Lesson video

Hello.

My name is Mrs. Buchmire and today we're going to be exploring, different strategies to count cubes.

So first make sure you have a pen and paper.

Remember, you can pause the video whenever you like.

So do pause when I say, so when I want you to do a task, but also pause if you need time to jot something down, you want to draw something or write something out, but go at your own pace.

Also just to remind you, it's fine to rewind the video as well.

So if I explain something you're not quite sure, sometimes it does help to listen again.

So do you remember just rewind and have another listen? Let's begin.

So your first task is, there are four solids here and I want to know how many cubes, are used to make each solid.

Now I also want you to explain, how did you work it out? So just write down how many cubes are used and then you can even say out loud or write it down how you worked it out.

Pause the video and have a go.

So first I'm going to count the cubes in each solid.

So here I have one, two, three, four, five, six.

So six cubes.

Here so this there's one, two, three, four, five, six in the top layer.

And the bottom layer is actually a copy of it.

So there's also six.

So there's six plus six.

So the total is 12.

Did you get the same? Good.

How about this one? Yeah, there's six again and then here so in this row there are six, add those two you get 12 and then all three of them there is 18.

So maybe from how I kind of wrote my answers in there, you can see how I worked them out.

Was your similar? Did you think about them in layers? So the top player six, the next one six, next one six.

So you count six, 12, 18.

Maybe you did.

Oh, I know the top layer six and they're three.

So it's three times six, 18.

Nice.

So let's just bring that together.

So this one we said was six and you told me this one was 18.

Here's a big one.

This one might take you a while.

How many are there, there? I'm only going to give you 10 seconds.

Can you do it quickly? So I can see it's got the same top, which is six.

And there is one, two, three, four, five, six, seven rows.

So the total number of cubes, what do we do with six and seven.

There's six there's seven sorry.

Lots of six.

So seven lots of six.

So it's going to be seven times six equals there's 42 cubes.

So why does this work? Good, it works because it's the same, shape throughout the whole 3d solid.

What's the name of that? When we have an identical face on top, the identical face on bottom, line segments are straight.

Same cross section throughout.

Yes, it's a prism.

So these are prisms. When we have a prism, we can actually find out that top layer and then we can multiply by how many layers there are.

Does it always work though? Will it work here? No, this is not a prism.

So we can see that the top layer has two.

The second layer has three and the bottom layer has, one, two, three, four, five, six.

So total there's 11 cubes here.

So this method, yes it works, when we have the same shape, persistently throughout our solid but it does not work for all solids.

So I want you to be thinking about, Oh, when can I apply the method? And when can't I have apply the method, in our next independent task.

So you have a go.

This I'm not going to give you any more hints.

but do have a go and we'll go through it in a moment.

So pause the video, can go and look at the worksheet to do it if it's easier but do make sure you pause it and answer these questions to the best of your ability.

So let's go through this then.

So Binh says this solid is made from eight cubes.

She is incorrect.

What is the correct number of cubes? So this shape is actually like it is a prism.

So our top row has one, two, three, four, five, and there are two rows.

So the number of cubes is 10.

What mistake do you think she's made? I think maybe she got eight so I think either maybe she just saw, Oh, this is one, two, three, four, five, six, seven, eight.

And forgot about the two below this arrow here.

That's what I think, I think maybe she missed out those two and just the one that she couldn't see, she didn't include maybe.

Maybe thought she did something different wrong, I'm not sure.

How many cubes are used to make this solid.

So this solid is not a prism, but you can still use the method of the layers.

So the top layer there's one, two, three, four, and the bottom layer, there's one, two, three, four, five.

So all together, there are nine cubes.

What are the least number of cubes that needs to be added to form a cuboid? So again, I'm going to do it thinking about layers.

So in the top, I need like another cube here to kind of finish this bit off another cube here so I need two there.

And then similar here, I need kind of two cubes here.

So at the top layer, I need four extra cubes.

And what about the bottom? So we can say at the bottom the front line is full, but in the back line there's only one.

So we need three more.

So three.

So all together, we need seven more cubes so that it can form a solid.

And that makes sense, because we want the top and bottom rows to have the, layers to be the same because in a cuboid it's, a prism stays consistent throughout and seven plus nine is 16.

So top has eight and the bottom had eight.

So yeah, it works out here.

So the final tasks, I want you to think carefully about this.

Xavier makes a cuboid out of 24 cubes.

What dimensions could Xavier's cuboid have? Now there is support on the next slide, so if you're not sure, hold on, if you think, I think I can have a go at this, pause the video and have it go now.

So just for a bit of support, firstly, I've kind of lined up our 24 cubes there.

'Cause sometimes it might have to tick them off or and do drawings of them.

And now I'm going to actually, I've also got a little outline of a cuboid.

Now we don't need to use it or you can just help visualise it.

So like, if let's say I'm going to draw one cube here.

So that's one of my cubes and actually let's do it.

So this side has, should we say four.

yeah, let me pop this out then.

So this is my badly drawn cube, but the point is oops, that it doesn't matter how you draw it.

It's more about just checking.

So you can see that my cubes here.

There's four put together like this.

So this length of my cuboid is two and the height of my cuboid so far it's two.

So I've got four as that front face.

So now how many lots of four do I need to get to 24? So I've got one here, but how many going this way do I need so that all together to this we counting four lots of cubes, but all together there to be, enough to get to 24 cubes altogether.

But that's a hint.

If you solve that then do try and have another go with maybe a different faces like that first start starting block and I keep adding on until you get to 24.

Have a little play around.

It doesn't matter if you get things wrong, mistakes are how we learn.

Pause in three, two, one.

So what dimensions could Xavier's cuboid have.

Now one of them might be like this.

So actually they're being, I'm going to kind of draw in the lines to help you.

'Cause that's what probably you've done.

So four going that way and then say I like this.

I can not draw straight lines and then six.

That's five.

So that's six going across.

So one, two, three, four, five, six.

Four going upwards one, two, three, four.

So in each of these kinds of groups here, let me draw on it for you as well.

So you got one lots of four and there's six lots of them.

So six times four is 24.

So it does work out.

So that's similar to the support example.

I have four in my first one.

Did you work out it was six.

that would be six.

So it was two by two by six.

So here, what I've actually done with this one, is I have halfed this side.

So I halfed decided to make two, so we only got two as my height, but now that means I need to lengthen this side so that it would be two is the front but I need 12 lots of them to get to 24 and similar there see a half and half.

So maybe he's pointing a relationship like that.

Well done if you did and here are some more answers.

So this one here is the one that I went through on the support.

Well done.

If you've got those ones.

Good job.

Hey, how did you find today's lesson? What was one thing you learnt.

If you want pause and write it down.

Really, really good job today.

I would love for you guys to complete the lesson by doing the exit quiz.

And if you'd like to share your work with me and you can share it on Instagram, Facebook or Twitter tag @OakNational and make sure your parent or carer is sharing the work and #LearnwithOak.

Bye.