Lesson video

Hello! My name is Mrs. Buckmire, and today, I'll be teaching you about prisms and cylinders.

So, first, make you you've got a pen and paper and we'll be ready to begin.

Okay, so, Cala wants to split each shape into five congruent pieces.

Which of these would she be able to use to achieve this, using four cuts? Okay, so first, that word "congruent." What does congruent mean? Good, congruent means exactly the same.

So, exactly the same size and shape.

So, you can write that down if you didn't know.

So, you need to look at all of these different 3D shapes here, and think which ones, using four cuts, could be split into five congruent pieces.

So, pause the video have a go now.

Okay, so, I'm going to give you one example first, and then, I'm going to go through properly.

So, this one, this shape can be split into five congruent pieces.

So you can see we can make the cuts there, and here you'll find five kind of shorter, squeezed in of the original shape.

So, five congruent pieces there.

This one, could you do it? No, you couldn't.

So, even if let's just say we do one split we can already see we're creating a sort of triangular shape at the top and at the bottom will kind of be like a part is being cut off at the top, but it's not going to be congruent.

And even if we slice it some more, it's not going to be congruent, not going to be equal size and shape.

So, just quickly going through these ones, let's just tick and cross which ones could and can't.

Hopefully, you looked at them all.

This one you can.

This one, yeah, you can.

You can cut one, two, three, four.

And they'll all be kind of little sandwich pieces like that.

So, this one you could.

This one, uh-uh.

This one, what do you think? Yes, you can! This one? Yes, very similar.

This one's the one I went through.

No.

This one? Yeah, you can.

You can keep slicing it here.

These are really bad slices, but you can imagine this is a really thin one to do.

If that was kind of a roll, you could definitely do that, so yes for this one.

Yes, this one, yes as well.

Okay, so what is the definition of prism? All those I ticked but one was a prism.

So, what do you think the definition is? Hmm, a prism always has two identical polygon faces whose corresponding vertices are joined together with straight line segments.

Okay, let's break this down.

So, a prism is what we're talking about.

It always has two identical polygon faces, so first, this word "polygon," Do you remember what it means? So, a polygon is a shape with straight sides.

Faces, do you remember what faces are? Yeah? Few lessons back maybe? So, faces are flat surfaces.

So, faces are the flat surfaces for our 3D shapes whose corresponding vertices- so, here, This pentagon here, this is one polygon face and this pentagon at the back is the other polygon face.

And we can see the corresponding vertices.

So, this vertex would correspond to this one.

And there is a straight line between them.

So, this one and this one, straight line between them.

So, that's why, yes, this is a polygon.

So, why is this, in a non-example, why is this cylinder not a polygon? Sorry, not a prism.

We're talking about prisms, so this one is a prism.

Why is this one not a prism? Good! So, it's because of these polygon faces.

It doesn't have straight sides.

A circle is not a polygon, so therefore, it can't be a prism.

Okay, what I would like you to do is all these shapes at the top, I want you to sort these into examples and non-examples.

So, is it a prism? Or is it not a prism? Okay? Pause the video and have a go.

Okay, did you pause it? Make sure you did.

Make sure you've had a go.

Okay, so this first one, example or non-example? Good, it's a non-example.

The front face and the back face are not polygons- are not identical polygons.

They are polygons.

They're both rectangles, but they're not identical.

They're not the same size, so it's not a prism.

Good, this next one is- what about this one? It is not.

The next one? Good, it is not.

And this one? Is.

And the final one is not.

So, if you need, you can pause the video to check your answers.

And maybe, let's just have a look actually.

What is similar about the examples? Yes, they do.

You can actually see all the identical faces.

So, the front and you know that the back is going to be the same.

The front and the back.

We can see there it seems to be like rectangles in all of them.

Hmm, interesting.

Okay, so hopefully, that set you up nicely for the independent task.

Now, it does rely on some prior knowledge, so if you can a quick skim and you think, "Ooh, I don't know some words." Hold on a moment.

Otherwise, just go ahead.

Pause it.

Look at the worksheet.

Have a go.

Okay, so if you looked at some of the words and thought, "Huh? What's that?" So prism, you know what a prism is.

Maybe you wrote down the definition just now.

We went through some examples and non-examples.

You know it.

Vertices.

What are vertices again? What do you think? Yeah, they're the corners.

Well done.

A face, kind of just went through that.

So, it's the flat surface of a 3D shape.

The edge.

So, the edge connects to the vertices.

So, it connects the two vertices.

Kind of like running your finger along it.

That's the edge.

And then the rest I think you should know.

So, do pause it now and have a look at the independent task.

Okay, welcome back.

Hopefully you had a good go at that.

If there's anything you're unsure, feel free to look back at other lessons or beforehand.

Otherwise, I am going to go through all of the answers here.

So, a prism with eight vertices.

And vertices were the corners.

So, which one had eight corners? Good, you could've got C or F.

A shape with four faces.

There was only one answer here.

Excellent.

E, the tetrahedron.

All prisms which do not have a triangular face.

So make sure first that these are prisms and they can't have a triangular face.

So, which one? There's a few.

A, C, D, and F.

So, remember, they must be prisms. They must not have a triangular face.

Okay, a prism with twelve edges.

Good.

Again, it could be C or F.

A 3D shape with nine edges? Excellent.

It is B.

A prism with at least one square face.

Excellent.

F.

Now, it could be C, but we don't know if it's even.

We're not given the dimensions, so I actually wouldn't include C here.

A non-prism with five vertices.

G.

So, which shape was not included in any of the answers? Well, if you got it.

It was H.

Okay, before we go on to explore task.

I just wanted to have a quick discussion about cross sections.

So, a cross section is the shape we get when cutting straight though an object.

So, if we were going to cut parallel to the base, so, in the same direction of the base on this shape, what shape do you think the cross section will be? What shape do you think we will get? Good.

It's a hexagon.

So, we could cut there or we could cut there.

We can see that throughout the shape we get a hexagon.

And that is a common feature in a prism is the the cross section, when we cut parallel to the front face, the front identical polygon faces then we get that polygon face throughout.

So, we saw in the try this with the congruent four cuts with the prisms how it actually it replicates and get similar, well the exact same shape in that task.

And here we can see we can always get a hexagon.

So, what about if I cut, though, perpendicular to the base? So, at a right angle to the base, so downwards.

Hmm, I'd get a rectangle.

Did you guess that? Okay.

I get a rectangle and as I move around, it's still a rectangle.

But maybe not exactly the same size.

Hmm, this one's hard.

What about diagonal to the base? What do you think? Quite weird.

Here I could get a trapezium.

Or maybe I could get a triangle.

So, different ways to cut it to get cross sections of different shapes.

And that's what we're going to explore.

Okay, so my favourite task, the Explore.

Each of these shapes is the cross section of a 3D shape.

In each case, name a prism or cylinder and a non-prism that each of these could be the cross section of.

Now, if you feel confident, pause now and have a go.

Okay, so quick hint.

Maybe you ought to look back at the worksheet independent task and look at those shapes and kind of pair them up.

Oh, which one could create a cross section on the circle.

Which one on the triangle? Which one on the rectangle? So you can use the past shapes to help you if you like, okay? So, everyone, pause it now and have a go.

Okay, so each of the shapes is a cross section and we're trying to name a prism or cylinder and non-prism.

So, the first one, I definitely can see that it could be a cylinder because it's got that circle, that face at the top.

Um, so if it's a non-prism, maybe we could do a cone if we lift it from below and we cut off the bottom.

What about this one? Excellent, a triangular prism.

And what about a non-prism? Good, a tetrahedron.

So, that was in the independent task.

And the rectangle? Yeah, a cuboid.

And the non-prism? Good, so we could have a sort of pyramid.

Well done if you get those.

And maybe you got some other ones.

Good job.

Really really well done today, everyone.

Hopefully, you do understand better what a prism is and what is not a prism.

Is a cylinder a prism? No! Good.

Well remembered.

Do have a go at the exit quiz, and I'll see you next lesson.

Ooh! If you want to share your work, you can share it on Twitter, Facebook, or Instagram, but you need to ask your parent or carer to share it first.

Tag @OakNational, #LearnwithOak.

I'd love to see your work.

`Okay, bye!.