn't need to look exactly like that for you to have got that question right. Okay, well done. Have a go at that final knowledge quiz then and see how you've got on with today's learning. And well done. Hopefully, you feel far more confident now with those terms, acute and obtuse. It fits in with your angle work and I will be back for your next lesson on angles as well. Thank you very much, year threes.

To recognise obtuse and acute angles

To recognise obtuse and acute angles

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UnitMaths / Angles and shape

Maths