Lesson video

Hi, I'm Miss Kidd-Rossiter and I'm going to be taking you for today's lesson of cutting and combining shapes.

I hope you're really going to enjoy it.

Before we get started, can you please make sure you've got something to write with and something to write on.

You're in a nice, comfortable place, free from distractions, and if possible, the place that you're in is nice and quiet.

So you can fully concentrate on today's exciting lesson.

If you need to pause the video now to get anything sorted, then please do.

If not, let's get going.

So for today's try this activity, we've got four hexagons on your screen.

Your job is to combine two or more of these hexagons, and you've got to form a rectangle.

How many different solutions can you find? Pause the video now and have a go at this task.

Excellent.

There are so many solutions to this.

I can't possibly go through them all, but I will give you a couple.

So, I could have combined two like this to form a rectangle, I could have combined two like this to form a rectangle, and then, of course, I could have combined all four of them together like that to find, to form a bigger rectangle.

If I also introduced reflections of these shapes, and, then, I could have created one that looks like this as well.

So, there are absolutely loads there.

So, really good job.

Moving on to the connect part, now.

we've got full hexagons on the screen, again.

We need to find that area and the perimeter of each shape.

Form a compound shape by combining the purple shape, which is shape A, and the blue shape, which is shape B together.

And, then what is the area and perimeter of that compound shape? So, can you pause the video now, and have a go at working those out.

Please.

Here are all area and parameters for those four hexagons.

So, pause the video here and check your work if you need to.

So, we're now going to look at combining the blue hexagon and the purple hexagon.

So, that they will be on the last slide together.

There are lots of different ways that you could have done that.

So, I'm just going to show you one way and you can see whether what we figure out applies to yours as well.

So here's my compound shape.

It's got area of 24 units squared, and the perimeter of 24 units.

So, what do we notice about the area and the perimeter of this shape compared to the two shapes that we started with? Pause the video now and think about that.

Excellent work.

The area is the two areas, of our original shapes added together.

Isn't it? 17 units squared plus seven units squared gives me the 24 units squared.

Does this apply to your combination as well? Excellent, It does.

Doesn't it? So, so long as we don't overlap them, whenever we combine two shapes, the area is always the sum of their areas.

Or if we combine more than two shapes is the sum of all the areas.

What about the perimeter then? Is the perimeter just the two perimeters added together? So, 18 units add 12 units would give me 30 units.

Wouldn't it? And I've worked out that the perimeter of my shape is 24 units.

So what has happened there? Really good.

We've had to subtract, haven't we? The side that we've put together.

So we've got three squares there of the blue hexagon and three squares of the purple hexagon.

So, for the perimeter, we've done 18 units add 12 units, which is 30 units.

But, then we've had to subtract those three units twice.

Haven't we? So, 30 take away three, take away another three gives me my 24 units.

Is that the same for your example as well? It should be.

Maybe it's not a perimeter of 24 units, but you should notice that the bit is overlapped is what you need to take off.

So, now you're going to apply today's learning to the independent task.

So pause the video here.

Navigate to the independent task.

And, when you're ready to go through some answers, resume the video.

Good luck.

Well done for giving that independent task ago.

I hope you had a really good time doing it.

Let's go through some answers then.

So, the area and the perimeter of these two shapes are now on the screen.

So, if you need play, pause the video here, so you can check your work.

Then you were asked to combine these two shapes to make a compound shape that had an area of 18 units squared and the perimeter of 22 units.

Now, we know that whatever way we put these two shapes together, we will get an area of 18 units squared, because one is 12 and one is six units squared.

So, when we put them together in whatever way, we will get the area of 18 units squared.

So, the tricky thing here was figuring out how we get a perimeter of 22 units.

So if we added 18 units of 12 units, we got an answer of 30 units.

Didn't we? So, we somehow need to get eight units away, from that perimeter.

Take eight units away from that perimeter.

So, that means that we need to overlap sides of how many squares? Tell me now.

Excellent, four.

Because we'll take four squares of one perimeter, and four squares of the other.

So, this is what your answer should have looked like.

So, we reduced the perimeter by eight units by putting together two sides of four units.

Question three then, your answers on the screen.

So, the compound area is just the two areas added together.

So, 22 centimetres squared add 22 centimetres squared.

If we added the two parameters together, 24 centimetres add 24 centimetres, we would've got 48 centimetres, but we're placing two sides of five together.

So, that means we need to take five centimetres of both parameters to give us our compound perimeter of 38 centimetres.

Really good work.

Well done.

Finally then the explore task.

Explain why Antony's perimeter calculation is correct.

And then, can you investigate what parameters are possible by combining the two hexagons? Pause the video here and have a go at this task.

Excellent work.

Let's look at Anthony's calculation first of all then.

So, he has added the two parameters together, 18 add 12.

So, we know that that's the correct way to start, and then, he's taken off two.

why has he taken off two? Can you tell me? Excellent.

Because here we've got one unit touching of each hexagon.

So, we have to take one of both parameters.

So, we're taking of two altogether.

Let's now look at combining the hexagons.

So, there was lots of different ways to do this.

You could have combined the two hexagons, so that any number of units between zero and four were touching.

And when you did that, you should have worked out that the parameters were equal to, or more than 22 units, but less than 30 units.

There was also one more way to combine them, so, that more than four units were touching.

So, that's on the screen now.

And when you worked this one out, you should have found that the perimeter was 20 units.

So, your parameters could have been anything equal to, or more than 22 units, but less than 30 units or exactly 20 units.

Excellent work on that.

Well done.

Because you've probably drawn some lovely hexagons today.

If you would like to share your work with Oak National, please ask your parent or carer to share your work on Twitter, tagging @OakNational #LearnwithOak.

Hope you've really enjoyed today's lesson, as much as I've enjoyed teaching it too.

Don't forget to go and take the end of lesson quiz so,that you can show me what you've learned.

And hopefully I'll see you again soon.

Bye.