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 solve problems involving marking and translating points in the first quadrant on a coordinate grid.

On the screen now you can see your keywords that you'll be using in this lesson, and I'd like you to repeat them after me: translate/translation.

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

Now, you may have seen these words before in previous lessons, but it's super important that we understand what these mean, especially for this lesson.

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

Sliding or moving a shape without rotating or flipping it means to translate.

Now, in this lesson, we're going to be solving problems involving marking and translating points.

So, this lesson is made of two lesson cycles.

Our first lesson cycle is all to do with using coordinates to translate a polygon.

Then we're going to move on to identifying missing coordinates, and we're going to be translating them as well.

Let's get started.

To help us with our mathematical thinking, we have Jacob and Sofia, who are going to be joining us too.

Jacob and Sofia are exploring drawing polygons on a grid.

The coordinates for the vertices of a square are: (2,2) (2,4) (4,2) and (4,4).

What do you notice about the coordinates? "Well, the first number in each coordinate, which is the position on the x-axis, is either two or four.

The second number, which is the position on the y-axis, is also either two or four." Jacob plots these points on the grid.

There we are.

"If the x-coordinate is the same, it means the coordinate will be on the same vertical line.

Any coordinate on this line will have an x-coordinate of 2.

Now, if the y-coordinate is the same, it means the coordinate will be on the same horizontal line.

Any coordinate on this line will have a y-coordinate of 4." This time the coordinates for this rectangle are: (7,4) (7,8) (9,4) (9,8).

What do you notice about the coordinates? Jacob notices a pattern again.

"The first number in each coordinate, which is the position on the x-axis, is either seven or nine.

The second number, which is the position on the y-axis, is either four or eight." Jacob plots these points on the grid.

"If there are four coordinates, and two have the same x-coordinate and two have the same y-coordinate, then I think this will always create a rectangle on the coordinate grid." Test Jacob's prediction.

Try two different sets of four coordinates.

Now remember, his prediction is, "If there are four coordinates, and two have the same x-coordinate and two have the same y-coordinate, then I think this will always create a rectangle on the coordinate grid." You can pause the video here, have a go, and click Play when you're ready to rejoin us.

So, how did you get on? Was Jacob's prediction correct? For example, you may have plotted (3,4) (3,2) (6,2) and (6,4).

And I can see a rectangle there.

Or you may have plotted (1,2) (1,10) (8,2) (8,10).

And that's also a rectangle.

Now, Jacob wants to translate the shape two places to the right, and the coordinates for this shape are (5,1) (5,3) (8,1) and (8,3).

"I think I can do this without drawing.

To the right means further along the x-axis.

I think I can add two to the original x-coordinates.

So the point (5,1), the x-coordinate is five.

Five plus two equals seven.

So (7,1) is the new coordinate." (7,1).

Now Jacob repeats this for the other coordinates by adding two to the x-coordinate for each.

So Jacob successfully translated his polygon to the right by using the coordinates only.

Jacob now wants to translate the shape two points to the left.

Hmm, I wonder what he's going to do differently here? "Well, I can use the original coordinates again.

Left means going backwards on the x-axis.

I can subtract two from the x-coordinates.

In the coordinate (5,1), the x-coordinate is five.

Five subtract two is equal to three.

So (3,1) is the new coordinate." Now, we are going to repeat this for the other three coordinates.

We're going to subtract two because we're moving left.

And we end up with the coordinates (3,3) (6,3) and (6,1).

So for each case we have subtracted 2 from the x-coordinate, not from the y-coordinate, because we're moving left.

Over to you.

Jacob wants to translate his shape two squares left.

Which statement is correct? Is it A, add two to the x-coordinate, B, add two to the y-coordinate, or C, subtract two from the x-coordinate? You can pause the video here, and click Play when you're ready to rejoin us.

So, how did you do? If you got C, you are correct.

Because we're moving two squares to the left, we're looking at our x-axis.

So to move to the left, we have to subtract two.

Jacob says, "So far I have found that you can find new coordinates after translation left or right by adding or subtracting from the x-coordinate." "But I know we can translate up and down too.

What happens to the coordinates when we do this?" Well, Sofia wants to translate the rectangle 4 places up.

Coordinates for this rectangle are (5,1) (8,1) (5,3) and (8,3).

Translating up means moving up the y-axis.

I can add four to the y-coordinates of each vertex.

It's not moving left or right, so the x-coordinate stays the same.

In the coordinate (5,1), the y-coordinate is one.

So because we're moving the rectangle four squares up, we're going to add four.

So one add four is equal to five.

So the new coordinates are (5,5).

We now do the same for the three other coordinates that we have there.

So we've added four to each y-coordinate, and we've got (8,5) (5,7) and (8,7).

The x-coordinate has stayed the same because we've not changed the x-coordinate.

Sofia successfully translated the rectangle by-adding four to each of the y-coordinates.

Now Sofia wants to translate this triangle six places down and one left.

The coordinates are (5,7) (8,7) and (8,9).

"I'll use (5,7) as my original coordinate.

This time I'll look at both x and y coordinates, because the instruction has a horizontal and vertical movement.

Moving one place left means I need to subtract one from the x-coordinate.

Five subtract one is equal to four.

So the x-coordinate is four, but I'm not finished yet.

Moving six places down means I need to subtract six from the y-coordinate.

Seven subtract six is equal to one.

So the y-coordinate is one." So the coordinate after translation is now (4,1) for one of the plotted points.

Sofia shows the coordinates in a table.

Translation: six down, one left.

So the original coordinates are there, and the new coordinates are to the right.

She plots the new coordinates after translation and checks her shapes are identical.

Now remember, if the shapes are identical, you're halfway there of making sure that the translation is correct.

The other half is making sure that you've translated the shape the correct amount of squares in the directions that you've been given.

Over to you.

Sofia wants to translate her shape two places up.

Which statement is correct? Is it A, add two to the x-coordinate, B, add two to the y-coordinate, or C, subtract two from the x-coordinate? You can pause the video here, and click Play when you're ready to rejoin us.

So, what did you get? B is correct.

And that's because we are just looking at translating two places up.

So the x-coordinate stays the same, and because we are moving two places up, we are adding two to the y-coordinate to get the new position.

On to the main task for this lesson cycle.

For question one, you're going to look at the shapes below.

You're going to use the coordinates to translate the polygons below and then mark the new position.

A: three places left.

Your original coordinates are (6,5) (6,10) (9,5) and (9,10).

For 1B, you're going to move two places up.

The original coordinates for this polygon are (4,3) and (8,3), and there's one coordinate missing.

You're then going to write down the new coordinates after translation.

For 1C, you're going to find all the original coordinates and then write down the new coordinates after translating it three places down and three places left.

For question two, Sofia has plotted this polygon onto her grid.

She translated the shape three places down and two places right.

What were her original coordinates? Can you use the new coordinates to find the original coordinates? You can pause the video here, and click Play when you're ready to rejoin us.

Off you go, good luck! So, what did you get? Well, for question one, the new coordinates were: (3,5) (3,10) (6,5) and (6,10).

Well done if you managed to find those new coordinates.

And you should have placed your rectangle here.

For question two, the new coordinates were: (4,5) (8,5) and (6,9).

Now, let's have a look at this in a bit more detail.

We needed to translate the shape two places up.

Immediately, I'm thinking about my y-coordinate because the x-coordinate's staying the same, we're not moving left or right, but because we're moving up, we need to look at our y-coordinate.

Now, because we're moving two places up, we need to add two to the y-coordinate, which means (4,3) will become (4,5) because three plus two is equal to five.

(8,3) will become (8,5) because three plus two is equal to five again.

And lastly, (6,7) would become (6,9), and that's because seven plus two is equal to nine.

So our new coordinates are (6,9).

Well done if you managed to get that correct.

And this is the new position of the polygon.

Now, this is what you should have got for 1C.

So the original coordinates of this polygon were: (4,5) (4,9) (6,9) (8,7) and (6,5).

Now, this is a two-step translation, so we were moving it three places down and three places left, which means both the x and y coordinates would've need to have changed.

So because we're going three places down, we would've had to subtract whatever our coordinates were for the y-coordinate by three.

And because we were moving three places to the left, you also should have subtracted three from the x-coordinate.

This would've given you: (1,2) (1,6) (3,6) (5,4) and (3,2).

And this is where the new polygon should have been plotted.

Well done if you managed to get that correct.

Now, for question two, did you notice that you had to work backwards? Now, the translation was three places down and two places right, meaning that to find the original coordinates you had to subtract two from the new x-coordinate and add three to the y-coordinate.

So you should have got (6,4) (8,4) (6,8) and (8,8).

Just remembering that working backwards would've given you the original position of the coordinates.

And this is where the original position of the rectangle was.

Great, let's move on to lesson cycle two, identifying missing coordinates and translating.

Jacob is solving a problem.

He needs to find the coordinates for point A.

What advice would you give to Jacob? Now, we can see that two coordinates have been given to us.

B is at (6,6) and C is (3,3).

"Well, we can use what we know to help us.

A is vertically aligned with C.

C has an x-coordinate of three, so the x-coordinate of A must also be three.

A is horizontally aligned with B.

B has a y-coordinate of six.

So the y-coordinate of A must also be six." So that means point A is (3,6).

Now Jacob needs to find the coordinates for point D.

"We can use what we know to help us.

D is vertically aligned with B.

B has an x-coordinate of six.

So the x-coordinate of D must also be six.

D is horizontally aligned with C.

C has a y-coordinate of three.

So the y-coordinate of D must also be three." Have you noticed how Jacob is using the coordinates to help him find the missing coordinates? So that means D is (6,3).

Over to you.

I'd like you to find the missing point using the coordinates only.

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

So, how did you do? Well, the missing coordinate was (6,3).

D is aligned with B, so the x-coordinate must be six.

D is also aligned with C, so the y-coordinate must be three.

Now Jacob wants to find the coordinate of A.

The two squares are identical.

That's a key point there.

"Since the two squares are identical, and the length of one side is three units, A is towards the origin, so I must subtract.

Six subtract three is equal to three." The x-coordinate would be three.

"I also know A is horizontally aligned with B, so that means the y-coordinates will also be the same.

That's three." So the y-coordinate is three.

A is (3,3).

Sofia says that the coordinates of C are (9,3).

"I know A, B, C will have the same y-coordinate because they are all aligned.

The y-coordinate will be three.

As both squares are identical, and C is three units more than B, the x-coordinate will be three more than six.

Six plus three is equal to nine.

So C is (9,3)." Over to you.

True or false? If the points A, B and C are aligned on the x-axis, the y-coordinates will be the same.

Is this true or 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 false.

And that's because if points A, B and C are aligned on the x-axis, their x-coordinates will be the same, not their y-coordinates.

On to the main task for this lesson cycle.

For question one, you're going to identify the missing coordinates.

You're going to translate each polygon using the coordinates and write down the new coordinates.

So the missing coordinate that you're identifying is D, and then you're going to translate this polygon three places up and one left, and then you're going to write down the new coordinates once you've done that.

You're going to repeat this for B.

You're going to find the missing coordinates for A and D.

And then, once you've translated this polygon four places left and three up, you're going to write down the new coordinates.

For C, you're going to find the missing coordinates for B and C.

You're then going to translate it three places right and one down, and you're going to write the new coordinates for A, B and C.

Question two.

Sofia has found the missing coordinates for B.

Is she correct, how do you know? "B is vertically aligned with A, so the y-coordinate is also three." What do you think? You can pause the video here.

Off you go, have fun, and then once you're ready, click Play so we can discuss the answers.

So, how did you do? For question one, the missing coordinate was (7,3).

And that's because we know B is aligned with D, and its x-coordinate is seven, so D's x-coordinate should also be seven.

D is also aligned with C, and the y-coordinate for C is three, so that means the y-coordinate for D would also be three, meaning the coordinate for D is (7,3).

The new coordinates after translation for this polygon were (2,10).

B was at (6,10).

C was at (2,6).

And D was at (6,6).

Well done if you managed to get that correct.

For B, the missing coordinates for A were (7,7).

And for D it was (9,2).

Again, you could have used your knowledge of alignment of the plots.

So A is (7,7), and D is (9,2).

And the new coordinates for these were, for A, would've been (3,10), B (5,9), C (3,6), and D (5,5).

Well done if you managed to get those points correct.

For question C, for the missing coordinate B, you should have got (3,8), and for C, you should have got (3,2).

Now, after translating three places right and one down, your new coordinates should have been (6,4) (6,7) and (6,1).

What did you get for this question? Sofia said, "B is vertically aligned with A, so the y-coordinate is also three." Hmm, well, B is vertically aligned with A, so it is the x-coordinate, and not the Y coordinate, which is also three.

Well done, you've made it to the end of this lesson.

I really hope you enjoyed it.

Today you were able to solve problems involving marking and translating points in the first quadrant on a coordinate grid.

You now understand that the coordinates are recorded in brackets with the numbers separated by a comma.

You can find or mark a coordinate by counting along the x-axis and then the y-axis.

You also now know that the shape made with the new points after translation should be exactly the same shape and size as the original shape.

Thank you so much for joining me in this lesson.

I hope you enjoyed it.

Bye!.