Lesson video

Hi, I'm Mrs. Warehouse.

Welcome to this lesson.

I really hope you find it useful.

Let's get started.

In this lesson, you're going to learn how you can use your knowledge of place value to solve various problems. These are the words that we're going to be using a lot in our lesson today.

Now, you may have seen these words before, but if you're a little uncertain, feel free to pause the video and just have a read of them to make sure these definitions are familiar to you.

When you're ready, let's get going.

In today's lesson, we've got two parts to it.

And in part one, we're going to be looking at maybe the same measurement but perhaps looking at different units regarding it.

In the second part of our lesson, we're gonna be determining what's a useful unit of measure depending on the context of the situation we're in.

Let's get started with part one.

Measures are not always written with the same units.

For example, here.

I've got two containers.

One of them holds 330 millilitres of liquid and the other holds 0.

33 litres of liquid.

Do the two containers hold the same amount of liquid? Now, remember, I'm going to want you to justify your answer.

Feel free to pause the video at this point while you have a go.

Welcome back.

So what do you think? Do these two containers hold the same amount of liquid? Well, let's investigate.

We know that one litre is the same as, or is equivalent to, 1,000 millilitres.

So, if I've got 0.

33 litres, I can multiply by 1,000 to turn this into an equivalent value that is in millilitres.

In other words, 0.

33 litres means the same as 330 millilitres.

Well, that means the two containers hold the same amount of liquid.

Let's consider this question.

You can see I've got a triangle on the screen.

In fact, this is a very special type of triangle.

It's an isosceles triangle, and that means that two of the sides are the same length.

What I'd like you to do is to pick three of the measurements you see below that would make an isosceles triangle.

So remember, I need two sides that are the same length and one side that is different.

Feel free to pause the video now while you have a go at this.

Welcome back.

Which measurements did you pick? Did you spot that you needed to maybe write these measurements in a slightly different way? Let's see what happens.

So we need to pick three measurements.

If we look at these three, the 4.

6 metres, the 460 centimetres, and the 4,600 millimetres, can we spot a connection between these? That's right, they're equivalent measurements.

They've just got different units.

4.

6 metres is equivalent to 460 centimetres, and that's also equivalent to 4,600 millimetres.

Remember, for every one metre, there is 100 centimetres.

And for every one centimetre, there are 10 millimetres.

In other words, we can convert from metres to centimetres by multiplying by 100 and from centimetres to millimetres by multiplying by 10.

To make an isosceles triangle, remember, we need two of those measurements because we want two sides of the triangle to be the same length, not all three.

So I can't use all three of those measurements, but any two will do.

The third measurement has to be the 406 centimetres because it's the only measurement that isn't the same as the others.

Now it's your turn to have a go.

Here I've got a scalene triangle.

Remember, in a scalene triangle, all the side lengths are different.

So which measurements could be the lengths of a scalene triangle? Set A, could that be? What about B? Perhaps C is the one to go for.

Pause the video now.

Welcome back.

Which measurements did you go for? If you picked B and C, then you're correct.

But let's go through and explore why these are correct.

Let's start with A.

You might have said that 0.

169 metres can be converted to centimetres.

We do that by multiplying by 100.

This means we have 16.

9 centimetres.

Hang on a second.

We've already got that measurement.

This means I'll have two side lengths that are the same.

Therefore, this cannot be a scalene triangle.

Remember, all the side lengths need to be different.

What about B? Well, you might have reasoned as follows.

The 230.

75 metres can be converted to centimetres by multiplying by 100.

If we do that, we get 23,075 centimetres.

Well, we can see that's different to the measurement in centimetres that we already have.

So that's a good start.

Now we just need to focus on the final measurement, the 0.

2375 kilometres.

Now, we can convert that to metres by multiplying by 1,000.

Once it's in metres, we can then convert to centimetres by multiplying by 100.

You may have spotted you could just multiply straightaway by 100,000.

Well done if you did.

That gives us an equivalent measurement in centimetres of 23,750.

And we can see that our three measurements, when they're in centimetres, are all different, and that tells us we have a scalene triangle.

But what about C? Did you spot that there's a different way to approach C? We don't actually need to convert these to the same unit of measurement for all three side lengths.

Let's see what I did.

I reasoned that there's no need to do this conversion because we know that multiplication and division when we use multiples of 10, so 10, 100, 1,000, et cetera, all that does is it changes the place value of our digits, but it does not change which digits are used or the order they appear in.

So I can see here, there is no way I can multiply or divide 292 to get the measurement 1.

87 or 3,000.

So I know this is definitely going to be a scalene triangle.

Now, remember, measures can be converted to the same units to make comparisons easier, but it's not always necessary, as we've just seen here in part C.

It's now your turn.

In Task A, you're going to be doing things similar to what you've just seen.

But I wanted to start with an important reminder about the two types of triangles.

An isosceles triangle has two sides which are the same length, and a scalene triangle has no sides with the same length.

You saw examples of these earlier on in today's lesson, but this is just a reminder to help you with the next couple of questions.

For each set of measurements, you must deduce, or work out, if they are the lengths of a scalene or an isosceles triangle.

So very similar to what you were doing earlier.

So each set, do I have a scalene triangle or a isosceles triangle? Pause the video now while you have a go at this task.

Welcome back.

Let's now look at question four.

Izzy has measured the sides of a triangle.

And you can see that she's got three lengths here: 31.

2 centimetres, 24.

9 centimetres, and 9.

3 millimetres.

Why might you think that Izzy has made an error? And if you do think she's made an error, what could we do to check? Pause the video now while you work this out.

Welcome back.

It's time to go through the answers to Task A.

Let's start with question one.

You had the measurements 1.

739 metres, 173.

9 centimetres, and 1,793 millimetres.

Now remember, this is just one particular way of approaching this question.

You may have a different method that is also valid.

The only lengths I needed to focus on were the 1.

739 metres and the 173.

9 centimetres because they have the same digits in the same order.

I know that there's no way to convert either of those to get to 1,793 millimetres because the 9 and the 3 are now in a different order.

So I'm only going to check the lengths that have the same digits in the same order.

To convert from metres to centimetres, I multiply by 100.

So 1.

739 metres is equivalent to 173.

9 centimetres.

And we can see that matches one of the lengths in the set.

Well, that means I have an isosceles triangle.

In question two, we have the measurements 0.

032 kilometres, 3020 centimetres, and 32,000 millimetres.

Again, I only need to focus on the lengths that have the same digits in the same order.

Well, only the lengths 0.

032 and 32,000 have the same digits in the same order, so those are the measurements I'll need to check.

Let's convert.

We know that to change kilometres to metres, I multiply by 1,000, metres to centimetres is multiplying by 100, and then centimetres to millimetres is multiplying by 10.

When I multiply 0.

032 by 1,000 and then 100 and then 10, or you could say multiplying by a million, I'll reach 32,000 millimetres, which is the measurement I already have.

So this is indeed the set of lengths for an isosceles triangle.

Let's look at question three.

Here, same argument.

I'm going to look at what digits I've got and are they in the same order? Well, hang on, I can see they're clearly not.

I've got 5.

1.

Well, that's 5 and then 1.

And the next one, 0.

000053.

So I've got 5, then 3.

Well, that's not the same as 5 and then 1.

And then lastly, 50.

3.

Or to put those digits in order: 5, 0, 3.

Again, that's not the same as the others.

Since I know this, I can say that none of these lengths will be the same when converted.

If you don't believe me, feel free to try it out.

Since none of the lengths will be the same, I know this is the set of lengths for a scalene triangle.

What about Izzy though? She measured the sides of a triangle and recorded these measurements.

Why might we think that she's made an error? Now, Izzy has measured one of her lengths in millimetres.

That does seem a little strange.

Why measure two in centimetres and then one in millimetres? Hmm.

Now, maybe that's okay, but when we convert that millimetre length to centimetres, it's 0.

93 centimetres.

And that seems an awful lot smaller than the other lengths she's recorded.

Hmm.

Does sound like Izzy might have made an error.

But we can check this.

Remember, I asked you what might you do to check whether or not Izzy's made a mistake? What did you put for this? Here are some suggestions.

I said that you could remeasure that side to see if you get the same measurement.

If you do, then it's likely that Izzy's right.

But if you don't, then it suggests maybe she's made a mistake.

I've also said you could try to draw a triangle that has the measurements that Izzy's recorded.

Now, you're very welcome to have a go at that.

So, you can, if you'd like, pause the video at this point and have a go to see if you can work out whether or not Izzy measured her lengths correctly.

It's now time for the second part of today's lesson.

And in this, we're going to be determining useful units of measure depending on the context of the question or the scenario.

Let's get started.

When measuring something, the units you measure in determine the place value of each digit.

Well, let's consider an example.

An ant measures 3 millimetres in length.

Seems reasonable.

But is there another way I could say that? Well, of course there is.

I could say, an ant measures 0.

3 centimetres in length.

Of course, I could say that another way.

An ant measures 0.

003 metres in length.

Can I say that another way? And ant measures 0.

000003 kilometres in length.

(exhales) That's a bit of a mouthful.

Which unit do you think is best when I want to measure the length of an ant? Which one did you pick? I know which one I'll go for.

That's right, the top one.

It's sensible to use millimetres because this unit results in an integer value.

The unit also gives us an idea of how big an ant is.

I know that millimetres are very, very small.

And therefore, since an ant is quite small too, it makes sense that I'd want to use millimetres.

I don't know about you, but I know roughly what a metre looks like.

And so thinking of 0.

003 metres actually is quite hard 'cause that's barely any distance on a metre rule.

Whereas I can get out my ruler and I can look at what 3 millimetres looks like.

That's a lot more reasonable.

The distance between England and France should be measured in millimetres, centimetres, metres, or kilometres? Pause the video and make your selection.

Welcome back.

Which one did you go for? Yeah, kilometres.

The distance between England and France is really quite far.

I'm going to want to use a large unit of measurement here, and kilometres make sense for measuring a large distance.

In fact, the shortest distance between England, and by this we mean Dover, a particular place in England, and France, and here we mean Calais, is approximately 34 kilometres.

And we say approximately, I am talking about straight line distance here, and we know that it's unlikely we can actually just get up and fly from Dover to Calais, especially because there isn't actually a plane route that does that.

Of course, I could convert that 34 kilometres.

So let's see what that distance looks like if I say it in metres, centimetres, and millimetres.

Well, that's 34,000 metres, 3,400,000 centimetres, or 34 million millimetres.

But of course, we've learned that there is more than just metric measurements.

We know about imperial units of measure too.

How do you think I might want to measure the distance between England and France if I'm using an imperial measurement? Would I want to use inches, feet, yards, or miles? Pause the video now and make your selection.

Welcome back.

Which one did you go for? Yeah, it's miles.

Again, we're measuring that really quite far distance, we're going to want to use miles.

But how far is it in miles? It's approximately 21 miles.

But, again, let's see what that looks like using the other measurements, just to see if miles really is the sensible choice.

Well, that's 36,960 yards, 110,880 feet, or 1,330,560 inches.

Yeah, I think miles is the sensible choice too.

It's now time for Task B.

For question one, I'd like you to fill in the gaps using an appropriate unit of measure from the box below.

Pause the video now while you have a go.

Welcome back.

Let's look at question two.

In question two, I'd like you to write down which metric measure might be used to measure the following things.

So we want the length of an ant, mass of a person, the capacity of a bucket, and the height of a house.

Pause the video now while you have a go.

Welcome back.

Our final question now.

So it's the same things I'd like you to measure, but this time, tell me which imperial measure you would use instead.

Pause the video now while you complete this.

Welcome back.

Let's go through our answers.

So for the first one, you had to fill in the gaps.

You should have written, "I recently visited Paris.

It took 2 hours and 37 minutes to get there by train.

I visited the Eiffel Tower, which is 330 metres tall.

Whilst at the Eiffel Tower, I visited a souvenir shop and bought 0.

5 kilogrammes of sweets to share with my friends." So in other words, the first two measurements were to do with time.

We then had measuring the Eiffel Tower, which is obviously a height, and metres makes most sense here.

And then we were measuring a mass, so we went for kilogrammes.

If I'd only had 0.

5 of a gramme of sweets, it's probably not even a whole sweet, so I'm not really gonna be sharing that with my friends.

Let's look at question two.

To measure the length of an ant, well, we discussed that earlier, millimetres is definitely the way to go.

The mass of a person would be in kilogrammes, capacity of a bucket in litres, and the height of a house is definitely a metres measurement.

What about question three, though, with the imperial measures? The length of an ant would be measured in inches.

The mass of a person, now you could have said stones, or you could have said stones and pounds, or just pounds, any of them would be okay.

We've then got capacity of a bucket, which is in pints, and the height of a house, which is measured in feet.

To sum up our lesson, we can think about the following two statements.

Measures can be converted to the same units to make comparison easier.

We saw that in the first part of today's lesson.

But remember, this is not always necessary as comparing the order of the digits can be enough.

Well done.

You've worked really hard today.

I look forward to seeing you in one of the future lessons.