To Plot Specified Points and Draw Sides to Complete a Given Triangle

Key Stage 2

Maths

Position and Direction

Which letter has the same number for both the x and the y coordinate?

﻿Hello, how are you all? How have you been doing since our last session together? Hopefully, you've been doing really well, and you're happy and you're healthy and you're being kind, but most of all, you are ready for some maths. We're going to be continuing with our Position and Direction this session and we're going to be looking at drawing triangles using coordinates and plotting them onto a grid. So let's talk a little more about that, shall we? But before we do, make sure that you've done our knowledge quiz and then come back when you're ready. Hi guys, welcome back. So, shall we take a look at our facts? Well, I was thinking about something I've missed doing so far this year. I do like in the summer months, spring and summer months actually to get myself off to a theme park and I haven't managed to do that. So I thought I'd have a little root around and find out what I can about some facts relating to some roller coasters and particular rides, and I found this one first of all, to start with this top one here, right up here in this black and white picture, this is a ride called Leap-the-Dips, and it's in Lakemont Park and that's in a place called Altoona in Pennsylvania, and it's the world's oldest roller coaster that is still going. Now don't get too excited because it's average speed is only 10 miles an hour, so it's not the fastest of rides, but it's history is unrivalled by any other because its definitely the oldest. This roller coaster, made of wood, was built in 1902. I wonder if you can figure out how old that ride is. It's the oldest functioning roller coaster in the world. Now I haven't been there and I have to admit, I think I'd be a bit scared of going on something as old as that made out of wood. Maybe I'm just a coward, who knows. Now on the other side, that is 10 miles an hour, there is another roller coaster called the Formula Rossa, which has the title of the fastest roller coaster in the world. Now from the Leap-and-Dips one in Pennsylvania, reaching up to 10 miles an hour, this one can go up to 149.1 miles an hour. Let's call it 150, shall we? That's a bit different, isn't it? 150 miles an hour. And you can see if you look at the track down here, how it's quite a long, straight track here, because is what we call a launch roller coaster, which means it's starts off very, very fast, just like a race car taking off. So if you've ever been to Thorpe Park, or if you've ever been to Alton Towers there are a couple of rides there, there's Rita, Queen of speed, or there is Stealth, that both do the same thing, go super fast to start with, and this is one heck of a feeling. It's a bit different to the feeling you might have on the Dips. In fact, I'll leave the Dips. I'd probably just take a book out and read 10 miles an hour. What's that? Anyway, let's move on. Otherwise, I'm going to just talk about roller coasters all day. So making sure that you've got the equipment you need for today, your pencil, your ruler, your paper for you to work on printouts if you're using them but paper is fine and somewhere quiet to work with no distractions. So the back of a roller coaster, the front of a roller coaster, or underneath the tracks of a roller coaster are probably not the best places to be while you doing today's work. So, here's our agenda. We've done a knowledge quiz. I've waffled at you about a bit of a fact there to do with roller coasters, then we're going to look at our key learning vocabulary in just a second. With our speedy tables, yes, warmup. Coordinates and how we work them out, just a reminder, and then we're going to be looking at plotting coordinates, linking it to triangles with a final knowledge quiz at the end. So, to plot specified points and draw sides to complete a given triangle, that is today's key learning. To plot, specify points, and draw sides to complete a given triangle. Our key vocab then for today, let's practise saying these out loud. My turn, your turn. 2-D. Grid. X axis, you know it. Y axis. Axes. Plot. Vertices. And I want you to tell me another name for the word vertices. What's another meaning? Did you say corners? Did you say angles? Brilliant. Origin. Coordinates, and then some words that we're going to lump together. Scalene, equilateral, isosceles, and right-angled triangle. Brilliant. Remember isosceles not ice sausages. All right, I'm just talking rubbish to you now, I know. So let's just move on with some actual learning instead of me waffling. Speedy times table challenge, you know the score, do it as quick as you can, go for the ones you can't do as easily. I'm going to say do that first. Do the tricky ones first, because you can always make up the time with the easier ones in the end. So let's go for the ones that you know you've needed to practise and really push yourself to beat your last time. Okay. So, give it the best go you can. I'm rooting for you, I know you can beat it, off you go. Welcome back. Did you beat your time? Let's see how you did with your scores. Amazing. Did any of you really push themselves this time and start with the eight times table or the seven times table? I don't know about you, but the sevens, I'm finding tricky at the moment, because with a lot of the others, there are quick ways of remembering them, but the seventh is just a bit of a cheeky one that kind of gets in the way, but if you've got it, you've got it, and you're brilliant. So well done. Let's move ahead. Let's recap then, coordinates, what are they? What do they look like? How do we work them out? Well, as we've said, so far in the last couple of sessions you need that grid, a grid that may look something like this to help you work it out. We've got our hmm axis and our hmm axis. Which is which? X axis, Y axis, and these would have helped you. So the Y axis is vertical, like I don't know why, oh, going to do it like this, look. The tail of the Y goes down. That helps me to remember that that's the axis that goes up and down. The X looks like a cross, a cross goes across and so on. This bit here, remember, what's that called? Everything is at zero. It's the origin I remembered. So, if we had our trapezium here, we need to plot the four corners at these points and joined them up to give the shape. I could be super sneaky now and go, okay, what if I did a little line, straight line, obviously, 'cause that's clearly a straight line from this corner to this corner, I've now created two triangles, okay. I could make it into four triangles. One, two, three, four, okay. I'm just mentioning triangles 'cause that's something we're going to be going over today. So let's do that straight away, shall we. There are, as we already know, four types of triangles that we're focusing in on today and they are equilateral, isosceles, right-angled and scalene. Now I've given you four definitions. Equilateral triangle, they have three equal sides and three equal angles of 60 degrees. Isosceles triangles have two equal sides and two equal angles. Right-angled triangles, one of the angles is the right angle that's 90 degrees and then a scalene triangle, they have no equal sides and no equal angles. Can you match the triangle to the definition? So you could think about drawing lines or just popping a number into each of those triangles. Which one is which? Now, remember, I wonder if you can remember one of the key words that I said to you. It was a real tricky word I gave you a while ago. In a right-angled triangle, the longest side is always opposite the right angle. That long side had a special name. Do you remember it? Think of hippos. Do you remember the word hypotenuse? Yeah. That's the longest side in the right-angled triangle opposite the right angle. Say for me, hypotenuse. Brilliant. Alright, so have a go at matching them to the correct triangle. Shall we find out how you did? Okay, so our equilateral triangle, is this little chappie up at the top. Our isosceles triangle is this one just having two equal sides, up this one and this one are equal and then this angle and also this angle equal. Our right-angled triangle is this one. Here's our right angle. Oh, look, there's our hypotenuse. Great word, I love that word. On our scalene triangle here where none of the angles and none of the sides are the same. Well done if you managed to match those up. Brilliant, start. So have a look here. I'm going to be asking you now to record the coordinates for each of those triangles. Now, just to make it really clear, you're going to have more than one set of coordinates in each of the boxes. So, if you look at the table I've given you, here, you're going to have three sets of coordinates because a triangle has three vertices, okay. So each of them remember, will be separated because they'll all be in their own sets of brackets. Okay, so x,y, x,y, x,y, x,y just to help you. Can you then work them all out. So for example, if I wanted to find this point on triangle A, I've gone one along and eight up. This point is not along, 'cause we stayed on the origin line, zero and nine up to zero nine. So I've got zero nine, one eight. And for this point, one along, 10 up. You don't have to have them in that order as long as you've got all three of the vertices. Give it a go, it's not really that tricky, it just means that you're going to have to make sure you can fit them into the table. Give it a go and I'll see you when you're ready. Shouldn't have been too tricky, right? I think if you'd have been systematic and gone for each triangle, you'd have been fine. So let's take a look at how we did with those answers. Remember, each of them should have three sets of coordinates in each bit of the table, so here they are. Have a look over those answers. Were there any of them that tricked you? I'm wondering if some of you got tricked by that one, that one and that one. Whenever there is a zero involved, it can be a little tricky, but don't worry. What do you notice about all of these triangles by the way? Let me just do this. What do you notice about all of those triangles now? They're all right-angle triangles. So look, we've got one, two, three, four, five, examples of what a hypotenuse is, well done. Okay. So, have a look here, let's just remember what a perfect grid might look like. There are a couple of things missing from this grid. Just spare a few seconds. If I wanted to plot coordinates on here, how is it difficult as it stands? If I say, okay, look, here we are, here's my point. What are the coordinates? Why is that tricky to start with? What is missing? Well, we need, I gave you a little flash forward to help you, axis, don't we, our Y axis and our X axis. We also need a starting point. The starting point remember is the origin, scene zero. I need my numbers, one, two, three, four, five, six, seven, eight, nine, and 10. And don't forget I'll just put X there to remind me, I'll put Y at the top here to remind me. Seven, eight, nine, and 10. Okay. Now don't forget, really important, those numbers go on the line, not in the square in between. They're going to go on the line, okay. So now I've got them. I can work out what the coordinates are for this. I can five along and seven up. So this is now, whereas before I couldn't have said that, that would have been trickier. I could have said, well, just count lines, but what if my grid had started here? And gone along there? Then actually I would have had a very different set of coordinates. So it need to make it very clear, okay. So, here's the task you're going to be looking at, and there are several steps. So task one, you need to create the grid, from zero to 10 for the X axis and the Y axis. Task two, you're going to draw the following triangles. So triangle A, B, C, D, E, and F. And you're going to plot them with those points. That's the first part you're going to do. Now i'd suggest that you do this in stages, do a little bit at a time, okay. So I'm going to leave that on the screen for you now. Have a go and see if you can complete those two tasks. Okay, now hopefully you've had a little time to do that and you've plotted those shapes and that's absolutely brilliant. And then what we're going to do is we're going to have a look at where they'll go in a moment. So let's take a look, shall we, at where they are. These are where you should have had your triangles. Okay. We've labelled our X and our Y axis. They're on there really clearly. Here's our X, here's our Y, and we've numbered them. We've got our origin, and we've plotted the points for each of those triangles. Now that you've got that, I'm going to be asking you to do something else, okay. There is a second part to this activity. I'm going to show that to you now. There are parts three and four now. If there are any equilateral triangles there, you're going to leave them as they are. If you've found any isosceles triangles on the inside of them, just make them stripey. Any scalene triangles are going to make them spotty, and any right-angled triangles you're going to just shade them in. And then we're going to go right back to challenge ourselves. We're going to go right back to when we're doing our angles work, and I'm going to be asking you to mark acute angles with the letter A, right-angles with the square that we would use and obtuse angles with a letter O. Okay. So let me give you an example and I'm going to show you now. So we're going to say, isosceles as a stripey, scalene are spotty. So I'm going to just give you an example here. Let's take a look and see. So I'm going to cast my eyes over that isosceles are stripey, scalene are spotty. Okay, I can see, let's go to this one. This is a scalene triangle. So I'm going to make it spotty and then acute angles, here's an acute angle, acute, obtuse, and labelling my angles to the type. Okay. That's what you now need to do, for the next part of this, so, I remind you of the instructions. I'll pop them upon the screen for you again. Sounds tricky, but it's really not. You can do this. Here are your instructions, give it a go. All good? Brilliant. Let's take a little look, then share some of those answers and just go through some of them together. So I already started you off with our scalene here, our spotty scalene. Isosceles remember, they were stripey. So this one is isosceles, and this one is, 'cause I've got two sides and two angles the same, and so is this one. Our right-angled triangles, we're going to colour in solid, imagine that's a solid colouring, and look, there's our other right-angled triangle, and then we've got, our right angle is here and here. We've got acute, acute, acute, acute. That one is bigger than 90 degrees so it's obtuse. That's an acute one, so is that. Look, these are all acute, and again, and there you go. Now, I am fully aware that that was a bit tricky 'cause it was in a few parts, but actually the hardest bit was the plotting, and I'm sure that's the bit that you all got right. I have faith that you did a great job there. So, you need to now make sure that you've gone back and you've taken our final knowledge quiz and that you're ready to move along. Welcome back guys. Hopefully you did brilliantly in our knowledge quiz, so all this left for me to say today is well done for all of your hard work. It was a slog in our main task, but I'm sure you did an amazing job. So, until next time, that is it for me, Mr. C, so I will see you soon.

To Plot Specified Points and Draw Sides to Complete a Given Triangle

To Plot Specified Points and Draw Sides to Complete a Given Triangle

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UnitMaths / Position and Direction

Maths