There are two systems used for measuring quantities - metric and imperial.

The metric system uses three main units for measuring:

Length in metres (m)

Mass in kilograms (kg)

Volume in cubic metres (m3)

The imperial system uses the following units:

Length in inches, feet and yards.

Mass in pounds (lb), ounces (oz) and stones.

Volume in gallons.

In this lesson, we are looking at units of measure. I will briefly introduce the different types of metric and imperial units, and then we will really be focusing on conversion alerting between metric units of length, area and volume. So these are the two systems used for measuring quantities. We have metric and Imperial for some examples of units used for metric quantities. Length could be metres or centimetres or millimetres.

Mass would be kilogrammes or grammes. Volume could be centimetres cubed or millimetres, cubed or metres cubed. For Imperial, we have length being measured in inches, feet or yards. Mass would be pounds, ounces or stones, and volume could be gathered. So we're really focusing on metric quantities.

So these are the four main metric units of length that you need to recall. So you could put these on flashcards, or you could just use these enough that you would start to remember them. Okay? And I'm going to be teaching you an arrow grid method to work through these. So the arrow method is essentially how do you go from the left to the right, where we're timing by 1000.

So the conversion between kilometres and metres is multiplied by a thousand. If we look at metres to centimetres to go from the left to the right, we've got times by 100. So that's that conversion to go from centimetres to millimetres, we are going from one to ten. So we're multiplying by ten, and the final one is multiplying by 1000. Now, if we were to work backwards, if we need to go from millimetres back to metres and so on, you would just divide by these four quantities instead.

So these are my arrow diagrams. So here's an example. A sunflower is 232 centimetres tall. Calculate the height of the sunflower in A metres and B millimetres. So if we look at part A, we're looking at going from centimetres to metres.

So this is the diagram that I'm looking at and centimetres to metres. I'm using this bottom arrow, so I'm dividing by 100 to give me 2.32 metres. Part B is going from centimetres to millimetres. So this is the diagram that I'm looking at, and we're going from centimetres to millimetres. So we're going forward this time, so I'm going to multiply by ten instead.

Okay, so the next part of this lesson is looking at metric units of area. So I've got two squares here. They're both equivalent. They're both the same size because one metre is the same as 100 centimetres. So both squares are the same.

It's just they're in different units. So if I find the area of square A by doing base times height, that gives me one times one, which is just one metres squared. And if I go for square B, I'm going to do 100 times 100, which is 10,000 centimetres squared. Now, because these two diagrams were equivalent, my area values are also equivalent. So I can make an arrow diagram out of that.

So if we could think back to the units of length, metres to centimetres was multiplied by 100 units of area. Just make me do that twice. So metres squared to centimetres squared is times by 100 squared and division would be divided by 100 squared. So I can apply that to a couple of the other unit conversions. If we look at centimetres squared to millimetres squared.

Well, normally centimetres to millimetres would be multiplied by ten, but I'm doing centimetres squared to millimetres squared. So I multiply by ten squared and divide by ten squared. So metres squared to millimetre squared would be times by 1000 squared and divided by 1000 squared. Now, you can probably guess what you do for metric units of volume. It's the same kind of concept, but I will still show you with a diagram.

So we've got two cubes here. Again, they are both equivalent because this is in metres, this is in centimetres and one metre is equivalent to 100 centimetres. They're both the same size. If I find the volume of a to find the volume of a cube, you do the area of the cross section, which is the front face. So just as a side note, cross section is basically if you slice the shape up, the front face should look exactly the same all the way through.

That would be the square. So I'm going to do one times one, that's the area of my cross section and I'm going to multiply that by the length of the 3D shape. So it's one times one times one, which is one metre cubed. To find the volume of b I'm going to do the same thing, area of the cross section, 100 times 100 and then multiply it by that third 100 and that gives me a million centimetres cubes. Again, because both cubes were equivalent, the areas are equivalent.

So I can make an arrow diagram and to go from metres to centimetres, you would normally multiply by 100. But because it's cubic, we are going to multiply by 100 cubes and divide by 100 cubes. And again, I can apply that to the other two conversions as well. So your timing by ten cubed and dividing by ten cubed times by 1000 cubed and dividing by 1000 cubs. So what we can say here really is if you memorise the metric units of length, you can then apply metric units of area and volume to those conversions.

So let's go through some examples. So what I would really suggest is you pause the video at this point and try these independently. If you are not that comfortable to do that yet, feel free to work on the first one with me and then maybe press pause again and try the next one. You could do that for question three or four as well. So feel free to pause and UN pause when you're ready to go.

So for this first question, we are going from kilometres to metres. So we are timing by 1000.

For the second diagram, we're going from centimetres to metres. So this time we're going backwards, so we're dividing by 100 kwh. For the third one, we're going from centimetres to millimetres, so we're multiplying by ten. And for the final one, to go from millimetres to metres, I'm dividing by 1000.

So let's now apply this to units of measure for areas. So again, I'd suggest you pause the video, give this a go, and then unpause when you're ready to go through the answers. So metre squared to centimetres squared. So I'm going forward. So I'm times in by 100 squared or 100 twice millimetre squared to centimetres squared.

I'm going backwards, so I'm dividing by ten squared, or dividing by ten twice. And finally, metres squared to millimetres squared, I'm time in by 1000 squared or 1000 twice.

And finally, volume conversion. So again, pause the video here, give these a go. Press play when you're ready to go through the answers. So we're going from metres cubed to centimetres cubed, some times by 100 cubed or 103 times. To go from millimetres cubed, two centimetres cubed and dividing by ten cubed, or divided by ten three times.

And to go from metres cubed to millimetres cubed and times by 1000 cubes, or 1003 times, we should now be able to confidently convert between units of measure for length, area and volume. The final conversion that I would like to show you in this lesson is litres, two millilitres. So one thing that I am just going to change really quickly is that this should actually be 1000 and likewise here. So I'm just going to adjust that really quickly. So to go from one litre to millilitres, we times by 1000, and to go backwards, we divide by 1000.

So let's go through this exam question. Here. We have a plant pot here which has a capacity of 650 millilitres. Okay, isabella has bought a plant pot. Will the plant pots hold zero point 64 95 litres of compost?

Show you're working. So what you really want to do is make sure that your units are the same. So either both need to be in millilitres or both need to be in litres. And I would say that actually working with millilitres avoids decimal work or decimal answers, so it's a little bit easier to compare. So to go from litres to millilitres, I'm going to time by 1000.

So that gives me 69.5 millilitres. Now, this pot can hold up to 650. So will the plant pot hold zero 64 95 litres of compost? Yes, it will. With 0.5 ML space left.

And that's it.

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Sanaa A

Sanaa is currently Deputy Head of Maths at a secondary school and has been tutoring GCSE Maths students for over 10 years. She tailors her approach so that no student is left behind.

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