Lesson video

Hello, I'm Mrs. Ashley, and I'm gonna be guiding you through your learning today.

Okay, so during our lesson today, we're gonna work on thinking about the place value of numbers, but in the context of measure.

So when we've got a unit attached, what number and what's the place value of it? So today we've got some keywords that we need to focus on.

The metric units is one of the systems that we could use and that's the one we're gonna focus with today.

There are seven standard units in the metric system and we're gonna focus on three of them today, which is the metre, the gramme, and the litre.

We're gonna talk about them a lot during this lesson.

And then we're gonna focus on the idea of prefix and how that helps us with place value.

So a prefix is a group of letters attached to the front of a root or a root word to create a new word.

So for example, you could think of tricycle where tri- is the prefix.

Hopefully, you recognise that from triangle.

Both of them are connected by the number three.

We're gonna focus on three prefixes today in this lesson and the first one being centi.

Centi means 100th of the unit.

So if you place centi in front of a word for a unit, then it would mean 100th of it.

Similarly, milli, where milli is a thousandth of that said unit.

And lastly, kilo, where kilo means a thousand times.

So we'll be using those prefixes during this lesson with the idea of the metric system as our unit system and working out what that means for place value.

So we've got two parts to the lesson.

We're gonna make a start on the first part.

And the first part is where we really just focus on the metric units.

In a moment, I'm gonna put up three images.

I want you to think about what units you could use to measure what I'm asking for.

The height of a tree, the capacity of the vase, and the mass of the eggs.

So what units might be used for each of these? If you're struggling with what does capacity mean, think of it about the liquid, the amount of liquid it could hold.

The mass of the egg.

Well, mass is actually the technical and correct word to use when we are discussing what we would normally, or in English might say weight of something.

So mass stays constant wherever you are.

If you was on the moon, if you were on earth, your mass is constant, whereas weight, technically from a science and a maths point of view would change depending on where you are down to the gravitational pull.

Okay, so I'm hoping you may have thought about metres for the height of the tree and litres for the vase and grammes for the egg.

So units are really important to give you an understanding of what is being measured and its size.

So we have different units all based around the metre, the gramme, and the litre and they give you an indication of the size.

The length, mass and capacity element tells you what is being measured.

So if it's a length, then there are certain units you would use.

If it was a mass, there are certain units and especially and capacity is same.

And as I've said a couple of times, the metric units are based around the standard units of gramme, litre and metre.

So the metre for the tree, the litre for the vase, and the gramme for the egg.

So if we now just focus about length for a moment, so that group of length units, there's a couple of illustrations of tools that you might use to measure.

So you've got a ruler and hopefully you've got one of those nearby and a tape measure.

So they're all based, all of these metric length units are based around the metre.

And we give that the shorthand m.

I want you just for a moment to think about what you estimate a metre to be.

Maybe there is a metre ruler nearby that you can look at.

So hopefully you've got an idea of what a metre might be.

And now what about a centimetre? Can you think about how large, how long a centimetre is? So just to help you, your finger is approximately a centimetre.

The width of your finger is approximately a centimetre.

And if you have got a ruler, I'm nearly certain it's gonna have centimetres marked along it.

So you can have a look, measure up your finger to the centimetre.

We use cm to stand for centimetre, so we don't have to write the word every time.

And then there are some smaller units of length, the millimetre.

And again, if you have got a ruler, there's probably millimetre marks on there and a millimetre is smaller than a centimetre.

So we've got the metre currently and then we've got our centimetre and then we've got millimetre.

But not everything can be measured sensibly using millimetre, centimetres or metres.

So we've got a longer one and that's the kilometre.

So kilometres, a much larger distance or length than a metre, a metre is bigger than the centimetre and the centimetre is bigger or longer than the millimetre.

So there our metric, our standard metric units of length.

If we now focus on mass, so again you've got an illustration of an electric digital scale, you might have something similar to that in your kitchen or in your science labs to allow us to measure mass very accurately.

So mass is based around the gramme and we'll just use the letter g for gramme.

And most things, most sort of everyday objects are probably used gramme, but there are gonna be times that we use a larger mass and that would be the kilogramme and would use kg for that.

So yourself, if you were to stand on top of a scale, you would measure yourself in kilogrammes.

That would be a sensible metric unit for mass of yourself.

But there are also items that we need a smaller unit than the standard gramme and that would be the milligramme.

And we use mg for that.

So these would be your tablets.

If you go to the pharmacy and you've got to have some prescription, the tablets would be mg, they're very light as a mass, and grammes would just be too big.

So we've got this smaller unit.

So they're the three standard ones you're gonna use, kilogramme, gramme, and milligramme.

And then lastly, we can think about capacity.

So here you've got some illustrations of a beaker, a measuring jug, and if you continue to think about capacity with this idea of the amount of liquid it can hold, but also you can think about capacity and volume.

So volume is about the amount of space inside of an object.

And therefore if you think about something holding liquid, it's filling the space.

So the volume and the capacity are very closely linked.

People may say the volume of water in a pool and that's talking about the capacity that the pool could have.

Standard metric unit is the litre, and we just use the letter l for shorthand for litre.

And so you can imagine a large bottle of pop would be in litres.

When your parents or guardians might fill up the car, their petrol tank would be in litres.

But there's oftentimes we're gonna have to use smaller units.

So we would use millilitres.

So ml or centilitres, cl.

The centilitres are less common in terms of a unit used for capacity here in the UK.

But in mainland Europe, cl is used quite frequently as a measure of capacity.

So just to be aware that they both do exist as common units of capacity.

A check for you now.

A centimetre is a unit of.

Pause the video to make a decision.

So hopefully, you went for length.

Metre is that standard unit of length.

A second one.

Kilogramme is a unit of.

Once again pause the video and have a think.

Kilogramme is a unit of mass.

So gramme is that standard unit of mass.

The kilogramme is a connected, a related unit.

So we can classify our units into length, mass, and capacity, but then we need to think about what they actually tell us, why we would choose that unit.

So the type of unit for the distance between two towns would be a unit of length.

A distance would be a length and therefore we are gonna think about those standard metre and all of the other connected units of length.

The sensible one would be kilometres, km, the largest unit of length.

A distance between two towns, regardless if it's the next town down the road is a fair distance away that would need the largest unit.

And so for example, just to put this into context for you, if you wanted the distance between Edinburgh and Cambridge.

So Edinburgh is in Scotland and Cambridge is in England.

The direct distance is 470 kilometres.

So our unit here tells us it's a length because it's kilometres and then because we've chosen kilometres, it tells us it's size, that it's a large length, a long distance.

And just to give you a little bit of tangible understanding of 470 kilometres.

If you were to take an average walking pace and walk or try to walk from Edinburgh to Cambridge, it's gonna take you approximately six days.

So that is a fair distance between them despite 470 not being a particularly large number.

The kilometres, the unit is what's telling us how large this is.

Another example would be about the liquid in a cup, and this would be capacity.

So we're now if we're thinking about our metrics in three sort of sets, we're now in the capacity units.

So this is litres, millilitres, centilitres.

So a sensible unit would be millilitres, ml for a cup.

And approximately a standard cup has about 250 millilitres in it.

And that's why litres just wouldn't make sense.

It's not enough, it's not big enough to justify using litres.

The millilitres gives you an understanding of the size.

So you're now gonna move on to your first task.

And so the first question needs you to sort the given units into those categories of length, mass and capacity.

Pause the video now and have a go.

And the second question needs you to decide what would be the sensible metric unit.

Pause the video now and when you are ready, come back for the answers.

Okay, so for question one, hopefully for length, everything to do with the metre, 'cause that's your standard unit has gone into the length box.

So centimetres, kilometres, metres and millimetres.

The m stands for metres.

And then similarly for mass, all to do with a gramme.

So everything with a g, grammes, kilogrammes and milligrammes.

And lastly, capacity, everything to do with litres.

So litres, millilitres, and centilitres.

So the second question needed you to choose some sensible metric units.

So really thinking about which type.

So firstly, would it be length or mass or capacity? And then which of the units within there would we use because of their size? So a, hopefully went for kilometres, the distance between two cities.

b, the height of a three-year-old child be centimetres, they're not gonna be 98 metres tall, and millimetres is way too small.

c, the capacity of a kettle, hopefully you went for litres.

So again, millilitres there just wouldn't be enough to make a cup of coffee.

And centilitres again, there just wouldn't be enough.

So litres would be the sensible unit.

Classroom, you might be sitting in one right now, you might not be, but six metres.

So again, if you just think about all the alternatives and are they sensible? Six millimetres, you could measure that with a ruler.

Can you measure your classroom easily with a ruler? Centimetres similarly, and kilometres is way too much.

An apple, 86 grammes.

Kilogrammes, that's a heavy apple and milligrammes would be too light.

And then finally, the capacity of a teaspoon.

So the teaspoon is sort of the smallest spoon you might have in your cutlery draw.

So it's not gonna be litres, it's not gonna hold a lot of liquid.

And so millilitres, that smallest unit is what you should have hopefully gone for.

Okay, so now we're moving on to the second part of the lesson.

And the second part is all to do with the prefixes.

So we've been using them in the kilometre, in the centimetre, in the millilitres, but we haven't really focused on what that really means for the place value of the number.

So the metric unit is based around those three standard units, the metre for length, the litre for capacity, and the gramme for mass.

But if we now attach a prefix to the standard, we understand a little bit more about the size.

So centimetre, because centi means 100th, centimetre means 100th of a metre.

And so if you go back to thinking about what a metre is and that centimetre, what that is telling you is that one of those centimetres fits 100 times within the length of the metre.

Another way of thinking about that is that the centimetre is a hundred times smaller than the metre or that the metre is a hundred times larger than the centimetre.

So it is 100th of a metre.

And so every time we use the prefix of centi, it's talking about a smaller unit compared to the standard.

Similarly, we've got the milli.

So millimetre is a thousandth of a metre.

So those very tiny small measures on your ruler, there would be a thousand of them that would make up a metre.

So it is 1000th of, it's a fraction of a metre and that's why it indicates it's a smaller unit.

And lastly, the kilometre with the prefix of kilo is a thousand times as long as a metre.

So when we are talking about those distances between towns, that's when we are gonna use that kilometre because it's a much longer distance or length.

So if we now put a place value chart into our thinking, because we want to think about the place value when we've got a unit attached.

So here we've got metres as our ones column.

So we're focusing just on length currently.

So if our metre is our ones, one metre would be that middle column.

On the right, we'd move into the decimal parts, in the fractional parts.

So we've got one-10th, 100th, and 1000th.

The prefix for 100th is centi and the prefix for 1000th is milli.

And they are, if you look compared to a normal place value, they're in the second column to the right for a hundredth and the third for a thousandth.

There are units between that as you can see in that 10th.

So that would be a decimeter, but that's not a standard unit that we would talk about and use.

So it's not our focus today.

On the other side we've got the kilometre and that's in the thousand column, place value column.

And because it is a thousand times our metre and our metre is our ones.

Once again there are 110.

So you could have a hectometer, which would be a hundred times and a decameter, which would be 10 times, but they're not standard and they're not our focus for today.

So let's put some values, put some digits in.

So if we've got six centimetres, we know from the first part of the lesson that that's a relatively small length, we could measure it using our ruler.

So the six holds the place value of a one.

The centimetre is our focus, that's our unit.

And so that column would be what we're thinking as our ones column.

We've got six lots of one centimetre.

So centimetres is our ones.

And hence the decimal point, if there were any decimal places would be to the right of that column.

But if we wanted to change our focus, if we wanted to change it from centimetres, we wanted to start to think about it in comparison to the metre, then our metre would become the one's column and hence the decimal point would be to the right of that.

So six centimetres, if we change the unit, we're changing it from centimetres, we're now thinking of it in metres.

We're gonna break that word back.

We're going backwards from the prefix being added on, we're gonna break it up.

So six centimetres means six hundredths of a metre in words, centimetre in hundredth, which means six times a hundredth, which is six hundredths.

All of those mean the same thing, but just thinking about them in breaking up that word from its prefix and its root.

So centi means the hundredth part and the root is metre.

So our metre is now our ones column and we're now gonna think about this as a decimal as 0.

06 where six is in the centi column or the hundredths column.

So when we had the unit of centimetres, six held the place value of a one.

When we have the unit of metre, six has the place value as a hundredth because we've broken the word from centimetres into just metre and the centi has now gone into the place value.

Let's have a look at that as another one.

So if we start with eight millimetres.

The unit is telling us this is very small length and we've got eight of them.

But if we now think about what millimetre actually means, milli is 1000th.

So it means eight thousandths of a metre.

Our unit is now metres.

So our ones column is now at the metres.

Eight thousandths is means eight times 1000th or eight thousandths, which is a decimal is 0.

008.

The eight is no longer standing for a one in terms of place value.

Instead it's standing for a thousandth because it's a metre rather than a millimetre.

So just to check.

True or false and a justification.

Pause the video whilst you make your decisions.

Okay, so hopefully you went for it being false because 1000th of a metre is less than 100th.

As a fraction, as the denominator gets larger, the actual size is getting smaller, there's more pieces and therefore they have to shrink.

So this time we're gonna think about the exact same concept, but we're moving away from length and this time we're looking at mass.

So three kilogrammes, the unit is written as kilogrammes and therefore we're on that column and that's our ones column, three holds the place value of one.

However, if we want to break it from its new word into its prefix and its root word, it means three times a thousand because kilo means a thousand times.

So we've gone kilogrammes means a thousand times a gramme and therefore there would be 3,000 grammes.

The three had the place value of one when we had the unit kilogrammes, and then it has now has a place value of a thousand when we use the unit of gramme.

Again, just another example to show it works also for capacity that if we're thinking about seven millilitres, so just a little bit more than your teaspoon, then millilitres would be your one's column.

The place value of the seven is one.

But if we break the word out of millilitres and we break it back to milli and then litre, then this means seven thousandths of a litre.

Seven times 1000 would be a way to write that as a fraction which is equal to 7000th.

As a decimal, 0.

007.

So seven had a place value of one when the unit was millilitres and then a place value of a thousandth when it was written as a litre because milli means 1000th.

Okay, so a check.

Six hundredths of a litre would be equivalent to six centimetres, six millilitres or six centimetres.

Pause the video whilst you make your decision.

So hopefully you went for a and didn't get caught out by c.

So centi is the correct prefix because of the hundredth, but we are based around a litre.

So centilitres.

Another check.

The decimal 0.

003 grammes is equivalent to 3 watts.

Pause the video whilst you decide what the word should be.

Hopefully you went for milligrammes because the 3 had a place value of a thousandth.

So if we then take 3000th of a gramme and use the correct prefix, that means three milligrammes.

Okay, so imagine there was a new metric unit, not the metre, not the gramme, not the litre, but a new one called a mast.

Sam says that the centimast would be a hundred times smaller than the mast, whereas Izzy believes that the centimast would be a thousand times smaller than the mast.

Who's correct about the centimast? Have a moment to think about that.

So hopefully you thought Sam was correct because Sam has identified that hundred is important.

Centimast would be 100th of a mast and hence it's smaller.

So centi is a fraction 100th, so it's a smaller unit.

Izzy would be describing the millimast, a thousand times smaller.

A check for you, pause the video to read it and make a decision on who is correct.

Okay, so hopefully you went for Jacob because Jacob has identified that a bat would be a thousand times smaller than a kilobat.

The kilobat is the largest one.

That kilo meaning a thousand times.

So the bat is smaller.

So your last task of the lesson, and you've got three parts to it.

So the first part, you're gonna have to write the prefixes into the correct boxes.

Pause the video and give that a try.

The second one, you need to order the units from smallest to largest.

Pause the video and have a try at this one.

And the last one, you need to work out what's the correct word with prefix and its root word would be.

Pause the lesson now and when you're ready come back to get the answers.

So question one, hopefully you went for kilo, centi and milli.

Kilos in that thousand column, centi is in the hundredth column.

and milli is in the thousandths column.

Hopefully, the word unit didn't put you off there.

So unit is standing for any of the three units.

So if it was the metre, the gramme, or the litre or any of those new ones.

Question two, hopefully you put them in order to really understand that the prefix is telling you about the size.

So for part a, millilitre, centilitre, then litre.

Kiloliter isn't a common or used unit.

b, millimetre, centimetre, metre, kilometre.

So all of them are used for the metre.

And then finally c, milligramme, gramme and kilogramme, centigramme isn't used particularly.

And lastly, another new unit.

Imagine this new metric unit was called an acorn.

Which prefix would you use to describe a unit that's a hundred times smaller than an acorn? Well hopefully you wen for a centiacorn, a hundred times smaller.

So it's a fraction of hundredths being the fraction.

And b, a unit that would be a thousand times larger.

Hopefully, you've gone for kiloacorn.

So well done today, well done for working through and thinking about the place value and metric units.

Hopefully, you've got an idea that.

Depending on the context, you can work out what the sensible unit would be.

So really thinking about, you know, is it a length, is it a mass or is it a capacity and then which sort of size.

The prefix informs you of its size compared to the three standard ones and the standard ones are metre, gramme and litre.