Lesson video

Hello, I'm Miss Mia 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 be able to draw polygons specified by-coordinates in the first quadrant.

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

Polygon, vertex/vertices, coordinate.

Great.

Let's find out what these key words mean.

So a polygon is a 2D shape made up of three or more straight lines.

A vertex is the point where two lines meet.

The plural for this is vertices.

Coordinates are a set of values that show an exact position.

Now this lesson is all about drawing polygons specified by-coordinates in the first quadrant.

This lesson is made up of two lesson cycles.

In the first lesson cycle, you will be identifying and writing coordinates of polygons, and then in the second lesson cycle, we're going to move on to drawing polygons using given coordinates.

So actually, by learning to draw polygons with coordinates, you're learning how to create and plan things just like a designer or an architect.

Let's get started.

Now, in this lesson, you'll meet Jacob and Sofia, who will be helping with our mathematical thinking.

Jacob and Sofia are exploring the coordinates of polygons on a grid.

What are the coordinates of the vertices of this polygon? Have a look.

Jacob says, "I think I'll start by marking my vertices.

So there will be three coordinates." So he's marked the vertices on his triangle.

Jacob now finds the coordinates for each vertex.

He marks the coordinate he wants to find first.

So he's marked the coordinate there.

He says, "I'll start at the origin and count along horizontally." So let's count together.

One, two, three.

That's three.

Now he's going to count vertically, so let's count together.

One, two, three, four.

That's four.

Jacob finds the coordinate for the next vertex, so he's marked it there.

The point is in line with the 3 on the x-axis.

So that's 3.

It's in line with 7 on the y-axis.

So that's 7.

Over to you, I'd like you to find the missing coordinates for the point circled.

Remember to find the x-coordinate first.

Pause the video here and click play when you're ready to rejoin us.

So how did you do? If you got 7,4, that's correct.

And that's because the point is on 7 on the x-axis.

And if we look up vertically, it's perfectly aligned with 4 on the y-axis.

So you should have got 7,4.

Let's move on.

Jacob has found the coordinates for all three vertices, and we can see them there.

"I can describe the vertices of the triangle at these points." Now, if Jacob moved the vertex at 3,7 to 5,7, would the polygon still be a triangle? Let's have a look.

It will still be a triangle because the number of vertices has stayed the same.

Now Jacob adds another point at 7,7.

He uses this as a new vertex.

What shape has Jacob made? The polygon now has four vertices.

It is a quadrilateral.

So by adding another vertex, 'cause we've got four points, the polygon now is a quadrilateral because there are four vertices.

So it has four right angles, so it is a rectangle.

Over to you, identify the vertices of this quadrilateral and write the coordinates.

What is the name of the quadrilateral? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? You should have got 0,3, 0,6, 7,4, and 7,3.

Well done if you got that correct.

"This is a trapezium.

It has exactly one pair of parallel sides." Well done if you managed to name the polygon correctly as well.

Onto the main task.

So for question one, you're going to look at the following grids, and then you're going to identify and write down the coordinates of the vertices of each polygon.

You're going to do this with these polygons as well.

Then for question two, you're going to draw your own polygon and identify the coordinates of the vertices.

Now remember, a polygon has straight sides.

There are no gaps.

So make sure when you're drawing your polygon, it follows the same rules.

Now for question three, if you place a point at 10,8, and use the four points as vertices, what shape is formed? You can pause the video here and start the task.

Click play when you're ready to rejoin us.

So how did you do? Well for question one, you were to identify the coordinates for the following polygons, so let's look at A first.

So Shape A is a triangle, more specifically a right-angled triangle.

and the coordinates that you should have got were 6,5, 6,9, and 10,5.

Shape B is a rectangle.

It has four right angles.

So the coordinates for this rectangle are 1,0, 4,0, 1,4 and 4,4.

Well done if you managed to identify the correct coordinates for the vertices on these polygons.

Now let's look at Shape C and Shape D.

So Shape C is a trapezium.

It has one pair of parallel sides, and the coordinates that you should have got were 0,4, 3,5, 3,7 and 0,8.

And lastly, Shape D is a pentagon.

So a pentagon has five vertices, and the coordinates that you should have got were 4,1, 8,1, 8,3, 6,4, and 4,4.

And just a quick note there, it's an irregular pentagon because the sides are not the same length.

Now for question two, you were drawing your own polygon.

Here is an example on the screen here.

So Sofia drew a pentagon, and the coordinates for this were 5,9, 8,7, 7,3, 3,3, and 2,7.

Now for question three, you are to place the point 10,8, and the shape that is formed is a trapezium.

It has exactly one pair of parallel sides.

Well done if you managed to get that correct.

Now we're going to move on to the second lesson cycle.

So you're going to be drawing polygons using given coordinates.

Jacob and Sofia are taking part in a treasure hunt where they unlock clues by plotting points and forming shapes.

Each shape they uncover will lead them closer to finding the key for the treasure box.

Now both Sofia and Jacob are giving us top hints here, so keep these in mind.

"Remember, when plotting points, we mark the x-coordinate first." "Let's also make sure we use a ruler." Hint 5, hmm.

"Let's remember the number 5." So Clue 1: plot points 1,1, 4,1, 4,4, and 1,4.

So Jacob says, "Start at the origin.

Move one step to the right to reach the x-coordinate of 1." So we're going to start off by plotting 1, 1, and by moving one step to the right, we move to the x-coordinate of 1.

"Then move one step up to reach the y-coordinate of 1." And then we're going to mark the point.

This is the point 1,1.

Now we have to do the same for the other three coordinates.

So 1,4 would go there, 4,4 would go there, and 4,1 would be placed there.

Ooh, okay, now we can connect the vertices to reveal the polygon.

Make sure when you're doing this for your own task use ruler.

It's a square.

It has four equal sides and four right angles.

Jacob and Sofia move on to Clue 2.

This time, they're going to start off by plotting the coordinate pair 5,2.

The x-coordinate is 5, which means the point is in line with the 5 on the x-axis.

The y-coordinate is 2, so it's in line with the 2 on the y-axis.

So we've plotted the point there.

5,2 is located with the grid lines across.

Now we have to do the same for the other three coordinates.

So 5,6 would go there, 8,6 would go there, 8,2 would go there.

Now we can connect the vertices to find out what polygon we have.

And there we have it.

It's a rectangle.

It has two pairs of equal length sides, but not all equal like the square.

Over to you.

A vertex is at 5,2.

Explain what the numbers 5 and 2 represent.

How would you find this point on the grid? You can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, Jacob says, "The first number, 5, represents the horizontal distance from the origin along the x-axis.

Move 5 squares to the right." "The second number, 2, represents the vertical distance from the origin along the y-axis." So you'd have to move 2 squares up.

Let's move on.

So Clue 3: plot points 3,7, 6,7 and 6,10.

Clue 4: add a point to make it a rectangle.

What are the coordinates? Hmm.

"If three points of a rectangle are already plotted, you can determine the fourth point.

The points 3,7 and 6,7 share the same y-coordinate, indicating a horizontal side.

The points 6,7 and 6,10 share the same x-coordinate, indicating a vertical side." Now to complete the rectangle, the fourth point should align horizontally with 7,10 and vertically with 3,7.

Therefore, the fourth point is 3,10.

So by looking at our coordinates in more detail, we can find out what that missing point is.

We can also visually plot the point by looking at where it is aligned to the x-coordinates and the y-coordinates.

Now Jacob and Sofia find the remaining polygons, two triangles.

To find the key, they must identify the irregular polygon created by the shapes.

Well, it can't be that.

"Remember the hint 5? I think I found it.

5 indicates the number of vertices for the last shape." Ah, it's right in the middle.

"That's where the treasure is." So Jacob and Sofia find the key to open the treasure box.

Yay.

"Yay! We found the key to the treasure chest." Over to you.

Sofia has plotted these coordinates.

Is she correct? So with the clue, she would've had to plot points 7,3, 10,3, 10,6, and 7,6.

Have a look carefully.

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

So what did you get? Well, Sofia has plotted the points correctly.

She's remembered that the x-coordinate is written first, and you find it along the x-axis counting from the origin.

And similarly for the y-coordinate, we start at the origin, and we look at the y-axis, and we count from the origin vertically upwards.

The main task for this lesson cycle.

So for question one, you're going to draw each polygon below using the coordinates, and then you're going to name each polygon.

So Clue A, you're going to plot points 2,4, 2,8, 5,4.

Clue B, you're going to plot points 7,6, 10,6, 10,9, 7,8.

Clue C, you're going to plot points 5,4, 3,0, 3,4, and 5,0.

Clue D, you're going to plot points 7,2, 9,4, 7,6, 5,4.

And lastly, Clue E, you're going to plot points 7,8, 7,9, 2,8, 2,10, 3,10, and 3,9.

Your hint is there, and it's 4.

For question three, you're going to identify the hidden polygon and the coordinates of its vertices to find the key and unlock the treasure.

You can pause the video here.

Off you go.

Good luck.

Have fun, and then click play when you're ready to rejoin us.

So how did you do? You should have got this.

So for Clue A, it was a triangle.

For Clue B, you should have got a trapezium, and it should have been positioned here.

Clue C, you should have got a rectangle.

Clue D, you should have got a square.

And lastly, for Clue E, it was an irregular hexagon.

Well done if you've got that correct.

Now did you find the key? The key is an irregular quadrilateral.

Its coordinates are 5,4, 7,6, 7,8, and 2,8 Well done if you've managed to find the key to unlock the treasure.

You've been successful in that mission.

Great.

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

I really hope you enjoyed drawing polygons specified by coordinates.

You should now understand that coordinates are recorded with the horizontal distance along the x-axis first and then the vertical distance along the y-axis.

And it's super important that we remember this rule.

Otherwise, when marking coordinates, we will get it incorrect.

You should also understand that plotted points can mark vertices of polygons, and that lines can be drawn with a ruler to connect points.

This will give you a more accurate drawing.

Thank you so much for joining me in this lesson.

I really hope you enjoyed it, and I look forward to seeing you in the next one.

Bye.