Lesson video

Hello, I'm Miss Brinkworth.

I'm going to be going through this math lesson with you today, which is building on your knowledge of perimeter.

So if we look at the learning objective, what we're doing today is we're drawing shapes after we've been given the perimeter.

So in previous lessons with previous learning, hopefully, you've had a bit of a chance to look at how we calculate perimeter.

This time we're switching that around, you've been given the perimeter and it will be for you to construct the shape.

We're going to go through it together.

So let's have a look at the agenda for this lesson.

We're going to be constructing rectilinear shapes.

So these are shapes that have the properties of rectangles, but we're going to look at that in a little bit more detail.

We're going to be investigating perimeter.

So we're going to be looking at what we mean by perimeter, and how we can work it out.

We are then going to have a chance with some independent tasks, and there'll an exit quiz at the end as well.

Nope, my apologies, sorry, there will not be an exit quiz at the end of this lesson, my apologies.

That's because it's an investigation style lesson, so you won't be having that exit quiz.

Just before we get ready, just make sure you've got a pen or pencil and some paper, a ruler would be quite useful, but if you can't find one, please don't worry, it's going to be absolutely fine with that one.

So take as much time as you need to get your equipment together please.

Okay, so let's start with a little warm up, have a look at these shapes and decide what, if anything, they've all got in common.

Well, they all look completely different, don't they? But hopefully you can see that they have all got right angles.

So these are sides that meet at 90 degrees, they make a right angle, which is the corner of a square.

It's a sharp corner which meets at 90 degrees.

So they all have got those.

This is what rectilinear shapes means, it means that they all include right angles.

Okay, so here's a bit of a warm up for you.

On your worksheet, you've got this dotted paper, can you have a go at making three different shapes, those rectilinear shapes, so the ones that have got right angles, with a perimeter of 16 units.

So for today's lesson, when we talk about units what we mean is that space between two dots.

So they must all have right angles that are 90 degrees.

All the angles must be 90 degrees, so you're only going to be drawing horizontal and vertical lines, and have a go at drawing three different shapes where the perimeter, the outside of the shape is 16 units.

Okay, I'm going to show you mine, but yours will probably look completely different.

So let me show you, here are some that I came up with, maybe yours look similar.

So they've all got a perimeter of 16 and they are all rectilinear, they've all got right angles, all the lines meet at right angles.

But as you can see, they all look different, and I'm sure yours all look different as well.

The point of that is that shapes can have the same perimeter but look completely different.

So that's going to come in really handy to remember as we go through today's learning.

So for today's learning, what's important is that you've got the worksheet out for you to have a go at drawing them.

If you can print it, that'd be great, if you need to use it on the screen and in some form as well, that's okay.

So have a go now, the first one is to, on your paper create rectangles that have got four equal sides of five units, and then another one with two sides of nine units and two of four, and then another one with two of ten and two of five, and then a four equal sides of seven.

Once you've drawn them, can you have a go at working out what the perimeter of them all are? So have a go at drawing them and then have a go at working out what the perimeter is.

Okay, let's have a look at how you have drawn them.

So the first task was to draw four equal sides of five units.

So that can only look like this.

It's got to be a square where all the sides are the same length, because you're told four equal sides of five units.

So yours might be somewhere else on the paper but it's got to look like that, it's got to be a square.

So when you get that, hopefully, you were able to work out that the perimeter must be 20, that's because we've got five, 10, 15, 20, five, 10, 15, 20, or four times five is the quickest way to work that one out.

Your next task was to draw a rectangle where two sides were nine units and two sides were four units.

So we know we've got two longer sides and two shorter sides this time.

How do you work out the perimeter then? Obviously, slightly different to a square because on a square all the sides are the same.

But on a rectangle we have two are the same, and two that are different, but again, same to each other, so adjacent segments that are opposite each other are equal.

So we have two short sides, which are fours, so we've got two fours and we've got two nines.

So we've got nine add nine, add four, add four.

Well, we could do nine times two add four times two, we'll get the same answer.

Really, really well done if you could see that actually what you could do is nine add four, and then times that by two, that's probably the quickest, most efficient way of working out the perimeter of a rectangle.

Okay, this third task then, task C, was one with two sides of 10 units and two sides of five units.

I wonder if, when you got to this point in your worksheet, whether some of you started thinking, I can work out what the perimeter of that is without drawing it out.

If you did, fantastic.

If you carry on drawing them out, that's obviously absolutely fine as well.

So we've got two long sides of 10 and two shorter sides of five.

And again, to work out, we could do 10 add 10, add five, add five, we could do ten times two add five by two, or we could do five add.

We could do one longer side add one shorter side, so 15, and then just multiply that by two, because it's that twice, isn't it? It's a long side and a short side twice.

I think this time we had four equal sides of sevens.

So again, you should have drawn a square where we have four equal sides, it must be a square.

And those are slightly easier to work out, we can do repeated addition or we can just do four times seven.

And well done if you got a perimeter of 28 for that one.

Okay, how can I then draw a rectangle with a perimeter of 24? I haven't been told what the sides are this time, I need to work that out for myself.

I can do that by, first, we need to understand the problem.

So first we need to think about, what do we need to do with 24? Well, we can split 24 in half to give us 12 and 12, but we are looking for four sides.

So if we split 24 in half, we get 12 add 12, and then each of those will need to be split into a length and a breadth, a length and a breadth, so a longer side and a shorter side.

This picture hopefully shows that to you.

So half of our 24 is 12, and that 12 must represent two sides, a longer side and a shorter side.

We then need to think about, what combinations of numbers can come together to give us 24? So we'll be thinking a little about what we know about 24, how we can split it up, we can do 12 and 12 and then go from there, or we could split it up in a completely different way.

So here are some possible combinations where we can split 24 up so that we have two sets of numbers which are the same.

So here are some, eight and eight and four and four, gives us 24.

16 for the two eights and eight for the two fours, gives us 24.

And then we could have two and 10.

That's a nice, easy way of thinking about it.

Split the 20 into 10 and 10 and the four into two and two.

Or it could be a square, with that all six, because six times four is 24.

And then we've got some more combinations here as well.

Now these are just some of them, there are other ways you could have worked out the perimeter of that rectangle.

So you can see that given the perimeter without being given the sides leaves lots of combinations available for us to work out what the perimeter is.

Okay, just to finish it, before you do your independent task, we're just going to have a really quick recap on how we work out perimeter before you go and have a go at doing it yourself.

So when we calculate the perimeter of a square, this will be revisions for you, but it's good to just go over it, what do we know about a square? We know that all four sides are equal length.

So when we're working out the perimeter and we're given the length of one side, which is six, all we need to do is either repeated addition or even better six times four because we've got six, six, six, six, four lots of six around the four sides of our square.

So if we do six times four, we've worked out the perimeter which is all the way around.

How about the perimeter of this square then? What do you think the perimeter of this square will be if one side is four? Hopefully that was quite straightforward for you.

Hopefully you could see that you could do repeated addition four, four times, which is four times four, and that is 16.

Really, really well done.

Okay, oblongs are different to squares, they have two longer sides and two shorter sides, right? When we work out oblongs, we're normally given the length of the two sides, we then need to double both of those because there are two long sides and two short sides.

So if we know that that top side is eight, the bottom side is eight.

If we know that that short side is four, the opposite side will also be four, so we need to double each of them.

Eight add eight, add four, add four, or eight times two add four times two, or we could do eight add four and then multiply that by two.

Okay, pause the video here and work out the perimeter of this oblong.

How did you get sum? So you could do three add three, and add 11, add 11, it doesn't matter which order you do those in either, you could do 11 add 11 first, if you prefer, or you could do three times two, so two lots of three, and then two lots of 11, or you could do 13, sorry, 11 add three is 14, and then double that to give you 28.

Okay, well done.

Right, time for you to complete your independent task now, and resume the video once you've done that.

Welcome back.

I hope you did really well on your independent task, let's have a look at your answers.

Well, it was an investigation, so it would be difficult for us to look at all the answers together.

But here's some questions for you to think of as you look at your work, and we're going to go through them in a little bit more detail in later videos in later lessons as well.

So, do shapes with the same perimeter always look the same? Can you make shapes with a perimeter that is an odd number or all perimeters even? That's an interesting question.

And what is the formula for calculating perimeter? Could you write a calculation which people could apply to any perimeter to work out what it is.

Well done.

If you would like to share today's work, we would really like to see your writing for your investigations.

So please ask a parent or carer, if you'd like to share it on Instagram, Facebook or Twitter tagging @OakNational and #LearnwithOak.

And that's the end of today's lesson.

So well done, everybody.

I hope you enjoy the rest of your learning.

Goodbye.