Lesson video

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My name is Mrs Buckmire and today I'll be teaching you about translations.

Now, make sure you have a pen and paper.

If you have a pencil that could be useful, but you don't need one, and same if you have a ruler or anything with straight edge, maybe you've got like a card or like a side of a book that you're allowed to use, then that could be helpful as well.

And remember, pause the video when you need to.

So, if you need more time or when I ask you to as well, when I want you to have a go at something, please pause it and do rewind it.

Or I said something too fast, you didn't quite understand something, please, please, rewind the video and listen again, and that can often help with your understanding.

Okay? Let's begin.

Okay, so for the Try This, find the coordinates of the points first, okay? Then, use the codes to describe journeys between two points.

So, the codes there, you've got North, so many steps, South, so many steps, East, so many steps and West so many steps.

I've got on the left hand side, little North arrow going up to kind of remind you about compass directions.

Now, for an example, let's say we were going from A to B, draw it with a pen.

So, going from A to B, how would it be written? Good, so we can see that it is, one, two, three downwards.

So, down that's going to be South.

So, A to B is going to be three, South.

And that's would be my code, that's how I'd write it down, okay? So, do pause the video, maybe if you want to give yourself a challenge, put a timer on, or look at the clock and wait for five minutes and see how many can you do in five minutes time, okay? Right, pause the video now.

Okay, then, so, first the coordinates.

Now the coordinate of A, was negative four, five, and the coordinate of B, was negative four, three.

What do you notice? Yeah, both have the same x-coordinate.

Remember X is the first one, they are along the quadrant of X is the first one, both have negative four, C was negative two, three.

Do you notice anything there? Yeah, B and C both have the same y-coordinate or y-ordinate, and then D, E and F there, three, negative three, three, negative five and five, negative five.

Check those carefully, pause if you need more time to check.

Okay, there were so many different example codes, so I did eight to be already and that was South three, D to C, so D to C would be West five, North five.

E to F, did any of you guys do that one? Yeah, it'd be East two maybe did F to E.

What would F to E be? Oh boy.

Yes it would be West two.

And B to F, maybe you did, East nine, South seventh.

Now there are so many I can't put them all into, please check your work carefully.

So the students are describing the transformation of C to F, so I can show that with an arrow there.

Now this person says C moves seven squares to the right and eight squares down.

Then this person says we can write seven negative eight.

What's the same and what is different? Pause the video and write down the sentence.

Okay, so what's the same? They both of them seven in them.

They're both describing the transformation from C to F and they both have a number which has an absolute value of eight, so eight and negative eight, both have absolute value eight.

Now they are actually saying equivalent things.

So Yasmin is saying it kind of more in our when we're talking to someone.

So we would say like, if I'm giving direction, you would go along both three roads along and then when you get to the next road, then you're going to turn left, then you go down this street and you use words when you're talking to people.

But when we want a computer, so when something like Google Maps use it, we want to use numbers because computers understand numbers better.

And our codes normally with movement and with positions.

So actually we use vector notation and that is what he's used.

So seven, negative eight is the type of vector notation.

So here he says both of them, there are some similarities and differences, one's a bit more informal and one's a mathematical formal and using vector notation.

Now what other transformations can be described with this vector? Have a little think.

Okay, good.

So you could have AD or BE, well done, so both them AE and BE both can be moved in that way, so A to D or B to E, interesting.

Okay, so what is translations? Translations are movement in a direction and it's when every point is moved the same distance on the same direction.

So column vectors can be used to describe translations.

Now this is the X value, it tells you the left or right movement.

So here, when you asked me said it went seven to right.

So that's one, two, three, four, five, six, seven to get here.

And then when it was eight down, is one, two, three, four, five, six, seven, eight.

So we represent that as negative eight.

So when it's positive, it's in the right direction and when it's negative, it's in the left direction for the top one number and the bottom number one is positive is going up, and when it's negative is going down.

You can pause it and write these notes to help you.

Okay, before I move on, why do you want to make it clear? What's great about vectors? It actually gives us distance and direction.

So I'm often actually talking to my year twelves about vectors.

It gives you distance and direction.

It's the seven is the positive, is telling you how far and because it's positive, as I was telling you the direction of it, the negative eight, the eight tells us how far it's the absolute value of eight tell us how far? But the negative is tells direction and that's what tells us going down.

So that's really useful to know as well.

I want you to just have a quick go at filling in the gaps in this table.

So do pause the video and just think the words down the left hand side, what would have been better notation.

It was written back to how could you tell someone what it how could you tell someone what it meant in words.

Do pause it and have a go.

Three, two, one.

So seven right, four down.

Now on the right-hand side, I've actually put a little axes here because some will help how well the X goes first and to the right, it gets more positive, so it makes sense.

And then it feels negative.

Is if there X values negative on this side, I mean, there's more towards the left.

So that sometimes help with the same with Y, it's a Y value, is positive, it's in kind of the positive region.

So it's going up, and if it's negative, that means is in this bottom region.

So it's going down, so that sometimes helps people.

So with this first one, what did you get, seven right and four down? Good, so it's going to be seven in the positive and four in the negative, so seven, negative four, make sure the top is X and the bottom is the Y and movement.

Negative three, two? Good, negative three is negative, is the X.

So it's going to be moving in the left direction.

And the two is positives that can be moved up, two up.

Negative five, negative six? Excellent, so five left and six down and finally, five right and eight up? Good, five is positive and eight is also positive, well done if you've got those.

So why wouldn't you do just a bit of practise, writing a vector from coordinate movements.

So C to F is up there, and this is hopefully familiar and diagram.

And then I want you to tell me the translation F to C and describe it using a vector notation, B to C and A to B, pause the video and have a quick go now.

Okay, for F to C then.

So F to C is going to go seven to the left.

So one, two I'd count it three, four, five, six, seven.

So let's write seven left and then it's going to go one, two, three, four, five, six, seven, eight, eight up.

So when that happens, seven left, what's that going to be? Good, negative seven, eight up, positive eight.

So make sure it looks like this.

Remember, there's no fraction by, it's not a fraction, this is vector notation, so this is a matrix here.

B to C, so B to C is just two right.

And it's not moving up or down at all.

So I can put zero movement there.

So the vector notation is going to be two, zero.

And now A to B? Yeah, it was just three down, so three down.

So there's no left or right movement.

There's three downstairs, negative three.

So three downwards, so it's going to be zero, negative three.

So sometimes finding words first can help you then put it into vector notation.

So I want to introduce now the words, object and image.

So an object is normally like the original items. So what were originally wanting to move, and the image is where artists transformation, where it's been moved to.

So object is the original images where it's been moved to.

So the object triangle, ABC is translated negative two, negative three.

What are the corners of the image? Now the really important thing is with translation, every point on the shape had been moved by the same distance in the same direction.

So why would do, is actually move each individual coordinate to help.

So negative two, first, I'd write this in words.

So it's two left or right? Good, left and then three down.

And then I choose a coordinator A, I'm going to do move it two left.

So one, two left and three down, one, two, three.

And then you can do that with each coordinate or because we know the whole shape of the moved by the same distance, the same direction, I can actually then just recreate the shape.

So I could actually then expect that since B is three below eight, well here, it's still going to be three below.

Since C was two to right, B it's still going to be two.

So I want to look like this, so you can do it for each one.

If I do it for B two and then one, two, three, and at the same place, but, or you can just recreate it once doing one point.

there's A dash, B dash, and C dash, that you create the image by actually asked for the coordinates.

You pause the video and tell me what the coordinates are.

So did you get negative six, two and negative six, negative one and negative four, negative one? Well done if you got those by having go this question.

Make sure you pause it.

Yes, we gave you some time.

So five is going to be five right, good, it's positive, two is two up.

So let's move it from D, so five right, one, two, three, four, five, and two up one, two.

So that ends up here.

And I could do with E as well, one, two, three, four, five, two up, one, two ends up here.

So I know that the other point is going to be here.

So it's going to look like this.

So if you worked out the coordinates, you should've got minus, negative two, sorry, negative one, you should have got negative two, negative four, and you should have got zero, negative four.

Make sure zero, negative four, remember, x-coordinate first, and then the y-coordinate.

Well done if you've got that right.

Okay, you are more than ready, now per Independent Tasks, now because you had so much practise, I feel confident you can do this trickier challenge.

I'll just give you a quick example.

So here, actually, the coordinate grid like lines are not on this grid.

So you have to think about how far it's moved.

So from A to B, so this translation, you need to think, oh, how far has it moved this way? How far is it moved upwards? Sometimes it helps to draw a little triangle, right-angled triangle to help and say, Oh, what's that right movement and what's that up movement.

Okay, I believe you can do this.

So do have a go, there's two pages.

This is page one.

Pause if you wants to do it from here, otherwise go to the worksheet and you can see both pages.

So here is page two.

So here, I want you to describe the transformation.

So when you do that, you're going to say it's a translation, and then you're going to put in the vector notation.

It could be easier to first do it to using words.

I would also recommend actually selecting one point that you're moving and make sure as a corresponding points, if I'm moving from A to B, I'd choose a corresponding point, which is going to be the top here and saying, oh, what is that translation? And you can even check your own work, so you can then choose a different point, maybe this point and try it out.

So from that point, the cost to that course, after you've worked out, okay? So do have a go describe the transformations, for each one there.

Okay, how was it? So from A to B, like I said, I would most definitely draw it right-angled triangle here.

And when I do that to get from the X value four to the X value eight, what did you get? Good, is going to move four.

So it's going to be four to the right.

And then it moves up from eight to 20.

Good, it moves up 12 to 12 up.

So my vector notation is going to be four, 12.

If that helps, you know, how many had done it, go back and do it again, have another go.

That's more than fine.

So C to B while it's definitely moving in that way, that way a newcomer, so it's moving to the left.

So there's left 12 and it's moving up four.

So left 12 Up, so there's going to be negative 12 and four positive.

What about eight D? So I could maybe draw my little triangle here if it helps my right-angled triangle.

That is not a good triangle, Mrs Buckmire, you do not know how to use a pen well here, let's do that again.

That should be a straight line, a split down.

So we're moving forward and positive 12 towards the light.

So I'd say 12 right.

And then we're moving down four, four down.

So it's going to be positive 12, negative four, and finally B to D what did you get? Eight negative 16, good job.

Okay, and when you would describe it now, so I did talk about that corresponding point.

So to get from A to B, we're moving one, two, three, four to the rights, I'll move in one down, that should be an ally.

So four right, one down was the vector for a negative one.

And even better if actually you wrote translation.

And then B to D? Excellent, it's just zero and then negative five.

So one, two, three, four, five downwards, A to D? Should be four, negative six, and B to C? Excellent, negative four.

And then let's redo it B to C, where's the pen gone? Here, so negative four, is a four left one, two, three, four, and how much down? One, two, three, four down as well.

So negative four, negative four was correct.

Okay, you are ready for our explore task.

Now what I would like you to do, it kind off just disappeared.

What I would like you to do is, tell me what vectors can you use to describe the translation between the shapes in this tesselation pattern? What's the tessellating pattern? This, so how would you describe this? Yeah, there's no gaps at all.

So the tessellate and patterns means where there's no gap.

So it's things like in Mosaics and there's a lot of, I think religion mosaic such a really beautiful without many gaps, are quite pretty actually.

Also tiles maybe if you have cold in your bathroom or kitchen, maybe there might be tiles and tessellations, they will just example the tessellations also actually bees and beehives, like those hexagons tessellate as well often.

Yeah, so just describe, can you get from J to K, can you get from J to F, J to A? I will spend a good 10 minutes and different relationships and just seeing what you can find out.

So maybe can you get from J to K and then K to H and then explore? What's the relationship between getting straight from J to H? Does that make sense? I'm going to write that down.

So can you do from J to K and then from K to H? Or can you do straight from J to H, can you spot any relationships? I just want you to just have a good time exploring it and just practising your vector notation at the same time.

How did you find that? You get lots and lots of different vector notations, lots of different transformations there.

Good, okay, so everyone just going to J to K, then it would be one shape right, so it'd be two, zero.

So remember it's super, super important that you're comparing corresponding points.

So let's say if we did this point, we'd have to compare it to this one, so we can see it's just been moved two to the right and not be moved up or down at all.

If we did down one row, it could be one, negative three.

Can you say an example of this? Yeah.

, so it could be, do you get J to F? It could be K to G, L to H, but you might have done down one maybe in J to E, if it was J to E, what would the vector notation be? Yeah, it would be negative one, three, one, to the left.

If I was choosing this one and then one, two, three down.

So it'd be negative one, negative three.

So depends on what you meant by going down one row.

Now you could also maybe go up two rows.

If I went from B to K, then actually, if I use this as a correspondent point, it goes up six, one two, three, four, five, six.

But actually it doesn't move left or right at all.

So what kind of things were you noticing? So a lot of these numbers, two and three will come out because the shape is two with the long and the bottom and it's three up.

So actually that's why I can see the two going to right, maybe two going left sometimes, three up and things like that.

What else do you notice? Did some of you do that little challenge? So it wasn't J to K to H.

So when you did J to K, we already did that, it was two, zero, wasn't it? I want you to do K to H, what was it? So it was one where that's used, so that point goes one, two, three to the right and one, two, three down.

So as three, negative three.

So what about if you did straight from J to H, what did you get? Yeah, I have a quick go now if you haven't done it, pause it.

Okay, so what did you get? So it'd be one, two, three, four, five, to right, so positive five, and then how many down? Three downs and negative three.

What do you notice about those? Yeah, so two zero, plus three, negative three ends up to equal to five, negative three.

Already adding vectors, you guys fantastic work.

So hope you enjoy, just having a go at exploring the tessellation pattern.

There's so many do come up with so many vectors you can come up with.

I can't go through them all, but I hope you have had a go mate and got some of the ones I got as well.

Really, really well done today everyone, if you had to get the Try This, the Different Tasks that I was giving you during the lesson, the Independent Tasks and Explore, I think you should be super proud of yourself, you've worked very hard.

Hopefully you have learned about vector notation.

Maybe just write down the key things you remember.

So what do you need to remember? What is translation and what is vector notation? What are the different parts? Excellent, and I think it would be super, super useful for you to do the exit quiz now.

The exit quiz helps you to check your understanding.

Also, I've given you some feedback as once.

If you get anything wrong, do read the feedback and then that will help you improve.

Have a lovely, lovely day, bye.