# Lesson video

In progress...

Hello everybody.

My name is Mr. Kelsall and welcome to today's lesson about calculating the area of a rectangle.

Now, before we start, you are going to need a pen, piece of paper, a ruler, and also some dice.

Please try and find yourself a quiet place somewhere that you're not going to be disturbed and don't forget to remove any sorts of distractions.

Put your phone on silent or move away completely.

Pause the video and then when you're ready, let's begin.

Today's lesson is about calculating the area of rectangles.

We will begin the lesson by looking at strategies for calculating area.

We'll then develop a formula for calculating area.

After that we'll move to our independent task.

I mentioned you'll need a pen, piece of paper, ruler and dice.

So what is area? When is it used? And also how is area different to perimeter? Pause the video and when you're ready, press play to continue.

So area is a measurement of the size of the surface.

We always measure an area in units squared.

A shape that has sides one metre has an area of one metre squared.

Now, area is different to perimeter because the perimeter is a measure of length.

And that measures something which is one dimensional.

Area however, is a measure of something two dimensional.

It's the amount of surface taken up by a two dimensional shape.

One dimensional would be something like a line, two dimensional would be a shape like a rectangle or square.

Take a moment to think, how can we calculate the area of these rectangles? Well we could count individual squares is like a one, two, three, four, five, six, seven, eight, nine, 10, 11, 12.

It's taken a long time this, isn't it? 13, 14, 15, 16, 17, 18, 19, 20.

I know the space within this rectangle is made up of 20 squares.

We count out the next one as well.

Well, this time we're going to do it a little bit differently.

See if you can notice how I do it differently.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12.

Did you notice I counted in multiples of three? Because I can see that I've got three squares, six squares, nine squares, 12 squares.

And I find this a little bit easier when I count if I know what the multiple is and I can count in multiples of that number.

Now, I can count me the way.

So for that example, I counted horizontally.

This example, I'm going to come particularly, two, four, six, eight, 10, 12, 14, 16.

So actually there is a faster way to find out the area of a shape.

We can think of these as arrays and we can work out the number of squares in an array by multiplying the length of the rectangle by the width of the rectangle.

So in this case, I know it's five units long and I know it's four units wide.

So if I multiply five by four, I get 20.

Let me show you what that looks like.

So I've got five, 10, 15, 20.

I know that that shape has an area of 20 units.

And just like arrays, I can do five times four.

I can also do four times five, four, eight, 12, 16, 20.

And I still get the same area, the same space inside this shape.

Can you take a moment to count the arrays, count the area in the other rectangles.

Pause the video and when you're ready, press play to continue.

Now, before we move on to start looking at a formula, we've got to think about when we would use area.

If we're trying to measure something, for example if we're putting up a shelf or if we're making a piece of wood to fit in a certain place, we need to measure the length and we need to measure the width.

We can't draw squares on this piece of shape every single time and count the number of squares.

It just wouldn't work, it's too inefficient.

So we need to have a quick way of doing it.

So, we're going to take the knowledge from counting the squares and we're going to use that if we don't know, if we can't draw on the squares and we just know length and we just know width.

So, can we apply work from the previous slide to create a formula for area of a rectangle? We just use length multiplied by the width or you could say the width multiplied by the length.

Now, depending on who you're speaking to or if you're reading a book, you might hear a different names for this.

You might hear the height, you might hear the base but essentially all these refer to the same unit of measurement.

We're looking at how long something is and how wide something is and we need to multiply these two numbers together to find the area.

So, have a look at these shapes.

Now, I know my first shape is three centimetres long and it's five centimetres wide.

So if wanted to remind myself, I could draw these three squares and the five squares.

But actually I don't need them because there's a quicker way of doing it without drawing these every time.

I know that three centimetres multiplied by five centimetres gives me 15 centimetres squared.

Remember we used the word squared because we're talking about something that we're measuring in square units.

You could also say five centimetres multiplied by three centimetres is 15 centimetres squared, both calculations are correct.

Have a look at rectangle number two.

Take a moment and think what is the area of this shape? You have five seconds to think about this.

So, you should be thinking about my length is nine millimetres and my width is three millimetres.

So nine millimetres multiplied by three millimetres is nine, 18, 27 millimetres.

You can check that by doing three multiplied by nine, three, six, nine, 12, 15, 18, 21, 24, 27 millimetres.

So I know that the area of my next shape is 27 millimetres squared.

I'm now left with my final shape.

Now, I've only been given one side and I've been told this is four metres long.

However, I know that this is a square and I know the properties of a square mean that I've got four sides, which are equal lengths.

So I've got four metres that way, and I've got four metres that way.

To find this, the area of the shape, I can just say I'm going to multiply four metres by four metres.

And it's also look 16 metres squared.

We're actually looking at area, take a moment to think if I knew that a rectangle, let's look at the first example.

If I knew this rectangle was 15 centimetres squared and I knew one of the sides was five centimetres, how could I work out the length of the other side? Well, I could draw my five centimetres on.

I know this is 15 centimetres squared in total, so I could look at, I could divide 15 centimetres by five and that would give me my other three centimetres.

We'll cover that later but it's just something to start thinking about right now.

Now, it's time for our independent task.

On this, you need to calculate the perimeter of the compound shape.

We're going to look at 100 grid.

We're going to find the closest to 100.

We're going to roll a dice twice and draw a rectangle with side lengths matching the dice.

And we're going to record the area in centimetres square.

We will keep going until we can not fit a rectangle in a three rolls in a row.

And at the end of the game, we'll work out the area of the grid that is filled and the area of the grid that is not filled.

I've done one example for you.

I've rolled the dice and I've got four and a three.

So, I've gone for a long and three down.

I know the area of this is four centimetres multiplied by three centimetres which gives me a total of 12 centimetres squared.

Pause the video, complete as much as you can, and I'll explain the end part in a moment.

So, I rolled the dice and I got these shapes.

You can see my first shape here.

I've got a three, I rolled a three and a four and the next shape was down here, I rolled a two and a six.

I then rolled a double four, a four and a three, a two and a three, a double two and a double three.

Well, at that point I realised that I've got very little space left and I kept rolling and none of my dice managed to fit in the space that I had available.

So, I need to count how much space I've used and how much space is filled.

Well, I've got a three by four rectangle here which is 12 centimetre squared.

I've got another four by three which is 12 again, two by three, which is six, four by four, 16, two by two, which is four, three by three, which is nine and a six by two, which is 12.

Now, I need to have all these numbers up but I need to think of quick ways to do this.

So I'm going to start with that 12 times tables, 12, 24, 36 I've then spotted a number bond to 10.

So that takes it to 46.

I'm going to add my 10 here, 56, add my six, 62.

And then to add a nine, I can add 10, which is 72, take one, which is 71.

So, I know that I've used 71 centimetres squared.

How many centimetre squired should I have unfilled? I should have 29 centimetres squared unfilled.

Let's check it.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17.

Now, I have 17 centimetres squared unfilled, and I think that creates a bit of a problem.

Let's investigate what happen one more.

Ah, there's one area I've not counted.

Let's go back and have a look.

I forgot to count 12 here.

So for my 71, I need to add on 12 which takes me to 83 centimetres squared.

And if you remember, I had 17 centimetres squared, which was unfilled, now that totals 100 centimetres squared.

And I know that that is 100 centimetre grid.

I can double check it, this is two, four, six, eight, 10.

Two, four, six, eight, 10.

So I know that a 10 by 10 makes 100.

Fantastic, I've checked it.

Can you go all way and can you find the area that you filled, the area that is left and can you check that these two numbers add up to 100 centimetres squared? Congratulations on completing your task.

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