Lesson video

Hello, I'm Miss Miah, and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

In this lesson, you'll be able to draw polygons on a grid according to a given translation.

Your key words are on the screen now, and I'd like you to repeat them after me.

Translate, translating.

Translation.

Horizontal.

Vertical.

Let's find out what these words mean.

So, sliding or moving a shape without rotating or flipping it means to translate.

Translation is a transformation in which every point of a shape moves the same distance and direction.

Horizontal is side to side like the horizon.

Vertical is an up and down direction or position.

Now, this lesson is all about drawing polygons specified by translations, and our first lesson cycle is to do with translating and describing polygons.

For example, if you move one piece of paper on your desk to a different position, it stays the same, but it's just in a new spot, just like translation.

Knowing how to translate or just knowing about it helps in games, drawings, and even understanding maps when you need to see how things shift, but stay the same.

Our second lesson cycle then moves on to describing the translation of a translated polygon.

This lesson, you will meet Jacob and Sofia, who are going to be helping us with our mathematical thinking.

Let's begin.

Jacob and Sofia are exploring translation.

Sofia says, "I want to translate the square right 1 and up 4." What advice would you give to Sofia? Now, first, we're going to mark the vertices.

Let's pick one vertex and translate that first.

So what we need to do is translate the square right 1 square and up 4 squares.

Sofia says she'll pick the red vertex.

"I'll translate it by moving 1 square right and 4 squares up." So we've moved it 1 square right, and 1, 2, 3, 4, that's 4 squares up.

So that is the new position of that vertex.

"Now," Sofia says, "I'll translate the other vertices using the same translation.

I'll mark in my shape for the new position." And it's quite important here to use a ruler so that the shape remains the same and is accurate.

The shape is identical and has not been rotated, so has been translated correctly.

Now Jacob has a go.

Jacob says, "I want to translate the rectangle right 2 squares and up 3 squares." What advice would you give to Jacob? Hmm.

First, mark the vertices.

Jacob says, "Let's pick one vertex and translate that first." Now, I would always suggest picking one vertex rather than moving all four at the same time.

We want to make things simple, so that when we translate the rest of the shape, it's far more accurate.

So by breaking it down, by looking at one vertex at a time, it makes it easier for us to translate.

So what we're going to do is we're going to pick that one vertex.

Jacob says he's going to pick the red vertex, and he's going to translate it by moving 2 squares right and 3 squares up.

Let's count together.

So, let's start by counting 2 squares right.

1, 2.

And 3 squares up.

1, 2, 3.

Fantastic, we found the new position for that vertex.

Now, we don't stop there, we carry on.

Jacob says he'll translate the other vertices using the same translation.

So that was right 2 squares and up 3 squares, and then we end up with the new position of those vertices.

Now, it's important to remember to mark in the shape for the new position.

And again, the shape is identical and it has not been rotated, so it has been translated correctly.

So when it comes to your turn and you're translating a shape, the key here is to make sure that the shape remains identical.

In other words, the same.

Over to you.

Is Jacob correct? He says he's translated this polygon A to B using these directions: 4 squares left and 1 square down.

What do you think? Pause the video here, and click play when you're ready to rejoin us.

So what did you discuss? Well, Jacob is incorrect.

He has translated 4 squares to the right instead of left, so he's confused his direction.

I used to do that, so it's very important you are aware of which way is right and which way is left.

That is where the shape should have been translated to.

Let's move on.

So, this time, we're going to try and describe the translation of A to B.

Now, it looks pretty complicated.

We've got a irregular polygon there.

Let's see what we can do.

Now, you can describe how a polygon moves from its starting position A to its new position B using directions and counting squares.

Find the starting position of one vertex of the polygon.

So it's really important that we mark the same vertices to help us.

So you'll notice with B, the vertex that was already chosen was on the left hand side, so we've chosen the same one for A.

Now what we're going to do is find the new position of the same vertex after the translation.

We can begin by counting the horizontal steps.

You can do this by counting how many squares you need to move left or right to go from one dot to the other.

So here, I've just placed an arrow, we're moving towards the right.

And that's 1, 2, so 2 squares to the right, or right 2 squares.

So make sure you remember that.

Now we're going to count the vertical steps.

You can do this by counting how many squares you need to move up or down to go from one red dot to the other.

So let's count vertically now.

And we can see here, we need to go upwards.

So that's 1, 2, 3, 4, so that's up 4 squares.

So the translation is right 2 squares and up 4 squares.

Over to you.

Describe the translation of A to B.

Remember, mark a vertex and begin by counting the vertical or horizontal steps.

You can pause the video here, and click play when you're ready to rejoin us.

So how did you do? The translation is left 2 squares and up 4 squares or up 4 squares and left 2 squares.

Well done if you got that correct.

Onto the main task for this lesson cycle.

So for question 1, we've got a grid here and we've got two polygons, A and B.

For question 1, you're going to translate the shapes by marking each vertex.

Shape A is translated 4 left and 4 down, shape B is translated 2 left and 3 down, shape C is translated 1 square left and 3 squares up, and shape D is translated 4 squares right and 4 squares up.

For question 2, you're going to describe the translation from A to B, B to D, and C to E.

For question 3, you're going to draw two of the same polygons on different parts of your grid paper.

Label A and B.

Then you're going to swap this with your partner.

Can they describe the translation from A to B? I wonder what the top hints might be for them to do this.

You can pause the video here.

Off you go, have fun, and when you're ready to rejoin us, click play.

So how did you do? Let's look at question 1.

So shape A is translated 4 left and 4 down.

Now, I would've marked one of the vertices first and then translated that point 4 left and 4 down.

This is where you should have ended up.

Now, we can see that this is correct because the polygon is identical.

And then for shape B, you should have got this.

So you should have translated it 2 left and 3 down, and this is the new position for polygon B.

And again, it is identical.

For 1c, shape C is translated 1 square left and 3 squares up.

Without drawing the polygon, I already know the shape is going to be towards the left side, so anything going towards the right will be incorrect.

So here is the new position of the polygon, and it is identical.

And lastly, shape D is translated 4 squares, right, so again, I'm imagining that D will be to the right side and not to the left side, and it will be in a higher position compared to where it is now, because we're moving 4 squares up.

And this is the new position, so this is where D should have ended up.

And again, it is identical, so it is correct.

Now, for question 2, A to B, the translation was right 3 squares.

You can see that because polygon B has moved to the right of polygon A by 3 squares.

B to D is down 5 squares and right 4 squares, and we can see that's correct as well, because if we move right 4 squares and then down 5 squares, we end up in the new position.

And lastly, C to E, you should have got up 4 squares and right 7 squares.

Question 3.

For example, you may have got something like this.

So I can see two parallelograms here, and to get from A to B, you would've had to translate up 5 squares and right 3 squares to get to the new position.

Well done if you managed to get all of those questions correct.

I'm super proud of you.

Let's move on.

Now, cycle two is about describing the translation of a translated polygon.

Describing the translation of a polygon is important, because it helps clearly communicate how the shape has moved, ensuring others can understand its new position while knowing the shape and size remain the same.

This is useful in tasks like mapping, design and problem solving, where precise movement is needed.

Let's get started.

Jacob and Sofia are playing a game: Where Did the Polygon Begin? Now Jacob says, "If B was translated 3 squares right and 2 squares up, what was the original position?" Hmm, "Ah, good question.

I'm not sure how to find this." What advice would you give to Sofia? Now, Sofia begins by marking her vertices.

Now, because a triangle has three vertices, she's marked all three.

"If I know the translation instruction, I can work backwards.

I'll have to reverse the translation by moving each vertex 3 squares to the left," which is the opposite of right.

There we are.

"Now I'll move each vertex 2 squares down," which is the opposite of up.

So by reversing the directions, Sofia was able to find the original position.

So here, what we've done is we've reversed the directions.

In order to do that effectively, you need to know the opposites of the directions.

So the opposite of right is left, left is right, and then the opposite of up is down, and for down, it's up.

So if you know this, you will be able to find the original position.

Keep that in mind.

"Well done, Sofia, you are correct." They then try another one.

So if B was translated 3 squares right and 1 square down, what was the original position? Hmm.

So again, Sofia starts by marking her vertices.

Now she says, "I'll have to reverse the translation by moving each vertex 3 squares to the left," which is the opposite of right.

"Now I'll move each vertex one square up," which is the opposite of down.

So again, by reversing the directions, Sofia was able to find the original position.

"Well done, Sofia, you are correct." Over to you.

So you're going to look at Jacob's directions.

How would you find the original position before translation? Explain your thinking to your partner.

So Jacob says, "If B was translated 5 squares left and 3 squares down, what was the original position?" You can pause the video here, and click play when you're ready to rejoin us.

So what did you get? Well, you might have said, to reverse the steps, you would have to go 5 squares right, because that's the opposite of left, and 3 squares up, because that is the opposite of down.

Well done if you got that correct.

Let's move on.

We're on to our main task for this lesson cycle.

Question 1: For each of the following, the end position of the polygon is given following translation.

You're going to find the original position and then you're going to mark it in.

So 1a, 3 squares right and 1 square down; 1b, 3 squares up and 3 squares right.

For question 2, you're going to write the translations for the polygons below: 2a, D to B; 2b, C to A; 2c, B to C; and 2d, D to A.

Think about the specific directions you're going to give, followed by the amount of squares that the polygon needs to move.

And remember to count carefully.

Question 3: Do you agree or disagree? Explain your reasoning.

Translating a polygon by 2 squares to the right and 3 squares down will change the size and shape of the polygon.

You can pause the video here, remember the top tips for when it comes to finding the original position of a polygon, and then once you're ready, click play so we can go through the answers.

So how did you do? So for question 1, this is what you should have got.

We were moving 3 squares right and 1 square down, so the opposite of that would've been 3 squares left and 1 square up.

So by reversing the directions and not changing the amount of squares that we were counting, you would've found the original position there.

You would've had to move 3 squares left and 1 square up.

Now, to find the original position from B to A, we know that the polygon was translated 3 squares up and 3 squares right, so in order to reverse that, we would've had to go 3 squares down and 3 squares left, and this is where the original position of the polygon would've been.

For question 2, this is what you should have got.

So to get from D to B, you would've had to translate 5 squares left; to get from C to A, again counting very carefully, you would've got 8 squares left and 1 square down, or 1 square down and 8 squares left; for c, you would've got 3 squares up and 4 squares right; and lastly for d, you would've got 9 squares left and 2 squares up.

If you got all of those translations correct, fantastic work, good job.

And lastly, for question 3, what did you get? Well, translating a polygon by moving it 2 squares to the right and 3 squares down will not change its size or shape.

Translation only changes the position of the shape on the grid.

The polygon stays exactly the same, just in a different place.

So the polygon remains identical to its original, and if it does change, it means we've not translated correctly.

Fantastic, we've made it to the end of the lesson, so let's summarise our learning.

In this lesson, you were able to draw polygons specified by translations.

You should now understand that up, down, right and left can be used to translate objects on a grid.

You can combine direction with a number of squares to give accurate translation instructions.

And lastly, you now know that the translation can include a horizontal and a vertical direction.

How did you find it? I really hope that you enjoyed this lesson, and I look forward to seeing you in the next one.

Bye.