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Welcome to our eighth lesson in our coordinates and shapes topic.

Today, we'll be solving problems involving 3-D shapes.

All you will need is a pencil and piece of paper.

Go and get your equipment now, if you haven't already got it ready.

So today we'll be solving problems involving 3-D shapes.

You'll start with a knowledge quiz to test your learning from the previous lessons.

Then we will look at identifying the nets of pyramids and prisms, before we solve net problems, and then some final independent learning.

There won't be a final quiz for today because what we're learning today is going to require lots of thinking, and lots of hard work, and then I think that that will be enough for today.

So, let's look at the nets of pyramids and prisms. I want you to look at these two nets and think about what 3-D shapes do they create? So the first net, you can see that it is made up of a pentagonal base, and then one, two, three, four, five triangles.

So you know that this is going to make a pentagonal pyramid.

The second shape is made up of two pentagons, and one, two, three, four, five rectangular faces.

So you know that this one will make up a pentagonal prism, which will have a pentagon at either end of the 3-D shape.

So now I want you to take a moment to look at the two nets and think about what is the same about them and what is different.

Well, we can see that they both have a pentagonal face.

This one has one, and this one has two.

So part of the 3-D shape is a Pentagon.

What else can we see is the same? I think that that is the only thing that we can see is the same.

The difference is that obviously this one has two pentagonal faces, but also in the second net, the five other shapes are rectangles.

And in this one, the five shapes are triangles.

So we know that when we fold this net up, these vertices here will join to meet at an apex.

Therefore they will be making a pyramid shape.

In this shape, however, these rectangular faces will fold over, to create a prism with these two pentagonal faces at either end.

So it will be more tube like, than this one, which will meet at an apex.

So let's have a look at these 3-D shapes.

Here We have a pentagonal pyramid, which is what the previous net would fold up to create, this pentagonal pyramid.

And here we have our pentagonal prism.

Now have a look at these nets.

And the key thing here is to visualise folding the nets.

In these three, one of them will fold to make the pentagonal pyramid.

So which of these three will fold to make the pentagonal pyramid.

And which of these three will fold to make the pentagonal prism.

Pause the video and visualise folding the net.

So for these three nets, we can see that this purple net is the only one, where, the top vertex of all of the triangles, are meeting at an apex.

And these ones, you can see that the top vertex, is not joining, therefore you can see for the rest of it, that they will not meet at an apex.

Therefore, this one will not make a pentagonal pyramid.

Neither will this one, because you can see that at the top, you will have some flat sides joined together, and not just the vertices.

It's all about visualising the folding here.

So this one will not create the pentagonal pyramid, because you have to think about this apex part of it.

And none of these will join to make an apex.

On this side, we've also got only one that will work.

Looking at the orange one, I can see that with these pentagonal faces being on the same side, they will not fold, because to make a pentagonal prism, because the two pentagonal faces have to be opposite each other.

So they needed to be separated by a rectangle, and they needed to then fold in to make the pentagonal prism.

So this one will not work because the pentagons are on the same side.

This one will work, because although they're not directly opposite each other, they're opposite each other on the sides of the net.

And they will fold around, this will fold around and they will meet to become opposite.

So this one will work.

Finally, this one certainly won't work, because we've got a pentagon here half way down, one of the rectangles, so that won't join to meet any of the other edges because it's in the centre, of one of the faces.

Now, this is a really tricky concept to get your head around.

It is very hard to visualise nets.

So, my advice to you is to sketch out the nets, cut them up and check whether they would work or not.

That's the best way to get your head around that.

Because it's a really tricky concept.

And if you're thinking about answering questions in an assessment, where you won't have the net to fold up, you need to be able to visualise that.

So while you have the chance now, it's a good idea to practise folding those nets.

So if you can, you can either sketch them and cut them out and fold them up or, even better if possible, if you can get the nets off the internet, and print them out and then cut them, then you'll have more accurate shapes.

So now we're going to move on, to solved problems with 3-D shapes.

And I'm going to put myself back on the screen, because I'm going to show you how to solve this problem.

So, hi.

This is a question involving a cube.

The cube has shaded triangles on three of its faces, and here we've been given the net of the cube, and I have printed out the net of the cube, okay.

You have to draw in the two missing shaded triangles.

So again, you need to learn how to visualise this, but in the meantime, it's a good idea for us to have a look at it on an actual cube.

So I've got my missing, one of my shade of triangles, and I'm going to fold it up, so I can see what part of the net, will be adjacent to which part, which will be opposite, because these are things that are going to help me when I'm coming to fill in my missing triangles.

So I can see folding it up, that this side here is going to be adjacent.

And I think that this will be an important part.

So if I unfold it, I can see that it was this square on my net.

So this square here, is going to be adjacent to this one.

It's going to fold up and they're going to be adjacent.

Okay.

Then if I fold it again, I'm looking for which face will make up the top bit here.

And I can see that it's this one.

So I unfold it and it's this one here.

So I can see that my triangles are going to be going on to those two squares, there, those two faces.

So I'll go back to my folded shape, and I'll get it in the right orientation.

Okay.

So if I look back to the picture at the top of the slide, I can see, that there's going to be a triangle on this face here.

Okay.

And I can also see that there's going to be one on this face here.

I'll show you this quickly in a minute.

Okay, so now I've got my shape that has got a triangle, on those three, the sort of, let me try and put this properly, to the outer parts of these three faces, where they meet at a vertex.

So if I unfold it, I can see where those two triangles have gone, okay? They are now on these two, I'll keep it this way so you can see.

That on these two squares here, like that.

And they fold over to meet and make up the image that was on the top cube, okay? So, it's what you have to do is visualise unfolding the cube and thinking about where each triangle will be on the net.

So you're going to do the same now with this next question.

A cube has been shaded, has sorry.

The cube has shaded shapes on three of its sides.

So you can see it's got part of a, part of the square here.

So it's got a small rectangle here, a small rectangle here, and it's got a semicircle on here and a semicircle on here.

So you've been given the net of the cube, and have to visualise how the net folds back, into the cubes so that you can add on the missing shapes.

So pause the video and take a moment to try and visualise how the cube folds to put in the missing shapes.

So I have printed this one off as well, so I've got it in front of me, and this is going to help me to visualise.

Now, the first thing I'm going to look at, is the semicircle.

So I think if I folded this down, which face, is going to take the rest of the semicircle.

And if I unfold it, I can see that it will be this face here, which on my net is this face here.

So the semicircle is going to go here.

And I'm going to add that on to my actual net, so that I can visualise it in real life.

Okay, so I can put my vision into reality.

So I can see now I've got drawn on the slides, is going to work with my cube.

Okay? So next, I'm looking at the square that has been separated into two rectangles.

So I know that if I fold this part round here, then I can see that this face is going to need to have the other part of the rectangle.

And I unfold it.

I can see that it's the one next, to the one with the semicircle.

So it's going to be this face here.

So I fold it round and I can confirm, that that is going to be the position for my rectangle.

So I put it on there, as neatly as I possibly can.

And then I'm going to add it onto my net.

Just check.

Okay.

So I'll fold my neck all the way up and then see, does this work? Sorry.

It's very fiddly.

No, I dropped it.

Okay.

So I've got my, circle at the top.

And then if I turn it round, I've got my rectangle over both of those.

I hope you can see that, okay.

So you can see that if you cut the actual net out, it's easier for you to visualise it.

Now, that is all that we're going to do.

There's going to be some independent learning time now.

So you've got lots of questions to answer.

Some of them are going to take quite a lot of thoughts.

And my recommendation is that you try to cut out the net, in order to answer the questions where it is necessary, especially on your last question, okay? So pause your video now and complete your independent tasks.

And once you finished click restart, so that we can go through the answers together.

Okay, well done for persevering.

So, let's have a look at question one together.

So Sope, has this shape, and he has moved it.

So it's in a different orientation.

And you had to draw the circles on the shape, in its new position.

So you could see, it looks a bit like an owl.

That you had a circle on the very top of the owl, and then a circle on this sticking out bit of the owl, the top of that as well.

So your circles should have been in these two positions.

Okay, started off straightforward.

Now we're going to move on to something that we've looked at before.

So we're looking at opposite faces of the shape.

So on each shape, you needed to draw one more dot so that they have dots on opposite faces.

So you remember that opposite faces needed to have a square or a space in between in the shape in between them in this case, a square.

So you know that on the first shape, that opposite face is here.

And then on the second one, you leave a space and it's over here.

So this is where your two dots should have moved to.

Okay, now we're moving on to some more complex visualisation.

So cubes have been stuck together to make this block.

And the block has the pattern on the two faces.

So we can see on the face, the face facing us, it has two Xs at the top, a circle and a square.

And then on essentially the top face, it has a square across, and a circle.

The block is then turned.

So you needed to draw the missing parts of the pattern on it.

So what you can see is that has been turned on its side, and then rotated so that this space is now here.

And it has been turned 90 degrees, in order to have the square up at the top.

So thinking in relation to where that face was, your new face is your new position of this top face, is here right in front of it.

So our X is the most straightforward one to do that goes in the middle, on the left.

Then we know that, the square goes underneath that at X, if what's in it's new position or next to it, if you imagine it in its own position, and then the circle at the top, in the middle.

Okay, now we have some visualising of the back of cubes to do here.

So, Iman has some cubes with a cross on each face, and some cubes with a circle on each face.

So she sticks the five cubes together.

So, we need to know how many crosses and how many circles are there on the outside of the sheet.

So we know that a cube has six faces.

So that's important information for us to remember.

Now, for each of these X cubes, there are actually two head and faces.

So we can't see the face, on top of this one.

And we can't see the face round to this side, and the same here.

We can't see this face here.

And we can't see this face under here.

So you have to visualise that.

So the X cubes, each of them had four Xs showing.

And because there are two X cubes, we can see that they would have eight Xs showing.

So we've got one, two, three, and then one behind it here.

And then one, two, three, and one behind there, so that's eight all together.

So we've got eight Xs.

And then if we look at these two circle cubes on the end, they each have one face hidden on the bottom here and on the top here.

So they've got five circles and there's two lots of them.

So that's 10 circles on the end too.

And then don't forget the middle one.

This has got this side blocked off and this side, so it's only showing four faces, so that's another four circles.

So we've got eight Xs showing and 14 circles showing.

Now this was the final question.

And this was a case of trial and error.

So below here, you can see, this is one variation.

You may have not found different variations of the same, of the combinations.

And the key here was to make the net of the cubes that you, oh, sorry of the faces that you could see and then build on them as you went along.

Now, if you would like to see a proper work solution, you can go onto this website here to search for the solution, which will show you how this answer was reached.

If you didn't manage to reach an answer, I really recommend that you draw these symbols, onto some squares and just do trial and error.

Try sticking them together in different orders and see if you can reach the correct answer for these combinations of shapes on the cube.

That was a really tricky one, though.

That would be very impressive, you persevered with that one.

So there's no final quiz today.

You've worked extremely hard on these really tricky questions, so well done.

In our next lesson, we will be illustrating and naming the parts of a circle.

And if you can get something that you could draw around, that has a circular face, such as a mug or a tin of beans, that would be great.

And you also need a piece of string.

I'm looking forward to seeing you then, bye.