Lesson video

Hi year six, welcome to today's lesson on translating simple shapes.

As I said yesterday, need a pencil and ideally, a piece of paper that is good paper, like your maths book.

In today's lesson, we'll be translating simple shapes, starting with a knowledge quiz.

Then we'll describe translations before doing some translations of shapes.

Then you'll do an independent task and a final quiz to test your knowledge.

So let's get started with today's knowledge quiz, testing your learning from our previous lesson.

Pause the video now and complete the quiz.

Great work.

Now let's think about translation, a translation moves a shape up down or from side to side, but it doesn't change its appearance in any other way.

The shape stays the same in size and appearance and orientation.

And we call that congruent.

So the shape stays the same, only its position has been moved and we can translate either single points on a coordinate grid or whole shapes.

And today we're going to be having a go at doing both of those translations.

So we're going to look at describing the translation of a point on the coordinate grid.

So first of all, we have a point on the grid and we want to describe the position.

We always start off with the x coordinate, that's going my pen went funny there, and then we move on to our y.

So the position of the x coordinate, we go along the x axis.

It's at three.

And the position on the y axis we go up is also at three.

So this position is at point three, three on the grid.

Now the point has been moved it has been translated, and we need to describe the translation.

We're going to stick to describing the translation first, by how it has moved along the x axis, and then how it's moved up or down the y axis.

So our translations will always start with right or left and then upward.

So we can see that this point has moved one, two, three places to the right.

So three right is the start of our translation.

And then it has gone one, two places up.

So it's gone one, so three right and then two up.

So it's gone, excuse me, it's gone from three, three to its new position, which is six, five.

Now let's have a look at the original coordinates versus the translated coordinates and see if we can do the translation within the coordinates.

So it's gone from three, three to six, five, it went three along the x axis.

So it went three further up.

So three plus the three is six.

So we can see that translation there.

And it went two up the y axis.

It went from three adding two up to five.

So not only can we see the translation on the grid, but we can also recognise it within the coordinates, if we compare them.

Let's look at another one together, this time we have a shape that will be translated.

So what shape has been drawn? Think back to our shape unit, we can see that it has one pair of parallel sides.

So the shape is a trapezium.

Now we're going to label the coordinates of the vertices.

So I'll start here and I'll call this one A.

So I can see that A is at minus seven, six, minus seven, six and then I'll go to B here.

B is equal to minus seven, four.

C, I will put here and that's at minus five, two, minus five, two, and D is at minus five, eight.

Now this shape has been translated.

So we can see that only the position of the shape has changed, not its size or its orientation.

Now we need to describe the translation.

And all we need to do is focus on one vertex because the translation will be the same for all of the vertices, because the shape stayed the same.

So if we start by looking at D we can see that on the translated shape, this is our D vertex.

So we'll look at the translation here.

We can see, we always go along the x axis first it's gone one, two, three, four spaces to the right, and then it has gone one, two down.

So the translation is four right, two down.

It should be the same for all coordinates because the shape is congruent, which means it's exactly the same.

Just the position has changed.

Let's check with C.

So we think it's gone four two down.

Let's check one, two, three, four to the right and two down.

So that's correct.

So you only need to use one vertex because the shape has not changed at all.

So the translation from each vertex is exactly the same.

Let's do another one up, so the triangle has been translated from position A to position B.

So we will focus on one of the vertices to help us describe the translation.

So I can see that this one is at currently four, minus two and I'm going to write that at the side so that we can compare the coordinates in a minute.

So I'm going to now look at this vertex and see how it has been translated to here.

Okay.

So it's gone one, two to the right.

So I'll write that down here, two to the right, and one, two, three, four, five, up, two right, and five up.

And it is now in position six, three.

So if we look at the coordinates, we can see the x coordinates have gone from four to six, which shows us that it's gone two right.

It's gone two higher up on the x axis and the y coordinates are minus two, three.

The difference between minus two and three is five.

So it shows us that it's gone five spaces up.

So the number has become greater.

Mind you, plus five gives us three.

Now it's your turn.

Pause the video and describe the translation of the shapes from position A to position B.

So you will have used one vertex to describe the position so we can use the top one for the triangle A.

It's gone across one, two, three to the right, and then we can see that it's gone down one, two, three, four, down to its new position.

So the translation is three right, four down.

In this one, I'm going to use this vertex here.

So it's gone one, two, sorry.

Yeah, one, two, three, four up and one, two, three, four to the right.

And it's always good just to check a couple so that you can check that you've counted correctly.

Now you're going to do some translation of shapes yourself.

So if you haven't done already, you may want to draw out the axis onto your squared paper so that you can do this on paper, alongside what I'm doing on the screen.

So, as we looked at before, we can use the comparison of coordinates to help us understand how a shape has been translated.

So I'm going to plot this first point minus five, two.

So I go minus five along the x axis and two on the y.

So my point will be here.

Now, it has been translated to position minus one, zero.

So I can go to minus one on the x axis and zero on the y will be.

So I can see by looking at the translation from A to B, that it has gone one, two, three, four to the right and two down, so four right and two down.

And then I can compare my x coordinates and I can see that the difference between minus five and minus one is four.

It has gone four greater on the x axis.

And the difference between two and zero is two.

And that shows the two down on the y axis.

So these patterns are always apparent in our coordinates.

So you can always look for them here as well as drawing onto the grid.

So these have all been translated four right and two down.

So we can look here.

The difference between minus seven and minus three is four and minus three is greater than minus seven, which tells us it's gone to the right on the x axis.

And the difference between four and two is two.

So now pause the video and have a look and see if you can recognise those patterns in the final two sets of coordinates.

Great work.

Now we're going to look at translating more points.

So we're going to look at the point, the pink one first and do this one together.

We're going to translate it three left and two down.

So I'm going to mark on my grid that it's going three left one, two, three to the left, and then four down one, two, three, four down.

And this is it's new position.

So it's new position is at minus eight, minus six.

And I'm just going to have a look at the original coordinates minus five, minus two.

And just check that I can see this three left and two down.

So it was minus five, minus two to minus eight, minus six.

So it's going three left.

So it's becoming smaller.

So three less than minus five is minus eight and it's going four down.

It's also becoming smaller and four less than minus two is minus six.

So that one is definitely correct.

Now here's some more for you to try.

I would like you to translate the different coloured points in the different ways that are shown on the slide.

Pause the video, while you translate the shapes independently.

Great work.

So your coordinate grid probably looked something like this, where you have translated your blue point five to the right, and six down to become minus two, minus one, your green point four to the left and five down to become zero, zero at the origin, and then your orange point four to the right and seven up to nine, two.

Now let's translate some shapes.

So we use the exact same strategy as earlier.

We're going to translate one of the vertices.

And we're being asked to translate it five to the right and four down.

I'm going to use this vertex here, which I will label B.

And I'm going to translate it five to the right one, two, three, four, five to the right, and four down, one, two, three, four down.

So this point B is now here.

Now either I can translate every one of those points in the same way, or I can focus on reconstructing the shape in its new position.

So I can see that the width of the shape is two units.

So I know that this point will be two units to the left of B.

So that's there and the height is three units.

So I know that this point will be three units below this one, one, two, three, I've reconstructed my shape there.

Now we're going to do another one together and then you're going to do some independently.

We're going to translate shape A three right and two up.

So again, focus on one vertex.

I'll stick with this one, one, two, three to the right, and two up, one, two up.

So it's going to go here and then I'm going to reconstruct the shape.

I can see that it's a square and each side is three units.

So three units to the left will be here.

It's like my original one disappeared.

And then three units down will be here and here.

So there's some overlap on this shape.

Now it's your turn to translate shapes B C, and D as shown on the slides.

Pause the video and have a go at these independently.

So you should have moved your shapes into these positions on your coordinate grid, where you translated shape B five to the right and five down.

C four to the left and two up and D two to the right and eight up.

The most important thing is that the shapes are congruent, that they have gotten the same length sides.

They look exactly the same.

The only thing that has changed is their position.

Now it's time for you to have some independent practise.

Pause the video and complete the task.

And once you're finished click restart, so we can go through the answers together.

So for question one, you were asked for the coordinates of point A and B, and then to describe the translation from point A to B.

So I can see that A, if I go along the x axis, is at minus four up the y axis is at two.

So A is minus four, two.

B is at minus six, five.

And to describe the translation from point A to B, I could either have looked at these coordinates and compared them, or I could do some drawing onto the grid.

So it's gone one, two to the right.

And then one, two, three up.

Question two the coordinates of point C and B, and then describe the translation.

So C along the x axis is four and then down minus three and point D we can see that it is six along the x axis, and it doesn't go either up or down the y.

So it is at six, zero.

And again, you can draw your thing on the grid or look at the comparison, but we'll do it on the grid first.

So it's one, two to the right and one, two, three up, which we can see in the coordinates four to six shows us that it's gone two right and minus three to zero shows us that it's gone three up.

Question three, you needed to translate point E four to the left and six up.

So currently it is in position minus three, two, and we're moving it four to the left one, two, three, four, and then six up, one, two, three, four, five, six.

So that's its new position, that's minus seven, eight.

Question four you to describe the translation of the triangle.

So focus on one vertex to describe its movement.

So it has gone one, two places to the left And then one, two, three, four, five, six down.

And you could have checked that with the other vertices as well.

And then your final question, you were asked to translate the delta, which you will recognise from our shape unit, and you were asked to move it four to the left and five down.

So we can start with point A, we're going one, two, three, four to the left, and then one, two, three, four, five down.

So point A is going to be here.

And then you could work on reconstructing the shape, or you could have translated each point.

So I can see that this point C is two units below A, so I can see that C will be here.

And then I can see that B is two below C and two across.

And the same for D, two and two across.

Now in this look more complex shape you might, may find it easier to translate each point individually, rather than trying to reconstruct the shape.

For that you would use a ruler to join these, you can see that we've got our shape translated, and then you were asked for the coordinates of the new position.

So A is now at zero on the x axis and one on the y.

Sorry, B, which is this one is at minus two, minus three, C, which is the middle point here is at zero on the x axis and minus one on the y and D, which is this one is at two, minus three.

Amazing work it's time for your final quiz.

So pause the video to complete the quiz.

And click restart once you are finished.

Great work today.

In our next lesson, we will be reflecting shapes on a coordinate grid.

Again, it will be really helpful if you could have grid paper for this lesson, I'll see you then.