To Describe Movement Between Positions as Translations of a Given Unit Left/Right or Up/Down 1

Key Stage 2

Maths

Position and Direction

﻿Hello, it's me, Mr. C. Good day to you, how are you all? Hope you're ready to get on with our learning today. It's another great session we've got ahead. So let's get cracking, shall we? We're going to be looking again at position and direction, but today we're looking at something called "translation," so it's a little different, but it will all become clear. I'm going to be looking at describing movements between positions as a translation of a given unit left, right, up, and down. It will make sense, it's not tricky. So make sure that this has happened first, that you've taken our Knowledge Quiz to start with. And I have a little treat in store for you today, and you'll see that in a moment when we look at our agenda. Welcome back. Okay, well, here's a little riddle for you to start with. Can you work out what number parking space this car is in? And you'd be surprised how many people get this wrong. Have a little look and see if you can figure it out. I'm going to give you five seconds. Four, three, two, and one. Shall we take a look, then? I wonder if you fell into the trap. I'm going to say look at it a different way, from the way that the driver would see it. Do you have a different answer now? Yeah, a lot of people do get this wrong. I wonder if you can remember what that answer was. Take a look. 16, 6, 68, 88, something and 98. So maybe we'll get this wrong. There's no pattern, right? But then when we look at it in terms of being the driver, we've got 86, something, 88, 89, 90, 91. So it must have been ... 87. Simple, but effective little trick. All right. You're going to need your pencil, ruler, something to work on, and somewhere quiet with no distractions, so probably not the middle of a car park. Okay. You'll notice something's different about our agenda today. Something a little different from usual, but look, we've got our knowledge quiz, which you've done. Our key learning and vocab is coming up, then the secret value warm up. We tried one of these a few sessions ago, and I'll recap on how we do it together in a moment. Then we've got an introduction to translation of points, our main translation activity, and translation challenge. And then we're done! Hmm. Something's missing. We'll see. All right. So here we are, this is our key learning. It's quite a mouthful, so just listen carefully. It is to describe movements between positions as translations of a given unit to the left, right, up, or down. Our key vocab then, today, are translate, position, unit, direction, grid, quadrant, X axis, Y axis, and then this always makes me think of computer games. Up, down, left, right. I want to shout fire at the end. Up, down, left, right. Brilliant! So. Here we are with our "To Start." Now you recognise this I'm sure. It's not the same as the last time around, the values are different, so take a look. We have four symbols, a heart, a cross, a star, and a triangle. Each picture is worth a slightly different value. So the heart is different to the cross, which is different to the star, which is different to the triangle. But for each row, going across here, we've been given a total. For each row, we've got a total. Okay. Which one do you think would make most sense to start with? So I'm going to double tick the row that I think you should start with. There's a reason. You've got four of the same. Four lots of this make 36. Four lots of mm make 36. Four times mm makes 36. That's your starting point, have a go at the task, and when you come back, we'll go over. So, start with the double tick row, good luck! How did you do? Was it okay? Let's take a look then. Here are my answers, and I'm going to explain how I worked them out. I think that probably makes most sense. Okay. So. Let's have a look. I said start with this row, because there were four of the same thing. So four lots of this make 36. Four times mm makes 36. Four times mm equals 36. I know that it's four times nine. So now I'm going to write in nine on all of my green crosses, just to make sure it helps. So that helps me with one more row now. I'm going to look at this row next. Nine and nine, so how many have I got all together? Yep. 18. I've got 18 after the 32. What do I need to add to 18 to make 32? Yep, 14. 14 is now important because I have two of these that make 14. Two times what makes 14? Yeah, seven. So now I'm going to write in seven right next to it. Seven, for all of my hearts. So now I'm going to look at this row. Seven and seven is 14. I need 30. What do I add to 14 to make 30? Yeah. I need to add 16 to it to make 30. Two lots of stars makes 16, so two lots of something is 16. Two lots of what is 16? Yeah, eight. So I've got seven and eight that gets me to 15. What are you going to need to add to 15 to make 27? I needed to add 12. That's my key number. So this and this makes 12. Well they're both the same, so two lots of what make 12? 6! Brilliant. Always start with the easiest bit and fill in the missing information as you go. Hopefully, that made sense. All right. Well let's take a look at what we're looking at today. We're looking today at translation. And translation has a couple of meanings. It's not like in language where it means you go from one language to another. But in math it means you're going from one place to another. If that makes sense to you. So it means that you simply move a shape or a point from one position to another on a grid. So let's look at this one here. Imagine I've started here and I've picked it up and I've put it down there. I've not made it bigger or smaller, so I didn't resize it, it stayed the same size. I didn't twist it or turn it so I didn't rotate it. It's still facing the same direction. I just moved it. I just picked it up and put it down. Nothing else has changed. We started here and finished there. Now the movement from here to here is called the translation. Okay? So how can we say that it's moved. Well. Let's just look at one point at a time instead of looking at a shape. Imagine we started with point A, and we translated it, we moved it to point B. So this is where it was, and this is where it is now. This is our start, and this is where we finish. Okay, so this is the important one. That's where it all ends. Now we can describe how it's moved by saying how it's travelled along the x axis and the y axis. All ties in with coordinates here, so how's it gone along and how's it gone up or down. So we would work out the translation by starting on point A, counting along until we got to the position under point B, and then count up. So along, and up. So we've gone along the corridor up the stairs, up from point A to point B. And that's it, we just need to count. That many along and that many up. That's it. So how does that help us? Well. First, we can say we've moved four places along the x axis. One, two, three, four. And we've moved places up the y axis. One, two. So four along, two up. So we're writing in the same way as coordinates. This point has been translated four, two. Four along, two up. Four places right, two places up. And that's how we would write it. What do you know? Really easy, right? Now, that's one of the beauties of things like coordinates and translations. Everything ties up so nice and neatly. So now that you know that, let's work through this one together. Have a look. Which axis did we always count along first, the x or the y? Mm-hmm , so let's mark an x axis, y axis. We start here, and we finish here. So how have I got from here to there? How many along? How many up? We just need to count. Let's see if you're right. Try working it out yourself first. So I want the x axis and then the y axis value. Can you work them out? How many along, and then how many up? Okay. Pin it, and see if you were right. So. X and then y. Just to remind us, that's how we're going to write it out. So we've got one, two, three, four, five along the x axis. And we've got one, two, three four, five, six up the y axis. So we've gone five places to the right and six places up. Simple, right? Now, I bet you didn't think it was going to be as easy as that. But it sure is. So, have a look here. Each of these pairs of symbols show you where they started and where they finished. So here we've gone from A to B. Here we've gone from C to D. E to F. G to H. All you need to do

I'm going to put this in to remind you - is write down the translation for each. How many along, how many up? How many along, how many up? How many along, how many up? How many along, how many up? And it's as simple as that. It couldn't be easier. It's as simple as one, two, three. And that's basically what it is. One, two, three, you're counting. So, I think you're going to do phenomenally at this. Give it a go, and let's share our answers in a moment. And we're coming back in three, two, and one. So let's take a look at some of those answers shall we? All right. So from A to B, I've gone x and then y

just reminders- one, two along, and two up. Is that right? Mm-mm . Remember we're starting on that point, so it's one, two along, and one up. Two, one. For C to D I've gone one, two, three, one, two, three. Three, three. Three along, three up. For E to F I've gone one along, and one, two, three, four, five, six, seven, eight up. And G to H, one, two, three, four, five, six, along. And one up. Brilliant. Not too bad at all. So, now that you know that, you can crack on with the next part. Let's go. So here we are. We've got two sets of grids. On one grid we've got pink crosses on the other grid we've got green circles. All of the pink crosses are going to be translated two, three. X, y. All of the green circles are going to be translated four along, and one up. So these are all going to go two along and three up, these are all going to go four along and one up. All you need to do for each of these points is write it's new position. So if A has gone two along and three up, I've gone one, two, one, two, three. That is my new A. Okay? And that new position is three, seven. Okay. That's all you need to do. So give it a good go. We'll do one set at a time. Each of these I'm moving two along and three up. What are the final coordinates? Two along, three up. Give it a go, and come back when you're ready. Ah. You're back. Great to see you. How did you manage that? Let's take a look at those answers, shall we? So just looking at the pink crosses to start with. So we're remembering with each of them are moving two along and three up. Yeah. So one, two, one, two, three. That's our new A, and that's three, seven. Yeah. B. One, two, one, two, three. Six along, ten up is my new coordinate. And so on. Taking a look over all of those. When you've done that, when you've checked them, when you've ticked them off, then you are my hero. Because we're ready to move onto this one. So this time we're starting with the green circles, and each of those are going to move slightly differently. We're not moving two along and three up, we're moving four along and one up this time. So F would go one, two, three, four and one up. There's my new position. What are the coordinates? Exactly the same as before, I know you can do this. This is no different to the other one. It's no trickier. So, give it a go. All right. You did the first lot, you certainly did that lot, so let's take a look shall we? Here are your answers this time. Casting your eye over that. I must say I'm really proud of you if you've done all of those right and you should be super proud of yourselves. So. We've talked about when a shape moves along this way and then up. But what if it goes backwards and down? How do we write that? Well, there's a really simple solution. So if a shape or point moves backwards or down, we just count the number of places again and record it, but this time we write it as a negative number. So we still do the x and the y axis in the same order, so x and y. Now I'm going to put my little correct spelling in there as well, look at that. Always looking for improvements. So I'm going to do the x and y in the same order. Okay. So for this one I've gone one, two, three, four back, and one, two down. But because I've gone backwards and down and not forwards and up, they're negative numbers. So instead of four, it's minus four, minus two. Minus four, minus, two. Okay. If I started here, and finished here, I've gone back one, so minus one, and I've gone down one, two, three, minus three. So it would be minus one, minus three. It's absolutely simple. Weird how people seem to think it gets harder when you put a minus sign in front of a number. But actually, it's just the same process, we're just counting the x axis and then the y and representing them with negative numbers. Okay. So now you know how to do that, here's your challenge for today. Take a look at this. Now I've shown you where each of those images starts and where they finish. You just need to work out what the translation was. Remember, it's x and then y. If I go backwards, it's negative. If I go down, it's negative. Well look, I've gone backwards and down. Backwards and down. Backwards and down. So each of them will have two sets of negative numbers. Can you work this out? So I've gone mm-mm-mm so it would be minus something, minus something. For each of them. Can you work it out? I know you can. Just by the way, we've gone beyond year four. Because you're brilliant. Go for it. What can you work out? Well guys, because we did a little bit of the work there on some trickier stuff, the treat is coming in a moment. But let's take a look at those answers, shall we? Let's see how you did. So we went for the first one, we've gone back one, two, three, four, five, and down one. So it would be minus five, minus one. Here we've gone back seven. One, two, three, four, five, six, seven. And down two. So minus seven, minus two. Here we've gone one, two, three, four, five, six, seven, eight, nine backwards. So it's minus nine. And one, two, three down. So it's minus three. Minus nine, minus three. Wow. You guys are something else. So because we've worked hard on something beyond our year four, here is a treat. Look, you may have spotted, there's no final knowledge quiz today. What I am going to say now is, as a deal. Go away, and explain to someone, how you've done the activity today. How do you work out the translation of a shape? If it goes forwards and up how is it different if it goes backwards and down? Okay? So go and talk to someone about it, that's the deal. No knowledge quiz. Just have a chat and impress someone at home. And, having said that. You've impressed me and I will see you in the next session with a little bit more on translations. So from me, Mr. C., over and out. Goodbye!

To Describe Movement Between Positions as Translations of a Given Unit Left/Right or Up/Down 1

To Describe Movement Between Positions as Translations of a Given Unit Left/Right or Up/Down 1

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UnitMaths / Position and Direction

Maths