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 describe translations of polygons drawn on a square grid.

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

Translate, translating.

Translation.

Well done.

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

The act of moving is to translate.

This lesson is all to do with describing translations of polygons drawn on a square grid.

You'll see how shapes translate from one place to another without changing their size or shape.

This is a useful skill because it helps you understand how objects move in space, which is important in maths and even in real life navigation.

Now this lesson is made of two lesson cycles.

The first lesson cycle is all about describing and marking all the points, and then the second lesson cycle is to do with translating one point.

Let's begin.

In this lesson, you will meet Jacob and Sophia who are going to be helping us throughout our mathematical journey.

Jacob and Sophia are exploring the movement of a polygon on a grid.

Jacob says, when we move a shape from one place to another on a grid without changing its size or turning it, we are translating the shape.

So we've translated A to B.

Think of it like sliding a toy car on a table.

You can move the car to the left, right, up, or down, but the car itself doesn't change.

It just moves to a new spot.

Sophia and Jacob are playing a game.

They have to get the polygon from A to B.

Now we've got a sentence stem here.

The polygon has been translated something squares something and something squares.

You're going to count four squares straight up from the starting point.

One, two, three, four.

Now count three squares right from the new position.

One, two, three.

The polygon has been translated four squares up and three squares to the right.

Now Jacob finds another way to translate from A to B.

Count three squares to the right.

One, two, three.

Now we're going to count four squares up from the new position.

And you can see that the polygon has been translated three squares to right and four squares up.

Over to you.

Look at the image below.

What translation is needed to move the polygon from A to B? Can you say more than one way? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? Well if you got that, the polygon has been translated three squares up and five squares right? You are correct.

You may have also got five squares right and three squares up.

So you may have changed the directions, but we'll talk about that in a little while.

Now, Jacob and Sophia translate from A to B.

So here's Jacob's translation.

The polygon has been translated four squares down and three squares to the right.

Three, four, so that's four squares down and one, two, three, three squares to the right.

Now Sophia says that the polygon has been translated three squares to the right and four squares down.

So one, two, three.

One, two, three, four.

What do you notice about Sophia and Jacob's translations? They both end up at the same final position.

The order of the instructions doesn't change the final position.

Now Sophia and Jacob move on to playing a game to test each other's knowledge.

Jacob gives Sophia directions for her to translate her polygon.

Two squares right and two squares down.

What's the new position? To make sure I am accurate, I'll mark a dot on one vertex of my polygon.

Then I'll translate the red dot.

So here we are, she's marked one of the vertices.

Then she's marked the translated dot.

Now I'll mark the other vertices and move each vertex in these directions.

So she's done the same with the green dot and the blue dot, and you can actually see here that the triangle shape is quite visual there.

Lastly, Sophia says that she'll draw the lines connecting these new vertices to form the translated triangle.

Well done Sophia.

That's correct.

By marking the vertices and following these steps, you can confidently find the new position of the shape after the translation.

And actually by marking the vertices, I would say it's far more efficient than moving the sides only.

Moving the sides is better for simpler shapes, but when it comes to, you know, a little bit more complex shapes, it's better to mark the vertices.

Now, Sophia tests Jacob.

Three squares right, and one square down, what's the new position? I'm going to follow you and translate one vertex at a time.

Jacob's marked the vertex there with a red dot and he's translated it three squares right and one square down.

Now he says that he'll mark the other vertices and move each vertex three squares, right, and one square down.

Lastly, I'll draw lines connecting these new vertices to form the translated triangle.

There we are.

Well done Jacob, that's correct.

So again, by marking the vertices and following these steps, you can confidently find the new position of the shape of translation.

True or false? Marking the vertex of a shape helps make sure you translate the shape correctly on a grid.

Is it true or is it false? And I'd like you to explain why.

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

So what did you get? Well, it's true.

And that's because marking the vertex of a shape gives you a clear point to count from when you move it.

This helps you translate the shape, the right number of squares in the right direction so it ends up in the correct new spot.

It also makes sure the whole shape stays the same size and looks the same after translation.

Let's move on.

Jacob and Sofia move on to another round.

Three squares right and two squares up, what's the new position? I'll begin by marking a dot on the vertex of my polygon.

Then I'll translate the red dot.

There we go, so he's translated that dot three squares right, and two squares up.

Now I'll mark the other vertices and move each vertex three squares right and two squares up.

There we go.

Lastly, Jacob says that he'll draw the lines using a ruler, then connect these vertices to form the translated polygon.

Well done Jacob, that's correct.

So remember to move the correct number of squares in the given directions.

Over to you.

Look at Sophia's directions below.

Which image shows the correct translation? So Sophia says two squares right and two squares up, what's the new position? Is it A or B? You could pause the video here and click play when you're ready to rejoin us So how did you do? Well, B is the correct answer.

And that's because each vertex has been translated by two squares right and two squares up.

Well done if you got that correct.

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

For one A, shape A is translated three right and two down.

One B, shape B is translated six left and one up.

One C, shape C is translated four squares left and one square down and one D, shape D is translated five squares right and one square up.

For question two, do you agree with Sophia? Explain your thinking.

Sophia says the order of translation steps does not affect the final position of the shape.

Do you agree? You could pause the video here and click play when you're ready to rejoin us.

So how did you do? So for one A, you should have got this, and that's because each vertex has been translated three right and two down.

For one B, this is what you should have got.

And that's because we translated each vertex six left and one up.

For one C, the new position of the polygon would've been here and that's because we've translated four squares left and one square down.

And lastly, one D, shape D is translated five squares right and one square up.

So you should have had your new polygon position here.

Now for question two, this is what you should have got.

The order of translation steps does not affect the final position of the shape because moving a shape up down left or right on a grid does not change its size or shape.

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

I'm super proud of you.

Let's move on.

Now we are moving on to the second lesson cycle and this is all about translating one point and we'll find out more about this now.

Now when translating a shape, you can start by moving just one point and then use that to find where the other points should go.

Hmm, so Jacob wants to translate shape A to shape B, and he is wondering if there is an easier way.

What advice might you give to Jacob to move A to B? Sophia says that she thinks that there is a more efficient way.

Marking the vertex will help you to move the shape.

Jacob says we need to count the number of squares I need to move the polygon in each direction.

So one, two, three, four, four to the right.

So Jacob says, I just need to move the dot four squares to the right.

Once you've done that, you can find the new positions for the other vertices by moving them the same distance in the same direction.

So by translating one point and then marking the others in relation to it, you make sure the entire shape moves correctly and stays the same.

If you move one vertex correctly, you can use that information to move the other corners in the same way.

For example, if you move one vertex four squares to the right, you can move all the other vertices the same amount.

Now this keeps the shape the same size and makes it quicker and easier to translate the whole shape.

Personally I love this method because it is so much more efficient when it comes to translating.

Now they look at another example.

What advice might you give to Jacob to do this? Well first we need to identify which polygon we are moving.

It would help to mark the vertex with a dot.

Marking the vertex will help you move the shape, then decide the direction in which you need to move the polygon.

Directions can be right, left, up, or down.

Now we need to count the number of squares that Jacob needs to move the polygon in each direction.

So one, two, three, four.

Jacob needs to move four squares to the left.

And there we have it, we have translated the polygon just by marking one vertex.

Jacob and Sophia now want to translate Polygon A four right and three down.

What advice might you give to Jacob to do this? I'm going to translate one vertex.

I will mark it with a dot.

I think that's a good idea.

Marking the vertex will help you move the shape.

Think carefully about the direction you need to move it.

Count carefully.

We need to count the number of squares I need to move the vertex in each direction.

So we know we have to move four right and three down, so let's count four right.

One, two, three, four.

Now we have to move three down, so let's do that.

Let's count that as well.

One, two, three.

So the new position of the vertex or the marked dot will be here.

Now I just need to draw the shape so it's the same size as before.

This strategy can be more efficient for more simple polygons.

So the sides are two square units long.

It's a square, so the vertices need to be right angles.

Over to you.

Which translation is correct to describe A to B? Is it A, the polygon has been translated five squares to the left and two squares up, or B, the polygon has been translated four squares to the left and one square up? What do you think? You could pause the video here and click play when you're ready to rejoin us.

So what did you get? If you got B? You are correct.

And that's because the polygon has been translated four squares to the left and one square up, not five squares to the left.

That's one too many.

Onto the main task for this lesson cycle.

So for question one, you're going to translate the shapes following the directions.

For each, mark and translate one vertex.

Use the polygon properties to redraw the shape.

So for A, you've got four squares to the right and two squares down.

For B, you've got four squares to the left and two squares down, and you are in charge of marking the vertex there.

For question C and D, again you are in charge of marking where you want to place that vertex or the dot on the vertex.

So for question C, three squares to the left and two squares up, and D three squares to the left and two squares up.

Question two, what advice would you give to Jacob? Explain your thinking.

If you move one vertex of a shape, four squares to the right and three squares up, how should you move the other vertices to keep the shape the same? You can pause the video here.

Off you go, good luck.

And click pay when you're ready to rejoin us.

So how did you do? For question one, this is what you should have got.

So the position of B is in the bottom right corner.

You would've got that after translating four squares to the right and two squares down.

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

So four squares to the left and two squares down.

For question C, this was the new position.

By marking a dot on any of the vertices, this is what you should have got for question C and for question D.

Well done if you managed to get those translations correct by marking a dot only and using that to help you identify the new position of the polygon.

Now for question two, you should move the other vertices four squares to the right and three squares up.

Just like the first vertex.

This keeps the shape the same size and shape, but in a new place.

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

I'm super proud of you.

You are now showing that you can translate a shape using one point.

We've made it to the end of this lesson and let's summarise our learning.

So today you are able to describe translations of polygons drawn on a square grid.

So you should now understand that if a shape has moved, you say it has been translated, that is the correct mathematical term.

You also understand that if a shape has been moved, you can describe the move using left, right, up, down, and the number of squares moved.

And this is because the directions need to be specific.

Otherwise we won't know where we're moving that polygon.

And lastly, you understand that shape can be translated in a vertical and horizontal direction.

Thank you so much for joining me.

Hope you had fun and I look forward to seeing you in the next lesson.

Bye.