Lesson video

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Hello, I'm Mrs. Goldie and I would like to give you a warm welcome to today's lesson.

In today's lesson, you're going to find out how to order, and compare a variety of measurements.

This builds on the work that you've learned already on metric units and also the work that you've done on place value.

Here are the key words that we'll be using in today's lesson.

The first is inequality.

You can use an inequality to show that one number, or a measurement is not equal to another.

You use special symbols to show an inequality.

There are two inequality symbols.

One which means less than and the other means greater than.

Today's lesson is in two parts.

In the first part, we're going to be looking at comparing measures, and in the second, ordering.

Let's get started.

Which of these two people drank more water? How can you tell? Aisha says that she drank 1.

75 litres of water today, whereas Alex says that he drank more, and he drank 1,705 millilitres of water.

How can we see who drank more? When you compare measures, it's often useful to write them using the same units.

Let's look at comparing 1.

75 litres, and 1,705 millilitres.

Can you have a think about which one of these statements is correct? Is it A? 1.

75 is less than 1,705, so 1,705 millilitres is more.

Or is it statement B? You can convert 1.

75 litres into millilitres in order to compare them.

Or is it statement C? Litres are bigger than millilitres, so 1.

75 litres is more.

Pause the video and have a think about which statement is right.

Did you choose statement B? That's the right answer.

You need to convert litres into millilitres in order to compare them.

Of course, you could also convert millilitres into litres.

Now, we're going to look at how you can use a place value chart to convert units.

We're looking at converting litres into millilitres.

So we need the place value chart that shows this.

Let's enter 1.

75 litres on the chart.

Now, let's think about converting it.

75 litres is the same as 17.

5 deciliters, and it's the same as 175 centilitres.

That's because one litre is the same as a hundred centilitres.

And you can also write it as 1,750 millilitres.

So all of those measurements are equivalent to each other.

Now, we can compare them.

Do you remember Alex had drunk 1,705 millilitres of water? So he has drunk less water than Aisha.

The symbols less than and greater than are called inequality symbols.

You can use an inequality to show that two quantities are not equal.

So for example, you can say that 1,705 millilitres is less than 1,750 millilitres.

You can write it the other way round if you like.

You can say that 1,750 millilitres is greater than 1,705 millilitres.

Both these statements are correct.

Can you select the correct statement here? 1.

75 litres is less than 1,705 millilitres, or should it be 1,705 millilitres is less than 1.

75 litres? Or should it be 1,705 millilitres equals 1.

75 litres? Which statement is correct? Pause the video while you think about the answer.

Welcome back.

Did you select answer B? That's the correct answer.

75 litres is the same as 1,750 millilitres.

Statement C, you should be able to see it can't be correct, because the digits are in a different order.

Let's look at another example now.

Is this statement true or false? Is 4.

334 kilogrammes greater than 4.

34 kilogrammes? Once you decide, think about how you can justify your answer.

Pause the video and think about it.

Welcome back.

Did you choose false? 4.

334 kilogrammes is less than 4.

34 kilogrammes.

That's because the first digit that's different is in the hundredths place, and three is less than four.

So 4.

334 kilogrammes is less than 4.

34 kilogrammes.

Let's look at another example.

You can use an inequality symbol to complete this statement.

Let's use a place value chart to help us.

A 166 centimetres is shown on the place value chart.

Now, let's convert that to metres.

You know that one metre is a hundred centimetres, so metres is going to be 1.

66 metres.

Can think about this another way.

One centimetre is 100th of a metre, which is 0.

01 metres.

So a 166 centimetres is a 166 hundredths of a metre, which is 1.

66 metres.

So which is more? 1.

66 metres is greater than 1.

6 metres.

And so going back to the original question, a 166 centimetres must be greater than 1.

6 metres.

Now, it's your turn.

Can you use an inequality symbol to complete this statement? Pause the video while you write down your answer.

Welcome back.

Did you use a place value chart? Here's what it might look like.

20 centimetres is the same as 0.

2 metres, and that's because one centimetre is a hundredth of a metre, so it's 0.

01 metres.

And so 20 centimetres is 20 hundredths of a metre, which is 0.

2 metres.

And we can see that 0.

2 metres is less than 0.

22 metres.

And so 20 centimetres is less than 0.

22 metres.

Did you choose the correct symbol? Well done.

Now, it's your turn to answer a task.

In this task, task A, question one, I'd like you to write the correct symbol into each circle to complete each statement.

You can choose between a less than symbol, a greater than symbol, or an equals.

If you like, you may use the place value chart to help you with the conversions.

Pause the video while you answer this question.

Welcome back.

Here's question two of task A.

Here, I'd like you to write a digit in each square.

So you may choose nought, one, two, three, four, five, six, seven, eight or nine, and write it in each square.

And a symbol, less than, greater than or equals in each circle.

Choose your digits and symbols wisely to make each statement correct.

If you like, we've got a place value chart there to help you with your conversions.

Pause the video while you answer this question.

Welcome back.

Here's question three of task A.

You've got six cards, one says seven, one, eight, one, nine, and then you've got three symbols, less than, greater than or equal in three more cards.

Can you use those cards to complete this statement in as many different ways as you can? So the statement says 0.

879 kilogrammes, something grammes.

See how many different ways you can find.

Pause the video while you answer this question.

Welcome back.

Now, it's time to go through the answers.

Let's look at part A.

23 metres is the same as a 123 centimetres.

So this is greater than 12.

3 centimetres.

Now, prob B.

456 kilogrammes is the same as 456 grammes.

So that is less than 465 grammes.

Now, part C.

570 millimetres is the same as 57 centimetres, so that is greater than 7.

5 centimetres.

Part D.

985,000 metres is the same as 985 kilometres, and that is greater than 958 kilometres.

Part E.

30,000 millilitres is the same as 30 litres.

So you'd use an equals symbol here.

Part F.

989 centilitres is the same as 9,890 millilitres.

So that's less than 9,980 millilitres.

Did you use the place value chart? How did you do? Now, let's look at question two.

You need to write a digit in each square, and a symbol in each circle to complete each statement.

In part A, there's only one option, 0.

29 metres is the same as 29 centimetres.

In part B though, you might have found more than one answer.

You could have written that 3.

48 kilogrammes is equal to 3,480 grammes, or you might decide to write 3.

48 kilogrammes is less than 3,490 grammes, or you might have written that 3.

48 kilogrammes is greater than 3,470 grammes.

Or did you find another answer? In part C, you might have written that 13,400 centimetres is less than 0.

15 kilometres, or you might have written that 13,400 centimetres is greater than 0.

05 kilometres.

What about Part D? You should have written that 0.

098 metres is less than 99 millimetres.

In part E, you might have written that 200 millilitres is equal to 0.

2 litres, or you might have written that 201 millilitres is greater than 0.

2 litres.

Or did you find another answer? In part F, you might have written that 78 milligrammes is less than 0.

08 grammes.

Or you might have written that 78 milligrammes is greater than 0.

07 grammes.

You might find different answers here as well.

How did you do? Here are the answers for part three.

You need to use the six cards to complete the statement in as many different ways as you could.

So you might have found that 0.

879 kilogrammes is equal to 879 grammes.

879 kilogrammes is less than 897 grammes.

Or you might have found that 0.

879 kilogrammes is less than 978 grammes, or that it is less than 987 grammes, or that 0.

879 kilogrammes is greater than 789 grammes, or that it is greater than 798 grammes.

There are only six possible answers here.

Did you find them all? Can you look and see how we can work systematically to find them all? The second part of our lesson is on ordering measures.

So we've looked at comparing and now, we can look at putting them into an order.

Look at these three children.

Izzy says her dog is huge.

"He is a 120 centimetres from nose to tail." Whereas Sofia says, "My dog's bigger than yours, he weighs 30 kilogrammes." And Jacob says, "My dog is the biggest.

He drinks 850 millilitres of water every day." Who is right? How can you tell? Pause the video while you think about your answer.

Welcome back.

Did you decide you can't tell? You're right.

You cannot compare different types of measurement.

We can't compare centimetres with kilogrammes, or kilogrammes with millilitres.

When you want to compare measurements, it is important they're all measuring the same thing.

So to order measures, length can only be compared with other lengths.

Masses can only be compared to other masses, and capacities or volumes can only be compared to other capacities or volumes.

Let's check this.

Can you select the list which can be ordered? Pause the video while you think about your answer.

Welcome back.

Let's have a look.

List A has litres, milligrammes, centilitres, and millilitres.

Litres, centilitres and millilitres all measure volume, but milligrammes measures mass, so you can't order list A.

List B has kilometres, metres, centimetres, and millimetres.

These are all lengths.

So you can order list B.

Let's check the other lists.

List C has kilogrammes, grammes, millilitres, and kilogrammes.

So that can't be ordered, because you can't order units of mass and units of volume.

And list D has kilogrammes, kilometres, metres, and litres.

So again, it has units of length and units of volume, and that can't be ordered.

So the correct answer is list B.

How can you order these journeys? Aisha walked 423 metres to school.

Sofia walked 2.

34 kilometres to school.

Laura walked 324,000 centimetres to school.

And Andeep walked 432,000 millimetres to school.

How can we put these journeys in order? We can write them all in metres, and then we'll be able to compare them.

So Aisha's journey is already in metres, we don't need to touch that one yet.

34 kilometres is the same as 2.

34 times a thousand metres.

So it's 2,340 metres.

That's because one kilometre is a thousand metres.

Laura's journey, she walks 324,000 centimetres, which is 324,000 hundredths of a metre, because one metre is a hundred centimetres.

So she walks 3,240 metres.

Andeep walks 432,000 millimetres, and a millimetre is a thousandth of a metre.

So he walks 432,000 thousandths of a metre, which is the same as 432 metres.

Now, we've got them all in metres, we can put them in order.

423 metres is less than 432 metres, so it's less than 432,000 millimetres.

And in turn, that is less than 2,340 metres.

So it's less than 2.

34 kilometres, and that is less than 324,000 centimetres, because that was 3,240 metres.

So Laura walked the furthest to school.

Now, let's check your learning.

Which of these lists is incorrect? Take a look at each list and decide whether it's in the correct order.

Pause the video while you think about your answers.

Welcome back.

Let's look at list A.

All of these say 2.

So we only need to look at the measurements, the units to compare them.

And we know that millimetres are smaller than centimetres, which are smaller than metres, which are smaller than kilometres.

So list A is in the correct order.

Let's have a look at list B.

2 millimetres is less than 0.

2002 metres, which is less than 22 centimetres, which is less than 0.

202 kilometres.

So list B is in the correct order.

Let's look at list C.

0022 kilometres is the same as 220 centimetres, because we need to times it by a thousand to turn it into metres and then a hundred to turn it into centimetres.

And 220 centimetres is not less than 202 centimetres.

So list C is incorrect.

Now, it's your turn.

Here's task B.

Question one is saying, "Starting with the smallest, sort these measures into ascending order." Ascending means going up, so you might ascend a mountain.

So if you are asked to sort a list into ascending order, it means you start the smallest one first, and go up to the largest measurement.

Pause the video while you answer the question.

Now, here's question two.

So here, you've got six cards and you can use those to complete each of those inequalities.

So think about where you can put each one of those cards to make those inequalities correct.

Can you find more than one way of doing it? Pause the video while you answer the question.

Welcome back.

Let's go through the answers.

Question one, part A.

All of the measurements say 99.

So now, we just need to look at the units.

We've got 99 millimetres, which is less than 99 centimetres, which is less than 99 metres, which is less than 99 kilometres.

Now, let's look at list B.

We've got litres, centilitres and millilitres, but two of the measurements are in litres, so it makes sense to change them all to litres.

We've got 0.

03 litres, we've got 30 centilitres, which is the same as 0.

3 litres, so that comes next.

303 millilitres, which is the same as 0.

303 litres.

And then lastly, 0.

33 litres.

Now, we've got list C.

564 millimetres is the same as 0.

564 metres, and 64.

5 centimetres is 0.

645 metres, and we've got 156 metres.

And then lastly, we've got 465 metres.

List D.

We've got 3.

57 grammes, and we've got 35,700 milligrammes, which is 35.

7 grammes.

Then we've got 7,503 grammes, and 7.

53 kilogrammes, which is 7,530 grammes, that comes last.

And now, list E.

List E.

We've got 689 millimetres, which is 0.

689 metres.

Then we've got 0.

896 metres.

Then we've got 0.

00869 kilometres.

So I need to multiply that by a thousand to turn it into metres, which is 8.

69 metres.

And then we've got 986 centimetres, which is 9.

86 metres.

So that's the correct order.

Need to use the cards to complete each inequality.

So for part A, you might have written 1.

2 centimetres is less than a 180 millimetres, which is less than 0.

29 metres.

Or you might have written 1.

2 centimetres is less than a 190 millimetres, which is less than 0.

82 metres, or you might have found a different way to do it.

Part B.

There's only one way to write it and that is 0.

08 kilogrammes is less than 89 grammes, which is less than a 100,000 milligrammes, which is less than 0.

2 kilogrammes.

Did you get those right? Well done.

I think you've done great work today.

Here's what we looked at today.

You can use a place value chart to help you convert between measurements and you can use an inequality symbol, less than or greater than to compare two measurements that are not equal.

And you can order a list of three, or more measurements by writing them all using the same units.

Well done.

I look forward to learning with you again.

I've finished the video