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Hi year six, welcome to our fourth lesson in the decimals and measures topic.

Today, we will be solving problems involving the conversion of length.

All you'll need is a pencil and a piece of paper.

So pause the video and get your equipment, if you haven't done so already.

In today's lesson, we'll be solving problems involving the conversion of length, starting with a quiz to test your knowledge from our previous lesson.

We'll then look at calculating perimeter before moving on to calculating area and then some independent work.

So we're starting off by looking at calculating perimeter.

Now, I want you to think about how do we calculate perimeter? What is the procedure for calculating it? So the perimeter is the length of the outline of the shape.

So it's the distance all the way around the shape.

And we calculate it by adding the lengths of the sides together.

So we could either, do it by adding, nine and nine, because we know the bottom one is nine and four and four, which is equal to 26 centimetres.

The distance around the shape is 26 centimetres or we could use our knowledge of multiplication.

So nine multiplied by two plus four multiplied by two is equal to 26 or we could use a nine plus four and then multiply that by two, which will give us 26 centimetre.

So whichever approach you use, these are different ways of calculating the perimeter.

So now, if I wanted to know, what is the perimeter of the shape in millimetres? How would I go about working that out? Well, I know that one centimetre is equivalent to 10 millimetres.

So if we think back to our previous lesson, centimetres to millimetres, the conversion is to multiply by 10.

So I would multiply my 26 centimetres by 10.

So I know that the perimeter is 260 millimetres.

Let's have a look at another one together.

So I would like to calculate the perimeter of this shape in centimetres.

Now, what you will notice is that my units are not the same, so it makes sense for me to convert them, see that they're in the same unit.

So if I'm being asked for my perimeter in centimetres, it makes sense to convert these both to centimetres.

So one centimetre was 10 millimetres.

So to convert from millimetres to centimetres, I need to divide by 10, 35 divided by 10 is 3.

5 centimetres.

So 35 millimetres is equivalent to 3.

5 centimetres.

So now I need to calculate my perimeter.

So I'm either using repeated addition or I can use multiplication as we showed on the previous slide.

Either way I know that these add up together to give me a perimeter of 22 centimetres.

Now, what if I wanted to convert that to millimetres? Well, I know centimetres to millimetres I'm multiplied by 10, so that would be, 220 millimetres as the perimeter.

So now I'd like you to pause the video and calculate the perimeter of each shape in the given unit.

So you may have to convert the units given so that you can give your perimeter in the correct unit.

Pause the video now and calculate the perimeter.

So for the first one, which is a square, you were asked to calculate the perimeter in millimetres.

So I'm converting this by multiplying it by 10 to 34 millimetres.

And I know that as it's a square, I'm adding 34, four times, or I'm doing 34 multiplied by four, which is equal to 136.

So the perimeter is 136 millimetres.

For the second one, I'm asked for the perimeter in centimetres.

So I can convert these both to centimetres first, or I could do it afterwards, I'll do it first, so I know dividing by 10, this is 5.

6 centimetres, and this is 10.

7 centimetres.

And to calculate the perimeter, I'm going to do 5.

6 multiply by two plus 10.

7 multiplied by two to give me the perimeter, which will be 11.

2 plus 21.

4, which is equal to 32.

6 centimetres.

Now, that takes us on to compound rectilinear shapes.

This is where we have shapes made up of multiple rectangles or squares.

Now this shape represents the floor plan of the kitchen in Simone's new house and it's a compound rectilinear shape, as I just said.

Now, we want to work out the perimeter of the kitchen in centimetres.

Now, as the measurements are all already in metres, it would be most efficient to keep them as metres, find the perimeter in metres and then convert my final answer into centimetres.

Now there's some things we need to add on before we can calculate the perimeter.

So the first one is this left hand side.

So this is five metres tall and this is three metres tall.

So the left hand measurement is eight metres.

And then we have this one here, well, I can see that this one is 8.

5 metres wide, and 3.

2 metres is taking up some of that.

So I need to find the difference between 8.

5 and 3.

2, which is 5.

3 metres.

So now I can calculate the perimeter by adding all of the sides together.

So I've done this already eight plus 8.

5 plus 3.

5.

3 plus five plus 3.

2 is equal to 33 metres.

So the perimeter is 33 metres, but I'm being asked for it in centimetres so I need to convert it.

Now, if you think back to our previous lesson, one metre is equivalent to 100 centimetres.

So to convert from metres, to centimetres, I multiply my number by 100.

So 33 multiplied by 100 is 3,300 centimetres.

So you need to make the decision about what is most efficient.

Is it most efficient for me to convert all of my measures into my ultimate desired unit? Or is it more efficient for me to do it afterwards? Like our model there.

So use that thought process to calculate the perimeter of this compound rectilinear shape.

I've put a hint up there.

You've got three missing length that you need to find first.

And then I'd like your perimeter in metres.

Pause the video now and calculate the perimeter.

So, first of all, you needed to add in your three missing length.

So we had one here, which we have from the other side is nine centimetres.

So actually you may have combined them both to be 11 centimetres.

We had one here, which is the same as this one, two centimetres.

And then we had this gap here, which was the difference between 7.

5 and five, which was 2.

5 centimetres.

Now you're asked for your perimeter in metres, but we think about being efficient.

It's going to be much quicker for us to calculate it in centimetres and then convert rather than convert each of these individual measurements into metres first.

So if we add them all together, we have a perimeter in centimetres of 37 centimetres.

So we need to convert this to metres.

We know that 100 centimetres is equal to one metre.

So to convert from centimetres to metres, we divide by 100.

So 37 divided by 100, is equal to 0.

37 metres.

Now, before we move on to area, we need to have a look at practising a scale, which will help us in our subsequent questions.

So we're looking at how do we efficiently multiply decimals? So here we've got eight times 0.

4.

Now we need to think about how do we efficiently do this? Now 0.

4 is the same as four divided by 10.

So I can do this in a more efficient way.

I can do eight times four and then divide my answer by 10.

Because 0.

4 is 10 times smaller than four.

It's easier for me to multiply integers than it is for me to multiply an integer by a decimal.

So another way of thinking about it, is like this.

If I have eight times 0.

4 and I multiply the 0.

4 by 10 to make it easier to work with eight times four, then what I need to do at the end of it is to actually then convert it back by dividing my answer by 10.

So you need to convert integers, but then don't forget to use your knowledge of decimals to convert back.

So eight times four is 32, and then we divide our answer by 10, which gives us 3.

2.

So you're going to pause the video and multiply the decimal by the integer.

We'll do this one together first and then you'll do the other three.

So six times 0.

2, 0.

2 is 10 times smaller than two.

So I will do six times two and then I'll divide my answer by 10.

So six times two is 12 and divide my answer by 10 is equal to 1.

2.

So use that as a guide for working out the other three.

Pause the video now and multiply the decimal by the integer.

So for the next one, what you could have here was four multiplied by 11 and then divide your answer by 10, which gives you 4.

4.

This one, this is the equivalent to seven divided by 10.

So we can do seven multiplied by 12 and then divide the answer by 10, which is 8.

4.

And then this one was exactly the same, but slightly greater to number.

So this was six multiplied by 45.

And then the answer divided by 10, which is equal to 27.

Now we'll look at multiplying a decimal by a decimal.

So 0.

8 is the same as eight divided by 10.

And 0.

4 is the same as four divided by 10.

So this time, if I do my eight multiplied by four, which is equal to 32, then I need to make it 10 times smaller and another 10 times smaller, which is 100 times smaller.

So that will be 32 divided by 100, which is 0.

32.

It's divided by 100 because we're dividing by 10 twice.

So I can write that a bit nicer eight times four divided by 100.

So we'll do the same again, okay.

I'm going to do the first one with you and then you can do the other three independently.

So 0.

6 is the same as six divided by 10 0.

2 is the same as two divided by 10.

So to figure out 0.

6 times 0.

2, I do six times two and then I divide my answer by 100, which is 0.

12.

So use that logic to calculate the other three.

Pause the video now and multiply the decimals.

So for this one, you are working on four multiplied by 11 divided by 100, which is equal to 0.

44.

This one, 17 multiplied by 12 divided by 100, which is equal to 2.

04 and finally 61 multiplied by 45 divided by 100, which is equal to 27.

45.

Now, we will use this multiplying decimals and integers when we're calculating the area.

So how do we calculate the area? The area is calculated by multiplying length times height.

And the answer is given in unit squared.

So if this was 12 centimetres and this was six centimetres.

It would be 12 times six which is 72 and the units are centimetres squared.

So in today's lesson, when we're calculating the area and our final units are different to our initial units, what I would like you to do is to always convert the initial units into the final units first.

And we're going to go over this in more detail in a couple of lessons time.

So I need the centimetres and millimetres.

If one centimetre is equal to 10 millimetres, then to convert, I multiply it by 10.

So 11 centimetres is 110 millimetres.

23 centimetres is 230 millimetres.

To calculate the area, I'm going to multiply 230 by 110.

And that is equal to 25,300 millimetres squared.

I'll pop that in down here.

So the most important thing is that today we are going to convert our measures into the final desired unit first.

So for this question, we're asked for our final area in millimetres squared.

So again, I need to convert these initial measurements into millimetres.

One centimetre is equivalent to 10 millimetres.

So I'm going to multiply each of my measures by 10 to convert them to millimetres.

1.

4 times 10 is 14 millimetres 2.

3 times 10 is 23 millimetres.

So then I'll use long multiplication to multiply 23 by 14, Three times four is 12, two times four is eight, plus one is nine place hold zero.

One times three is three, one times two is two and then add those together.

So my answer is 322 millimetres squared.

Now it's your turn to calculate the area of each shape.

Look at the given unit and convert your measures first.

Pause the video now and calculate the area.

So for your first one, you will have converted 3.

4 centimetres into 34 millimetres and 34 millimetres multiplied by 34 millimetres as it's a square is equal to 1,156 millimetres squared For your second one, you are converting them into centimetres.

So that's 5.

6 multiplied by 10.

7.

So using our multiplying decimals approach before that would have been 56 times 107 divided by 100, which is equal to 59.

92 centimetres squared.

Now let's look at area of compound rectilinear shapes.

So it's the same rules applying here.

We need to think of it as two separate shapes.

So we find the area of each and then we add them together.

So we find the area of A then the area of B and then add to them.

We're being asked to calculate it in metre squared, but they are in centimetres.

So remember we need to convert 100 centimetres is equal to one metre.

So to convert for centimetres to metres, I divide by 100.

So this would be one metre by 0.

4 metres.

And this would be 0.

5 metres by 0.

2 metres.

To calculate the area of A, I'm doing one metre times 0.

4 metres, which is equal to 0.

4 metres squared, that's the area of that.

And for B I'm multiplying 0.

5 metres by 0.

2 metres.

So remember that's the same as two multiplied by five divided by 100, which is 0.

1 metre squared and then I add the two of them together to get my total area of 0.

5 metres squared.

So use the same approach.

this time you're calculating the area in metre squared, so you need to address these two numbers first.

Pause the video and calculate the area.

So converting from centimetres to metres you're dividing by 100.

So 700 centimetres is equivalent to seven metres and 200 centimetres is two metres.

So if we call this A, the area of A, is seven multiplied by two, which is 14 metres squared.

B was already in metres for us so that was nine metres multiply by five metres is 45 metres squared and then we were just adding the two shapes together, which is equal to 59 metres squared.

Now it's time for some independent learning.

So pause the video and complete the task and click restart once you're finished.

So for question one, we have a floor plan of a museum.

In the museum the manager needed to close off the Math Zone so that it could be updated.

She needed to put a rope around the perimeter.

So we needed to figure out how much rope she would need by calculating the perimeter of the shape.

So you had some missing measures to add on.

This one here, would be the total 12, subtract this part eight.

So this is four metres.

This part here is 6.

25 metres.

And then this one here is 9.

5 metres.

So you were adding all of these measures together to calculate the perimeter.

And the perimeter was 55.

5 metres.

That's those numbers added together, but you were asked for that in centimetres.

So you know that you have to multiply it by 100 to convert metres to centimetres.

Which is equal to 5,550 centimetres as the perimeter.

Now here you were asked to calculate the missing length.

So you know that 14 multiplied by W is equal to 294.

So using your knowledge of the inverse, you will have done 294 divided by 14 is equal to W so, therefore, W is equal to 21 centimetres.

21 multiplied by 14 is equal to 294 centimetre.

Here we were looking at the perimeter and you were asked to calculate the missing length.

So first the perimeter needed to be converted into centimetres, as all of the others were in centimetres, divided by 10 is 31.

2 centimetres.

So we know that this measurement 8.

2 plus this one, plus two lots of something is equal to 31.

2.

So using the inverse, you subtract the known numbers, and that leaves us a 14.

8.

So this side and this side are 14.

8 divided by two means that each of these sides were 7.

4 centimetres.

And finally, you were asked to calculate the area and perimeter of the shape in the given units.

So your first one was asking you for centimetres, which meant that you needed to convert your millimetres to centimetres first.

So 15 centimetres and four centimetres, 15 multiplied by four is 60 centimetre squared.

And then add those sides together gives you 38 centimetres.

In your next one, you're given units with millimetres, so you needed to initially convert to a 100 millimetres, 40 millimetres, 50 millimetres and 20 millimetres, and then find the area of each shape and then add them together.

So you were working on, 100 multiplied by 40 is 4,000 millimetres squared.

And 50 multiplied by 20 is 1,000 millimetres squared.

And then you were just adding those two together.

So that gave you 5,000 millimetres squared.

And then adding all of these known sides together, is 380 millimetres.

The final one you were asked for your answer in metres squared.

So you needed to convert these measurements into metres by dividing by 100.

So 0.

1 metres and 0.

03 metres.

0.

1 multiplied by 0.

03, is equal to 0.

003 metres.

And this one was 0.

06 , 0.

05, multiply those two together you also get 0.

03 point metres.

And that means that when we add those two together, we get an area of 0.

006 metres squared.

And then if you add all of the sides together in metres, we reach 0.

38 metres as our perimeter.

Great work today.

That was a really tricky lesson.

But well done for persevering with it.

In our next lesson, we'll be learning to calculate the area of parallelograms and triangles.

I'll see then.