Lesson video

Hello, everybody.

My name is Mrs. Johnson.

I'm really excited to be here today to help you with some of your maths learning.

I hope that you are ready to work hard and have lots of fun? Let's have a look at what we're going to be learning about today.

Today's lesson is called, Explore ways that cubes could be composed into different arrangements.

It is from the unit, Recognise, Compose, Decompose, and Manipulate 2D and 3D Shapes.

By the end of this lesson, you will be able to explore, discuss and compare the different arrangements that can be made with cubes.

Don't worry if you haven't learned about anything like this before because I am here to help you and we will work hard together.

There are two key words that we will be using in this lesson, which are cube and arrangement.

Let's practise seeing those.

Ready? My turn, cube, your turn.

Well done.

My turn, arrangement, your turn.

Well done.

Listen out for those two words, cube and arrangement, throughout this lesson, they are going to help you with your learning today.

There are going to be two parts to this lesson.

To begin with, we're going to look at arranging cubes, and in a little while, we're going to look at how we can change arrangements.

Let's start by looking at arranging cubes.

There are going to be three friends helping us in this lesson today.

We are going to have Izzy, Laura, and Andeep as well.

Sometimes these children can give us helpful hints and they can tell us things to look for, so make sure you're looking out for these three today.

Have you ever played with cubes like these? I wonder if you have any in your classroom at school or maybe at home? You might have done some counting with them before or you might have built things with them before.

They're lots of fun to play with, aren't they? Andeep has been playing with some cubes like that.

Look carefully at what he's made, think about what you notice.

He's made three different things.

I'm noticing that there is something the same about all three of the things that he has made, I wonder if you've spotted it too? He has used four cubes each time, but he has built different arrangements.

"First," he says, "I joined four together in a straight line." That's what we can see in the first picture.

"Then," he says, "I joined three together in a straight line and put one on top of the first cube, and next I joined three together in a straight line and put one on top of the middle cube." So that's how he put his cubes to make three different arrangements, but they are all the same because they all have four cubes in them.

Let's explore this together now.

I would like you to use four cubes of your own and to go and find out what arrangements you could make.

Laura says, "Make sure that they are connected," so that means joined together.

Go and use your cubes to see what arrangements you can make.

Okay, shall we have a look at the type of arrangements that you might have made? I wonder if you made four in a straight line, like this.

Did you make three in a line with one connected, maybe like this one or maybe like this one? Did you make two lines of two cubes that might have looked like this or like this one, or did you make a different arrangement? Maybe you made something that looks like this.

There are lots of different arrangements that you can make with four cubes.

Let's check that you understand an arrangement of four cubes.

Who has made an arrangement of four connected cubes? Is it A, or B, or C? It is C, well done if you said C.

A does have four cubes, but they are not connected, and B does not have four cubes, it only has three.

How many different arrangements of four cubes do you think there might be? I'm going to show them to you, let's see if you can count them.

How many different arrangements are there, ready? One, two, three, four, five, six, seven, eight.

There are eight different arrangements that you can make with four cubes.

You're going to do a quick check now to make sure that you can match the photo to the correct arrangement.

Look carefully at this photo.

Whose arrangement matches the photo? Do you think it could be A, B, or C? The arrangement that matches the photo is B, well done if you said B.

Let's try another one.

Look carefully at this photo, whose arrangement matches the photo? Is it A, is it B, or is it C? This time the arrangement that matches the photo is B again.

Okay, you've got one more question.

Whose arrangement matches this photo? Is it A, is it B, or is it C? The arrangement that matches the photo is C.

Well done if you said C.

Now we're going to think about what these children might be able to see.

I can see that they are both looking at a shark, but they're standing in different places.

Andeep is standing near the tail of the shark and Laura is standing near the mouth of the shark.

Can you picture what Andeep might be able to see and what Laura might be able to see when they look at the shark? Let me show you.

Andeep would see the shark from the back, so he would see the tail first, whereas Laura is near the mouth, so she would be able to see the head of the shark at the front.

So even though both children are looking at a shark, what they can see looks different because they're standing in different places.

Sometimes things can look different because we are looking from a different perspective, that means we are looking from a different place to somebody else, so Andy and Laura can both see the shark, but they can see different parts of the shark because they're standing in different places, they have a different perspective.

Other times things can look different, but not because we're coming from a different perspective, but because the object has moved or been rotated.

That's what we're going to look at a bit more now with our cubes.

Andeep is building an arrangement of four cubes.

Let's listen and watch to what he's going to build.

He says, "First, I will make a tower of two cubes." There is his tower of two cubes.

"Then I will join one cube on the right at the bottom." Let's see where that one's going to appear, can you picture where it's going to show? There it is.

"Then I will join another cube behind that one." Can you imagine where that one's going to go? Let's see if you're right.

There it is.

So Andeep has built an arrangement of four cubes.

And then Laura says, "I am going to rotate your arrangement." Let's see what happens.

Laura is rotating the arrangement.

She's spinning it round.

I'll let you watch it a little bit longer.

The arrangement is rotating.

Okay, so we just watched that Laura rotated the arrangement, and while it was rotating, sometimes it looked like this, but other times it looked different, so it could have looked like this or this one or this one as she was rotating the arrangement around.

But what do you notice about the arrangement? Let's have a think about that together.

Do you think any of the cubes moved? Do you think the arrangement changed or do you think the arrangement stayed the same? Laura says, "I can see the arrangement is still the same." She didn't move any of the cubes, she just rotated them, so she didn't change the arrangement, the arrangement stayed the same.

Andeep says, "Maybe you could arrange four cubes and see what they look like when you rotate them so you could be like Laura." Maybe a bit later on you could go and get yourself four cubes, build an arrangement, and then rotate it like Laura did and see what it looks like.

Let's check if you can match the arrangement to the photo, but this time the arrangements have been rotated.

Are you ready? Look carefully at this photo.

Whose arrangement matches the photo? Do you think it's A, B, or C? If you have got some of your own cubes there, you could use your own cubes to help you work this out.

Pause the video if you need a little bit longer to do that.

The arrangement that matches the photo is C.

Well done if you've said C.

Let's have a look at another one.

Look carefully at the photo.

Whose arrangement matches, do you think it's A or B or C? It is B that matches the photo.

Good job if you said B.

We have one more check.

Look at this photo carefully.

Which arrangement matches? Do you think it's A or B or C? The arrangement that matches the photo this time is A.

Well done if you've said A.

Now it's time for you to go and do a little bit of practise with making arrangements of cubes.

What I would like you to do is use your cubes to make each arrangement that you can see here.

See if you can rotate them and explore what they look like when they are rotated.

The last thing I would like you to do is look at the pictures carefully, see if you can match the arrangement on the top row to the arrangement on the bottom row that is the same.

Off you go.

You have worked really hard building all of those different arrangements, well done.

Did you make sure that you joined your cubes together to make sure they were connected in each arrangement? Good job.

Let's see if we can match the top row and the bottom row to show which arrangements are the same.

I'm going to make each pair a different colour so that you can see which arrangements go together.

The two orange arrangements are the same, these two purple arrangements are the same, these two pink arrangements are the same, and the last two blue arrangements are the same.

Well done if you were able to match those arrangements, good job.

Now it's time to move on to the second part of our lesson where we're going to think about how we can change arrangements.

Izzy has made two arrangements.

Let's have a look at them.

Here's her first one and here's her second one.

Can you see anything that's the same about those arrangements or can you see anything that's different? Hmm, let's think about that together.

There is something the same.

Both arrangements have a straight line of cubes, but they are not exactly the same, they are two different arrangements.

Let's see if Izzy can help us to tell us what is different.

Izzy says, "One arrangement has four cubes in a row, the other only has three cubes in a row and one on the bottom." If you look carefully at Izzy's two arrangements, you can see that you can move a cube to a different place to make a new arrangement.

That is what Izzy has done.

Watch these cubes to show how she moved one cube to make a new arrangement.

Ready? She moved one cube from the end and placed it on the bottom, making a new arrangement.

Let's watch Izzy do that a few more times.

So Izzy has this arrangement.

Let's watch her move one cube.

She has made a new arrangement.

Let's see if she can do it again.

She has made another new arrangement by moving one cube.

And one more time, which cube is she going to move this time? Did you see it move? Let's check if you can do this too.

Izzy has an arrangement here.

If she moves one cube, which arrangement could she make? Could she make A or could she make B? If you would like to use your own cubes to help you, you can pause the video to go and do that now.

If Izzy moves one cube, she could make the arrangement that is in B.

Well done if you said that.

Let's watch her move it.

Okay, and let's do one more check to make sure that you can do this too.

Same question, if Izzy moves one cube, which arrangement could she make? And again, if you'd like to go and get your own cubes to do this, you can.

Could she make A or could she make B? If Izzy moves one cube, she could make the arrangement in B, well done if you said B.

Let's watch her move that cube.

And there is the new arrangement.

Sometimes when you move a cube it will be the same as another arrangement that you have already made, but it might look different because it has been rotated.

Let me show you an example of that.

Izzy has made an arrangement and Laura has made an arrangement, which is different.

Laura says, "I'm going to move one cube to make the same arrangement as Izzy." Let's watch what Laura does.

Did you see that cube move? And now Izzy can see, "We have the same arrangement, but yours is rotated." So Izzy's arrangement and Laura's arrangement look a little bit different because one of them is rotated, but they are the same arrangement.

Let's see if you can do that too.

Izzy has made another arrangement.

Here it is.

But she was trying to copy Andeep's arrangement.

She hasn't quite got it right yet.

Can you help her to see which cube could she move so that her arrangement and Andeep's arrangement are the same? If you would like to go and get your own cubes to help you with this, pause the video to go and get them now.

Let's see which cube Izzy is going to move.

There we go.

Did you say that she should move that cube? Well done if you did.

Now Izzy's arrangement and Andeep's arrangement are the same, one of them is just rotated.

Andeep says, "We both have a corner shape with one more cube in the middle.

That is how we know that the arrangements are the same.

They are both a corner shape with one more cube in the middle." Now it's time for you to go and do a little bit more practise.

This time you're going to make an arrangement with four cubes, and then you are going to move one of your cubes, and I want you to find out what other arrangements can you make by only moving one of your cubes? When you've done that, I want you to look carefully at A and B.

I would like you to have a think.

How many cubes do you need to move to change arrangement A into arrangement B? Make sure you have your cubes ready.

Off you go.

Well done for trying so hard to change your arrangements, you have done such a good job.

Let's have a look at some and see if you've done something similar to this.

You might have started with an arrangement like this and you could have found out that if you move only one cube, you can make any of these arrangements.

You could make this one, or this one, or this one, or this one, or this one, or this one.

Wow.

Only by moving one cube, you could make six different arrangements.

That is amazing, well done if you found that out.

Now let's have a think about how we could change arrangement A into arrangement B.

How many cubes would we have to move? Let's have a look.

If we move one cube, the arrangements still don't match, do they? Let's see if we need to move another cube.

Now that we have moved two cubes, the arrangements are the same.

Now that we are at the end of the lesson, you know that you can make eight different arrangements of four cubes by joining them together in different ways.

You have learned that you can move cubes to make different arrangements.

You have also learned that sometimes you can match arrangements together, because even though they look a little bit different because they might have been rotated, the arrangement is still the same.

You have worked very hard today.

Well done, everybody.

I will see you again soon for some more maths.

Bye.