Lesson video

Hi there, my name is Miss Darwish and for today's maths session we are going to look at both translating shapes and reflecting shapes so two types of transformations today.

But before we start with the lesson, if you can just take yourself to a nice quiet place ready to start.

Okay so the agenda of today's lesson is the following, first of all we're going to talk about what the four different types of transformations are and then we are going to take a closer look at two of them and they are reflections and translations.

We are then going to have a look and see if a shape has been reflected or has been translated and knowing what the difference is and then as always there will be a quiz for you to complete on today's learning.

So before we start today's lesson you will just need three of the following items, a pencil, something to write on, a notebook, a piece of paper, anything will do and a ruler.

If you want to go and grab those three things you can stop the lesson.

Okay, ready to start? So, transformations.

There are four types of transformations, and they are, the first one is translation, which you would have heard of.

Second one is reflection so we can translate a shape and that's the type of transformation or we can reflect the shape and that's the type of transformation as well and the third one is rotation.

So if we rotate a shape we are transforming it, we are changing something about it and the last one is enlargement so enlarging a shape again that is a type of transformation.

I don't need to worry about three and four rotation and enlargement do another time.

So first of all this lesson is just about translating and reflecting shapes and knowing the difference.

So in front of us we've got some coordinates and a grid and you can see a what shape? A rectangle, a blue rectangle.

Now, my question to you, has this shape been reflected or has it been translated.

Has it been translated or reflected, tell me, which one and why.

So if you think reflected tell me why, if you think translated tell me why.

Okay, shall we look together? So, Xavier, this is Xavier, say hello Xavier.

Says it's being translated, okay Do you agree or disagree with Xavier? Okay, Yasmin says it's being reflected.

So Xavier has said it's being translated Yasmin has said the shape is being flipped or the shape has being reflected.

What do you think? Who's correct? Has it been reflected or has it been translated? Shouldn't we look together? Okay, so when we look at transformations, what I want you to see is here, we've got the coordinates so can you see that? The vertices are in different colours.

Now, if we want to know which friend is correct, I know that Xavier said it's been translated then why did Xavier say it was translated? Has the shape moved in some way? It has.

It's been translated I think.

One, two, three, four, five, six, seven, eight to the right, so the shape has been translated and that's what Xavier said.

So we could say that Xavier is correct.

But then, what did Yasmin say? She said its being reflected.

Do you see why maybe Yasmin said or thought it was reflected? If you have a look at the y axis lets say that y axis is a line of reflection, or the mirror line.

So if the y axis is the mirror line then the rectangle if its being flipped onto the y axis or reflected onto the y axis then it has been reflected, hasn't it? So actually, we don't know if the shape is been translated or reflected, they're both correct.

Xavier and Yasmin are both correct, we don't have enough information to know if its been translated or its been reflected because if the shape was been reflected on the y axis it would look like this and if the shape was translated one, two, three, four, five, seven to the right, then that is what it would look like so we do need a bit more information to actually gauge as to which it is.

So as I was saying the vertices here what you notice, they're all different colours.

Correct? Okay.

Now, lets say I asked you the question again.

Has the shape been translated or reflected, which would change your answer this time? So the orange matches with the orange, the black matches with the black.

So what do you think, translated or reflected? Now that we see which vertices belong to which vertices, we could see the original vertices, one of the original vertices and then the vertices that are being trans that have been reflected or translated, transformed.

Okay we can see that this has been reflected, can you see for example if we take the orange and the black are closer to the line of reflection which is the y-axis and then on the other side the orange and the black are the closest also to the y axis or the line or the mirror line the line of reflection of the mirror line and that shows a reflection.

Now this time I've changed the colour slightly.

Can you see what's happened? If the vertices look like this and not like how we previously had it like this, so notice how the colours have switched here, then, this wouldn't be a reflection would it? What would it be? This is a translation.

Now, before, can you see the orange and the black are closest to the mirror line? The y-axis, are they the closest to the y-axis to the mirror line? No, that means that it a reflection hasn't happened the y-axis cannot be a mirror line.

This shows a shape that hasn't been changed, all that's happened to it hasn't been flipped, it's just shifted to the right can you see that? So we know this type of transformation is a translation, this shape has been translated.

So actually before when we were saying that Yasmin and Xavier are both correct we didn't have, I'm going to go back to the question, we didn't have enough information, did we? Because we couldn't work out which of the vertices were the same, because they weren't marked out we just had the shape.

So sometimes it's only clearer to work out if a shape has been how a shape has been transformed, we don't know if a shape has been reflected or translated unless the vertices are really clearly marked out ,like we've seen in these examples and it makes it so much clearer.

Okay, now I'm going to answer your question again hopefully it shouldn't be too confusing, why? Because I put the colours on the coordinates and the vertices for you.

Has this been translated or reflected? Tell me what you think and why, off you go.

Okay so translated or reflected, hopefully that was okay.

It's been translated if we say the triangle at the bottom is the original, it doesn't really matter which is the original, let's say the triangle at the bottom is the original then it's been translated four spaces up, if we pick one of let's say the orange, the orange coordinate, one, two, three, four, it's moved four up.

So this shape has been translated.

let's have another look, okay another example, translated or reflected? What do you think have a think and tell me why and three, two, one, It's reflected and not only is it reflected, it's reflected onto the x axis, so for example let's take you pick any of the vertices, so pick a colour, so pick the black one, if this is the mirror line or the x axis is the line of reflection then it's one square away from the black and it's also one square away so, well done if you said reflect it.

Shall we do one more example? Okay.

Translated or reflected? What do you think? Choose one and tell me why.

Okay let's have a go together.

Translated six right and five down and the key here because it's a rectangle it's a bit tricky to see, is that we take each of the colour of the vertices and we see where they are on the reflected or the translator shape on the transform shape basically.

Okay, we can see the purple the orange the purple and the orange.

So this is being translated and we can say six right, five down or what else can we say? Five down and six to the right doesn't matter which way.

Okay well done.

So, let's look at transformations then in general, so we're just going to focus on the two types of transformations, translations and reflections but that was just a bit of an exercise just so you can see sometimes when we reflect or translate a shape, it's not too clear which one it is so we do have to mark the vertices in order to know.

Okay so we can see some, we can see two triangles, one triangle is in the first quadrant and the second triangle is in the second quadrant.

Now, I've got some vertices.

Do you think the shape, let's say the one on the left is the original, doesn't really matter, let's say the one on the left is the original shape, the triangle.

What kind of transformation has happened here? What do you think, tell me.

Is it a reflection or a translation? Okay so you have a look together? So the coordinates are clearly marked with the colours aren't they? We've got the black we've got the purple, we've got the orange and we can see where they are.

So now the question is, what type of transformation has happened? Is it a reflection or is it a translation? So if i showed you so, that's the black coordinate, that's the orange coordinate and that's the purple coordinate.

What's changed? So if i go back, this is the first one so what type of transformation is this one? Is the black coordinate enough to tell us which type of transformation? No, because the black coordinate whether it's being reflected or translated it would still be at the top right? So now we have to look at the purple and the orange, so this type of transformation we can see one of them the purple is closer to the y-axis and the other one the orange is closer to the y-axis, so it's being translated we wouldn't say there's a mirror line and now, if we switch the purple on the orange round just by switching those two colours at the bottom, those two vertices as the transformation changed? Yeah, both the purple coordinates are the closest to the mirror line or to the y axis.

So if the purple is two squares away and the other purple is also two squares away, then that y axis becomes the mirror line, so this a reflection has happened here.

Okay, now this time we've got four triangles, one in each quadrant, in the first quadrant we have triangle a, in the second quadrant we have triangle b, in the third quadrant we have triangle c and in the fourth and final quadrant we have triangle d.

Now I'm going to give you some thinking time, a few seconds to see.

What type of transformations do you think have happened? I'm just going to give you some thinking time.

Okay let's have a look together.

So we can say one option is that a has been reflected onto the x-axis, so we're saying, the x-axis is the mirror line or the line of reflection, to give us d.

Is that correct? Yeah, if a is reflected onto the x-axis we get shape d.

Okay, what else can we say? We can say that d has been translated left to give us seven.

So seven space is left and that gives us c, so if we get we look at shape d in the last quadrant and if it's translated left seven spaces it gives us shape c is that correct? Yeah, but is there something else we can say different about that? We could also say, instead a second option is that so the first option we said that d is being translated up to to get c.

Now we can say d has been reflected onto the y-axis to give us c.

So because we don't have different coloured vertices and the vertices aren't marked we've got two different ways of saying something.

So if a shape like a triangle is translated it gives us another triangle so d translates to c, but also if we reflect the shape d onto the y axis, it still looks like c, so both of these ways you can say you can describe the transformation from d to c in two different ways.

What's the first way? Tell me.

Good, d has been translated left seven to give us c and how else, what's a different way we can describe the transformation from triangle d to triangle c.

Tell me.

Good, that has been reflected onto the y axis to give us c, so see how we've got two, the shapes are exactly the same, exactly the same position but we can describe the transformations in different ways and we still get the same answer.

Okay, well done.

Now i would like you to pause the video right now, have a go at the independent task for today's lesson and then once you've checked over it and you're confident with your answers then come back and we'll go through the answers togethe,r good luck.

Okay welcome back.

Hopefully you found that okay, not too tricky.

Should we go through the answers together? Okay, let's have a look at the question first.

So we have got shapes a, b and c rectangles and Yasmin says that a, b and c show reflections and translations, so both reflections and translations can be seen here.

Now Xavier says there are only reflections.

Who is correct, Yasmin or Xavier? So Yasmin is saying between a, b and c it shows, it just shows reflections and ,oh sorry it shows reflections, and translations but Xavier says that he can only see reflections.

So, who is correct and explain.

So should we have a look at what Yasmin's saying first of all and then what Xavi is saying and I'll pick both? Okay, so Yasmin says that a, b and c show reflections and translations.

So, to help us i have used some colours as well.

So we can see that a, shape a and shape c.

There is a translation there so i understand she said translations and reflections, let's focus on the translation first.

So a has been translated to c, how has it been translated? So if a is the original it's moved down how many squares? Five squares, one, two, three, four, five squares down.

Well done.

Okay and she's also said a reflection, why was she said reflection, and a translation, so through the origin, through zero zero is a diagonal mirror line and that means that a and b are reflections of each other, okay.

So that mirror line there is a reflection from a to b, so that looks right.

So Yasmin said there are reflections and translations, we've seen a reflection from a to b and we've seen a translation from a to c.

So so far yes there is a reflection and a translation, so well done Yasmine.

So let's have a look at what xavier said then.

He said that there are only reflections.

So let's have a look at the same reflection line that Yasmin also saw, so the same reflection line is there showing us a and b, but then what about a and c? Translation or reflection? It could be either couldn't it? So that Xavier is basically assumed or he's saying that the x-axis works as a mirror line or a line of reflection and then a has been flipped to shape c or a has been reflected to shape c, so a has been reflected to shape b and a has also been reflected to shape c.

So actually both of them saw the shapes in different ways.

Yasmin saw a reflection and a translation and Xavier just saw reflections, so both of them are actually correct, so well done to Yasmin and Xavier.

Did you see that they were both correct as well? Okay, well done.

So if you would like to share your work with Oak National then please ask your parent or your carer to share your work onto Twitter.

I would love to see the work that you completed today.

Make sure to ask them to tag at Oak National and to use the hashtag learn with oak.

Now before I let you go to complete the quiz, I just want to say well done on all the brilliant and fantastic learning that you have done today, should be really, really proud of yourselves so good luck on the quiz.