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're going to learn how to translate polygons in the first quadrant.

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

Vertex.

Vertices.

Translation.

Fabulous, let's find out what these words mean.

So a vertex is the point where two or more lines meet, the plural is vertices.

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

Now, imagine your favourite superhero flying from one spot to another without changing shape or size.

They're just zooming to a new location.

So today you get to be that hero.

We're going to be moving shapes called polygons across a grid just like a superhero.

But here's the catch, the polygon must stay the same.

So are you ready to make some shapes fly? So that is what our first lesson cycle is all about.

We're going to be describing, plotting, and translating a polygon.

We're then going to move on to translating a polygon and giving the new coordinates.

To help us do this, we've got Jacob and Sofia who are going to be helping us with our mathematical thinking.

Let's begin.

Jacob wants to describe how the vertex at A has translated to point B.

"I have translated shapes on square grids before.

I'm counting the points by looking at the lines.

It's four places down.

Then we'll count how many places to the left.

That's four places down and three places left." The polygon has been translated, four spaces down and three spaces left.

"Now, I'll mark the vertices.

I'll translate all the vertices following the instruction." There we are.

"I'll now join the points with a ruler.

The two shapes are identical.

It has just changed position." Now tracing paper helps you translate polygons by allowing you to easily move the shape to a new position without changing its shape or size.

You can trace the original polygon, then slide the tracing paper across the grid to see exactly where the shape will be after the translation.

It's a simple way to make sure that translation is accurate and it helps you understand how the shapes move on a grid.

So, "To use tracing paper to check if two shapes are translations of each other, what you're going to do is first place the tracing paper over the original shape and trace it accurately, marking all the key points." There we go.

"Then you're going to lift the tracing paper and slide it over the second shape without rotating or resizing it." There we go.

"If the traced shape overlaps perfectly with the second shape, covering all vertices and sides exactly, then the two shapes are translations of each other." Over to you.

Jacob has translated shape A to shape B.

Is he correct? I'd like you to explain your thinking to your partner.

You could pause the video here.

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

He has translated one of the points incorrectly.

He could check using tracing paper and make sure both polygons are identical to each other.

And you can see that B is not identical to A.

At first glance, the two polygons do look the same, but when you look more closely, B is definitely not the same as A.

So we know that the polygon has not been translated correctly.

It should look like this.

Let's move on.

Jacob and Sofia translate in different ways.

So this is Sofia's way.

Sofia marks all the vertices and translates each point one by one.

That's what I used to do in school and I found this method easier.

Now, it's Jacob's turn.

Jacob marks one vertex and then counts squares to determine the length of each side.

He then draws it in.

Now, I also used to use this method, but only when the shapes were simpler.

So which method do you prefer and why? Well, Jacob's method is more efficient, but Sofia's method would be more accurate to use if the polygon has more sides.

I definitely agree with that.

Let's move on.

Sofia has translated a shape.

What's the same and what's different? Have a think.

Well, the shape, size, orientation of the polygon remains the same when translated.

Very key that, make sure you remember.

The shape is in a different position, so the coordinates of the vertices change.

Over to you, true or false? Translation slides a shape to a new position without rotating or resizing it.

The shape changes in size and angles depending on the translation.

Is this true or false, and why? You can pause the video here, have think and when you're ready, click play to rejoin us.

So what did you get? It's false and that's because translation slides a shape to a new position without rotating or resizing it.

The shape stays the same in size and angles, remaining congruent to the original.

Onto the main task for this lesson cycle.

For question one, you're going to translate the remaining vertices for the polygons below.

So for question 1-A, you've got a rectangle there, and you need to translate it from A to B.

And then for 1-B, you're translating the triangle from A to B.

Now, for 1-C, you will be translating the pentagon, and for 1-D, you are going to be translating the irregular hexagon.

For question two, Sofia has translated shape A to B.

Is she correct? Explain your thinking.

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

So how did you do? For 1-A this is what you should have got.

Making sure that the polygons are identical to each other and remain congruent.

And this is what you should have got for 1-C and 1-D.

You may have also used tracing paper to check that the shapes remain identical and that the translation is correct.

Now for question two, Sofia had translated shape A to shape B.

I wonder what you got? Well, Sofia is incorrect.

She has plotted two of her vertices incorrectly.

The shape is different, which means she's not translated it correctly.

This was the correct translation.

Sofia could have used tracing paper to check her translation as well.

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

Let's move on with our learning.

Onto lesson cycle two.

For this lesson cycle, you're going to translate a polygon and give the new coordinates.

Let's get started.

Jacob and Sofia find a secret treasure chest hidden in Mrs. Hopper's maths cupboard.

Ooh! Ooh! "Look, there are some notes with coordinates here, One down and two right." "I found some more notes with directions here." Jacob and Sofia plot the coordinates on a coordinates grid.

"I know it's going to be a triangle straight away." "How?" "It's because there are three points to plot." Ah, now Jacob and Sofia have to translate the shape.

So that note said, "One left and five down." "Let's label point A." "Now we can translate A one place left and five down." Let's see where the triangle ends up.

"Yeah, that gives us the new position for A, let's label it B." Brilliant, Sofia and Jacob repeat this for the remaining vertices.

So they translate B and C, one place left and five down.

And by doing this, they've uncovered the new position.

Right, over to you.

I'd like you to write down the new coordinates for the translated shape.

"Remember to find the X coordinate first and then the Y coordinate." You can pause the video here.

So what did you get? You should have got (1,1), (3,3), and (5,0).

And this is by finding the X coordinate first, followed by the Y coordinate for each point.

Jacob and Sofia find another note.

And this time the coordinates are (4,4), (2,6), (4,8) and (6,6).

Jacob says, "I know it's going to be a quadrilateral straight away." "How?" "It's because there are four points to plot." So he's plotted (4,4), he's plotted (2,6) and then (4,8) and (6,6).

And he's right, it is a quadrilateral.

Now, Jacob and Sofia have to translate the shape.

So they need to translate the shape one down and two right.

"Let's label a point A." There we are.

"Now we can translate A, one square down and two right." "Yes, that gives us the new position for A, let's label it B." So B would be there.

Sofia and Jacob repeat this for the remaining points.

Jacob is stuck.

"I can't see where I plot that last point." What advice would you give to Jacob? Well, "You could use tracing paper or you can visually check if the shape looks the same." Back to you.

You're going to write down the new coordinates for the translated shape.

Sofia gives us a hint.

"Count the squares to find the exact point." Remember to start off with finding the X coordinate first, then the Y coordinate.

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

So how did you do? So you should have got (6,7), (8,5), (6,3) and (4,5).

Well done, if you managed to locate all of those coordinate pairs.

Let's move on.

Jacob and Sofia now move on to another note.

This time the coordinates are (6,9), (6,7), (8,5), (10,7) and (9,9).

"I knew it was going to be a pentagon straight away." "How?" "It's because there are five points to plot." There we go.

It's an irregular pentagon, because the sides and angles are not equal.

Jacob tests Sofia and asks her to move the pentagon five squares to the right.

You can mark one vertex and translate it first.

So Sofia does that.

Hmm, "I can only move it two squares to the right, not five, so it won't work." Back to you.

Look at the polygon.

Write down the translation of the new coordinates.

So you've got two polygons there, A and B.

SOMETHING squares SOMETHING and SOMETHING square.

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

So how did you do? Now, remember when writing down a translation, you need to tell us how many squares we're moving and in which direction.

So you should have got four squares right, and one square up, as your translation.

Well done, if you managed to get that correct.

Let's move forward.

So now we're going to be starting the task for this lesson cycle.

Question one, in pairs, each player thinks of four polygons.

Write down the coordinates for each onto separate pieces of paper or Post-it notes.

One polygon must have three vertices.

Two polygons must have four vertices and one polygon must have five vertices.

You will then exchange the coordinates and plot them.

For question two, you're now going to translate the polygons you have drawn according to these translations.

So Player One, you're going to translate Polygon one, one up and four right.

Polygon two, four down, three left.

Polygon three, two down, two right.

Polygon four, two up, four left.

Player Two, you're going to translate, Polygon one, four down, one left.

Polygon two, four up, three right.

Polygon three, one up, two left.

And Polygon four, two down, four right.

Were you able to plot all the points? And is there anything that you noticed? You could pause the video here and click play when you're ready to rejoin us.

So how did you do? Now this is what you may have got.

Here's an example that Sofia got.

She's already plotted the point (4,7).

Now she's plotted (7,5), (0,5) and (4,3).

And once she's drawn in her polygon, so we've got a quadrilateral here.

Now she's translated this two down and two right? If you and your partner managed to plot each other's points correctly, fantastic work.

And then if you were able to translate those polygons correctly as well, fabulous.

You are now showing that you can translate a polygon and give the new coordinates.

We've made it to the end of the lesson.

Fantastic work.

We're now going to summarise our learning.

So in this lesson you were translating polygons in the first quadrant.

So you should now be able to move the point in the horizontal direction in the translation.

You should also be able to move the point in the vertical direction in the translation.

You can now count along the X axis and then the Y axis to find the coordinates for the marked point.

And lastly, you know the shape made with the new points should be exactly the same shape and size as the original shape.

Well done, for completing this lesson with me.

I really hope you took some key information away from this lesson about how to translate a polygon.

I look forward to seeing you in the next lesson.

Bye.