Lesson video

Hello, and welcome to this lesson on tessellating quadrilaterals.

With me Miss Oreyomi.

For today's lesson, you'll been needing a paper, squared paper if you can get square paper, a pen, a pencil, and also a pair of scissors might come in handy too.

So that's a pen, square paper if you have one, plain paper is just fine, pair of scissors and pencil.

If you need to pause the video to get those things then please do so.

And then when you're ready, come back and press play to resume the lesson.

Okay, in today's lesson, you will be able to use the properties of triangles and quadrilaterals to create and describe tessellation patterns.

If you're not sure what tessellation is, hang in there, and we're going to find out very soon.

Okay, you'll try this task, use a squared paper.

If you don't have squared paper, you can draw a four by four grid on line paper.

And you can also draw the shapes as well, this four coloured shapes, on plain paper as well.

Using what you've drawn, place this four coloured shapes into the grey square, so that they fill in the space.

So there shouldn't be no gaps, after you filled in the space.

How many ways can you fill in the square? So Pause the video now, and attempt different ways you can fill in the square ,with these shapes without space.

These are some of the ways we could fill in the, fill in the square grid, using the four coloured shapes, so that they fill in the space.

You can have, you can fill it eight ways without.

If we ignore the rotations, and it will be 32, if we do not ignore the rotation, so eight ways, ignoring the rotations and 32 ways if we don't ignore the rotations, how many ways did you manage to come up with? Okay, what do we mean by tessellation then? Tessellation, is the arrangement of a 2D shape that covers a surface.

And when I arrange this 2D shape over the surface, there are no overlaps and there are no gaps.

when I tessellate them.

So this student, as they've drawn a tessellation pattern using a kite.

So we started with this white kite, and they have tessellated the shape, onto the surface and you can see there are no overlaps there are no gaps.

So the pink, kite, isn't jumping over the white Kite and the white Kite, isn't covering the pink Kite, they're just tessellated, next to each other, they just tessellated next to each other, no gaps whatsoever.

So your turn, can you, cut out a picture of a square or perhaps just draw it in your book? Can you tessellate? create a tessellation pattern, for each of the following tiles.

So you can either cut out a square, a parallelogram, a right angle, scaling triangle or an isosceles triangle.

So you can choose to do two or three, can you create tessellation pattern, for each of the following tiles.

Once you finish, resume the video, and then we can carry on with the lesson.

Okay, if you manage to complete that task, these are some of the ways you could have started tessellating your rectangle and tessellated your parallelogram.

You would notice then that, if I am tessellating my rates and the scaling triangle, I am tessellating my isosceles triangle, I could have done that, by splitting, the, my parallelograms along the diagonal.

So I could find, tessellated patterns for my triangles, by splitting my quadrilaterals along the diagonals.

Right, your task now is using a square grid , Can you sketch and cut out eight identical scaling quadrilateral.

These are some examples, that you could use to, you could use as your scalene quadrilaterals, but you can draw any quadrilateral.

Any scaling quadrilateral, and then your job is to cut out and arrange the quadrilateral so that they tessellate, So pause your screen now and attempt this, and I am going to show you a video of what I did of my tessellation when you resume the lesson.

Okay, it is now time for your independent tasks.

So pause the video now.

Complete your task and then come back when you finish, and will go for the answers together.

Right, for the first one, it's a fill in the gap activity, a tessellations.

So tessellation should have been the first word there, is the tiling of a region using one or more shapes called tiles, with no gaps and no overlaps.

In this example, the tiles used are a kite and a delta.

Yeah.

Secondly, create a tessellation pattern using eight copies of each of the following triangles.

I have tried my very best to do this.

And this is what I came up with.

So this is the first one, the second one, this line should be a bit blurred just there, but you get the idea of, and the tiling of a pattern with no gaps or overlaps.

And again, C and D is looking something like this.

Did you get something similar? Did you go that way? Or did you go that way, the way i did it? Okay, next one, copy and complete the tessellation pattern using an additional eight deltas.

I decided to put five here and three here, or in your case, five here, three here.

So, that is me completing the tessellation pattern using eight additional deltas.

Let's do this question very quickly, we want to to find out, the angle for each of the tile.

So I've got my arrowhead right here.

And I know that angles around a point, is 360.

And I've got one, two, three, four, five, So I want to work out the angle for one, part of, this.

So I'm going to divide that by five and that is going to give me 72 degrees.

So this here is 72 degrees.

If I go to the other two, I've got my Kite being been tessellated.

And again, angles around this point add up to 360.

So this bottom angle here would be, 72 degrees.

Okay, let's move here.

I've got my arrowhead here, and I also have my kite at the bottom here.

So I've got arrowhead or delta rather, delta, delta, delta, then kite, kite, so also, the angle.

So if we go to the third one, I've got my Kite here, if you can see the outline of my kite shape here.

So I am trying to work out what this angle here would be, this angle over here.

Again, it's angles around a point add up to 360 and there are one, two, three, four, five points.

So this angle here would also be 72 degrees.

What do we know about a kite? We know that this angle here, is the same as this angle over here.

So this is 72 degrees.

Can you work out what the missing angle will be at the top? Let's move on to this one.

So I know that I've got 72 degrees here, and also have 72 degrees here.

So I want to know what this angle over here would be.

So this shape here, again, I know that angles around a point, add up to 360, So I've got 360.

Takeaway away 144 and that's going to give me 216.

So my angle here would be 216.

Well, am I done? Not quite.

I've got this and I've got that.

I know that angle in a quadrilateral will give me 360, so I need to work out what this is, and what this is.

So I am going to add, 216 take that away, add 216 to 72, and take that away from 360.

That is going to give me 72.

And I divide that answer by two, because I know that, this angle over here and this angle over here are equal.

So this is going to be 36 degrees, and 36 degrees.

Have you worked out what the angle on the top should be? It would be 144 degrees.

So, every time you see that angle over here, you just add it all up to find the interior angle.

So for example, this one here would have 36, 36, 72.

You do that five times, and you work out the interior angle for each one of them.

If we explore that, but taking a bit further now, instead of just using one pattern, instead of just using one shape to tessellate, can you create a tessellating pattern using two of these shapes? So, there are three different types of quadrilaterals on your screen, can you create, a tessellating pattern using two of the shapes? So I want you to pause your screen now and attempt this task.

And then one year once you're ready, press play to resume.

Here are some of the answers you could have come up with, using two different shapes would give me a pattern like so.

So seeing if you've got the same thing or if you've got something different.

Okay, we have now reached the end of this lesson on tessellating.

There are so many opportunities for you to see tessellation in real life, and for you to keep on practising as well.

So please do so.

And I'll see you, at the next lesson.