What kind of angle is MORE than 0° but LESS than 90°?

Shape and symmetry: To investigate angles within shapes

Key Stage 2

Maths

2-D Shape and Symmetry

What kind of angle is MORE than 90° but LESS than 180°

Which answer is the closest estimate for the following angle?

﻿Well done for making it back. Glad you're here. We've got a couple more sessions to go until we get to the end of our exciting first few introductory sessions to angles and a shape. You're going to need some equipment today. You'll need your pencil and your ruler, something to work on, and somewhere quiet with no distractions. So if you are in a room where you can't move, because it's full of or garden gnomes, maybe move somewhere else where they're not going to get in the way. So here's our agenda for today. We're going to be looking at our knowledge quiz Well, you've already done that so well done. We're going to move on in a second to our key learning and vocabulary. So number sequences and rules, then we're going to recap on angles. We're going to focus again on acute and obtuse angles and look at them in shapes. And then we're going to have a go at, an activity that I'd like to call sometimes, always, never. And I'll explain that a little more. And I've got a final knowledge quiz to see what you've remembered. So should we move on to looking at our key learning for today? Our key learning today is to identify angles within shapes. So instead of just looking at them on line's where two lines meet. We're looking at them within a shape. And we started to do that in our last session or the session before that as well, where we were looking for right angles. Our key vocabulary then are angle, degree, acute, obtuse, right angle, order, compare, 90 degrees, and 180 degrees. Brilliant. All right. Well, we're going to start by looking at these number sequences and your task is to find the missing numbers and then be able to express what the rule is. Now, before we've done it, where we've just filled in the numbers. What I'd like you to do now is be able to put into words what the rule is. So let's have a look at this first one together. Now I've got my first one here for you. Where I simply worked out, that looks 25. Then I had a gap 35. Then I had a gap 45. Then I had a gap. I had to figure out what was happening here. Now it made sense to me that if I'm increasing by 10 in between the black numbers, the numbers in between that must also be increasing by 10. However, they also need to be halfway between the two black numbers. So I knew that it just made sense to me thinking about my five times table, 25, 30, 35, 40, 45 and 50. And that way I know I'm adding five every time. So your job is to work out the missing numbers and figure out that rule. Now remember, and I've said this to you before, when we're looking at number sequences, one of the most important things is the gaps in between, okay? The gaps in between the numbers really help you understand what's happening in that sequence. So here is your table of number sequences, have a go. And rejoin us when you're finished. And coming back in five, four, three, two, and one, here we are let's move on ahead then and see how you did here are the answers. So the first one we don't need to cover again, because we'd already talked about that. I gave you that answer. So having a look here, our second one, we were adding two every time. And if I wasn't sure I would have said, okay, 104, I add two gives me 106, but then the next number I had was 112. So I had to just check it 106 to see if there were enough spaces in the 108, 110 Now that follows that pattern. So adding two every time. Here, this was trickier because it wasn't a whole number we're taking away 0.2 every time. Here we're adding threes. Here you should have noticed with your Eagle eyes that we are 2000, 1000, 502. We're going down by halving, It's getting smaller. So the last one, let's check here 62.5. We could also have called that. What if we do use a fraction in there What else could we have called it? Yeah, we could have called it 62 1/2 it's the same. Then we were subtracting 12 each time and then this one we would doubling. Okay, well done. Let's move on. So let's just recap on the type of angles we have. I'll give you a few seconds just to have a look at that information in front of you. All right. Shall we go through again? I try to catch you up the other time when I didn't tell you what an acute angle was more than, but now you've got that in front of you. And actually I'm sure a lot of you didn't get caught up by that at all that was just my attempt. And you scuppered my plans. You were too clever for me. So an acute angle is an angle which measures more than zero, but less than 90 degrees. And we know that 90 degrees can also be called a right angle. And a right angle measures exactly 90 degrees. It's right on the mark, it's 90 degrees. An angle which measures more than 90 degrees, but less than 180. Yep that's an obtuse angle. And then I've touched on this briefly, a straight line or a straight angle is an angle, which measures exactly 180 degrees. So here's a question for you. If a right angle is 90 degrees, how many right angles make a straight angle? Yeah, two. If I were to draw a straight line, let me see if I can manage to draw a straight line shall we. If I were to draw a straight line up here, it was almost straight, not bad. I can see that I've got on this side, 90 degrees and also 90 degrees. So a straight angle is made up of two, right angles. Just 90 times two gives me 180. And if, I didn't know, 90 times two, I could do nine times two and then make it 10 times bigger, because both of these numbers are 10 times bigger. 180 degrees, okay pretty straightforward. Yeah. So really quickly have a look at these, name them. Name the acute angles, name the obtuse angles and name the right angles. And if you want to be super efficient with your right angles, you would mark them off in the correct way. Remember most often, and I'll do it on this one here. Most often when we're looking at angles, we'll see them marked off in that way. But how is a right angle marked off differently? Because it does look different. So give it a go, have a look at those and fill them in. Three, two, one and-- hello we're back. So should we take a look at the answers then? So we had our right angle, we had an obtuse. Obtuse because it's a bigger than 90, less than 180. And acute angle because it's less than 90 and so on. Just check on over those answers and hopefully on your right angles, you would have done something like this. Just to make them really clear. Now, right angles don't always face in the same direction. Any angle can face in any direction. Don't let that trick you. Done? Brilliant. So let's move on to our main task. I don't really need to go over too much in terms of the learning, because we've done it so many times. Now we know what each of those types of angles are. So today we're looking at something I had to call sometimes, always, never. Is it sometimes true? Is it always true? Is it never true? So let's take a look. Let's start with this one. A four sided shape has four, right angles. First of all, bonus points. If you can remind me what we call a four sided shape. Yeah. It's a quadrilateral. Those every quadrilateral have four right angles? Well, you're going to have a go at proving or disproving. So is it sometimes true? Is it always true? Is it never true? Now if I said never, I know I'm wrong because a four sided shape, for example, that has four right angles, oh a square. So I know that I can't say it's never true. What about if I did a four sided shape It's not a square this time, yours are going to be much neater than mine. This is old person trying to use technology here. There's my four sided shape. Imagine the lines are perfect all along. Oh, look, there's another one with four right angles. But are there some shapes that don't have four right angles, but do have four sides, so you'll have a go at that. And then underneath you'll tell me sometimes true. Always true or never true, you can just write, sometimes, always, or never. Think the same for each, a triangle cannot have two obtuse angles. Is that sometimes true? Is it always true? Is that never true? A five-sided shape does not have any acute angles. Sometimes true, always true, or never true. I'm going to be breaking it down. Okay. We're going to do a few at a time. So have a look and think, how can I prove or disprove what the activity is telling me? And you're going to draw your proof, into these grids here. Give it a go and come back when you're ready. Getting there? Fabulous. Let's move ahead then shall we and see. So, I've given a couple of examples here. First of all, let's start with this one. A triangle cannot have two obtuse angles. Well, I struggled with this one because I couldn't get any obtuse angles here. I've got an acute, an acute, an acute angle. I've got a right angle here and an acute, an acute, I could have had one with an obtuse angle, so for example, let me see if I can draw. Imagine this is perfectly drawn. And then I would draw a line between these. This is why rulers are important. This here is an obtuse angle, but these two would be acute. So if I'm saying a triangle cannot have two obtuse angles, I think that's always true. If I had two angles, bigger than 90 degrees, my triangle would never close, so this is always true. A triangle cannot have two obtuse angles. And when we look more later about how many degrees are in certain shapes, this will make more sense. A five sided shape does not have any acute angles sometimes true, always true or never true. Well, look here one, two, three, four, five sides and look, an acute angle and an acute angle. However, I can draw five sided shapes that don't have acute angles, A regular pentagon. Think about that one. This is irregular because you can see that the sides are all slightly different lengths, it's an irregular pentagon. But this is sometimes true. Four-sided shape has four, right angles. Sometimes, always or never. While I know a square does, but this trapezium and this parallelogram doesn't. So again, sometimes there are other four-sided shapes that aren't regular, that wouldn't have right angles. It might have one right angle, it might have two, but it doesn't have to have four. Not every four sided shape needs to have four right angles. And you can experiment with that. See how many different four-sided shapes you can do and see how many of them have less than four right angles. It's quite an interesting little investigation to do actually, so maybe go ahead and do that. So now you've got the idea of what it is that you need to do. Let's move on and have a look at some more statements. We have three more statements here. A rectangle has four, right angles. Sometimes true, always true, never true. And the keyword that we're looking at here is rectangle. A four sided shape cannot have four obtuse angles. Is that sometimes true? Is that always true? Is that never true? And an octagon only has obtuse angles. Sometimes, always, never true. So again, think to yourself, how can I prove what I'm saying? If I think it's never true how can I prove that? What diagrams can I use? What images can I use to prove and back myself up. Coming back in three, two, one, let's go. Let's see how we did this time. So a rectangle has four, right angles. Well, we know that a rectangle is either a square or an oblong and let's look one, two, three, four. One, two, three, four. So in this case, a rectangle has four right angles. That is always true. These are the only two rectangles we have. A four sided shape cannot have four obtuse angles. Now I struggled with this because look, one right angle, an obtuse angle, an obtuse angle, and then one, two, three, four sides. And look, it's just, I can't make it meet. If I close those in, they would no longer be obtuse angles. So I struggled with this. How about you? So I think it's either sometimes true or never. Something for you to investigate now. And you decide, can you prove whether it is sometimes true or never true? That's up to you. And then we had another one. An octagon only has obtuse angles. Now I'm being sneaky again. And that's not like me to be sneaky is it? But I haven't told you whether it was regular or irregular. Well, in this case, I've drawn in irregular one because remember irregular means that all the sides are slightly different. This one is definitely irregular, but it has got one, two, three, four, five, six, seven, eight sides. Here's an obtuse angle, here's an obtuse angle, but I'm there. This one, this one and this one, are all acute. So an octagon only has obtuse angles. Sometimes true. If you looked at the regular octagon, you might see that that is different to this. You might see that you only have obtuse angles. Give it a look. So main task part three. Three more things to prove or disprove. A pentagon cannot have three acute angles. Acute angles are what kind of angle? What can you tell me about an acute angle? It is-- Yes less than 90 degrees. All regular shapes with more than four sides only have obtuse angles, will see. A triangle only has acute angles. Well, if you think back to question one, from the first part of the main task, we've actually gone towards proving or disproving that anyway. So let's get back. Take a look If you need to. Remember, we're looking for proof of what you think. My coming back in three, two and one. So here we go. This is not regular it's irregular. And this is a pentagon the one I know, because the Pentagon has how many sides? Yeah, it has five. So one, two, three, four, five sides. A Pentagon cannot have three acute angles. Well, no. One, two, three. There are some pentagons that don't have the three. So this is sometimes true. All regular shapes with more than four sides only have obtuse angles. Well, look, these are examples of regular. Can you see how this regular pentagon is very different to the irregular pentagon? Okay. But you see how it's regular because it's kind of following a uniform look, all the sides are the same, all the angles are the same and they are all obtuse. These do look like right angles but trust me, they're not. All, look, these are all obtuse angles, obtuse angles. So I would say that this is always true. And then a triangle only has acute angles. Well, look here. We've got a pesky one. That's not acute and neither is this. So this is sometimes true. Now, I have a challenge for you, that's not on here, but I'm giving you a challenge. I wonder if you can think of some statements based on angles to do with shapes that you could get somebody else to prove or disprove. So you might say does every four sided shape have-- or are all the angles in a seven sided shape always-- whatever you could think of, you can go away and investigate some more and challenge some people around you. So before we move on and close up for today, very well done.

Shape and symmetry: To investigate angles within shapes

Shape and symmetry: To investigate angles within shapes

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UnitMaths / 2-D Shape and Symmetry

Maths