Lesson video

Hello everyone.

My name's Mr. Gratton, and thank you so much for joining me for today's lesson.

In today's lesson on place value, we'll be looking at converting and comparing between different metric units and seeing if those conversions make sense in a real-world context.

We'll be using a handful of keywords.

Metric units, which are meters, grams, and liters, and the prefixes, centi, milli, and kilo.

Pause here to familiarize yourself with these to keywords.

We will approach this lesson in three parts, starting with converting metric measures using place value.

We can use place value charts to visualize conversions.

You must always focus on the ones digit first no matter how big or small the number is.

The unit is meters, so I need to place the ones digit, which is two, into the meters column.

All other digits are placed in the correct space so that it matches the original number at the top, in this case, 12.

As we are converting into centimeters, we then insert placeholder zeros up to and including the centimeters column.

The decimal point goes to the right of the unit we are converting to, but because 1,200 is an integer, we do not need to keep it.

However, other conversions may require you to keep the decimal point, so this step is important to consider.

Our answer is then 1,200 centimeters.

Here is a similar example.

Note the decimal point, it does not change our procedure at all.

We always focus on the ones digit first.

The ones digit is seven.

This goes in the kilograms column because the unit is currently kilograms. The five goes to the right.

Because we are converting into grams, we include placeholder zeros up until and including the grams column.

As before, the decimal point goes after the number that we are dealing with.

But because 7,500 is an integer, we can ignore it.

The answer is then 7,500 grams. Looking at a place value chart is always helpful, but sometimes it's a bit impractical and long-winded.

We can also convert by looking at the prefixes of our units.

Kilograms means 1,000 grams. So 7.

5 kilograms means 7.

5 lots of 1,000 grams. The calculation is 7.

5 times by 1,000 which is 7,500 grams. The same answer as before.

Final check, Jun says, if I convert 0.

47 liters into milliliters, I get? Choose the right value to finish off his sentence.

Pause the video now to make your selection or wait a little bit to get a hint.

Okay, here's the hint.

The correct answer is D, 470 milliliters.

Whilst B also represents the same value, it is best not to have leading zeros to the left of your answer unless absolutely necessary.

Notice how all of our answers so far have gone from a smaller number to a larger number.

This is because we have converted from larger units to smaller units.

We can also do the opposite.

The process is identical with a few small adjustments later on in the process.

As with before, start with the ones digit, place it in the milliliters column, and grow the number out from there, to get 6,050.

We are converting into liters.

As with before, we need to place the decimal point to the right of the unit you are converting into.

In this case, I put the decimal point to the right of the liters column.

The decimal point is now necessary to keep and so the answer is 6.

05 liters.

This makes sense as 6,000 milliliters is exactly six liters.

And so slightly above 6,000 milliliters will be slightly above six liters.

6.

05 matches this.

We can also convert this using the prefixes.

So milliliter means 1/1000 of a liter.

So 6,050 milliliters means 6,050 over 1,000 of a liter.

This can be also described as 1,000 times smaller than 6,050.

1,000 times smaller than 6,050 is 6.

05 liters, the same answer as before.

Right, check time again.

Complete Jacob's sentence.

I have a bottle of water that says 660 milliliters.

This is the same as? Pause the video to think what the answer could be.

Remember, when you're converting into liters, you need to include placeholder zeros up to and including the liters column and have the decimal point after the liters.

The answer is 0.

66 liters, B.

Well done if you got that correct.

Okay, here are a few practice questions for you to try.

You can use the place value charts to help you if you want to, but you can choose not to use them if you feel confident enough.

Pause the video to do those conversions.

Okay, as with before, I've given you an even less filled in place value chart for you to use if you want.

Pause the video to attempt these conversions.

Right, let's go through question one.

If I were to convert seven kilometers into meters, I would have to multiply the number by 1,000, so the answer is 7,000 meters.

To convert from meters to centimeters, I multiply it by 100 again, which gives me 700,000 centimeters.

To convert from centimeters to millimeters, I multiply by 10 one more time, which gives me 7 million millimeters.

Well done if you got those three correct answers.

Similarly for question two, if you got 0.

425 liters, very well done.

Remember, you have to include placeholder zeros here on the left underneath the liters header.

Okay, question number three is very similar to question number two.

The answer is 0.

163 kilograms. Well done if you got that right.

Notice how question four is different to questions three and two.

We are converting from a large unit capacity to a small one, making our answer 1,150 milliliters.

Well done if you spotted those details.

Now that we're familiar with converting into different units, let's put this into some practical use by comparing the size of different measures.

For example, Lucas and Sofia both give the distance they travel to school, but Lucas gives it in kilometers and Sofia in meters.

Who walked further? Remember, kilometer means 1,000 meters.

We can use this to convert one of the two values and we can choose either, it does not matter.

So let's do both one at a time.

First up, Lucas, converting kilometers into meters.

1.

2 kilometers means 1.

2 lots of 1,000 meters.

So we multiply 1.

2 to 1,000.

Therefore, Lucas traveled 1,200 meters and Sofia 850 meters.

Onto Sofia, converting from meters into kilometers.

850 meters means 1,000 times smaller than 850 kilometers, which is a division that gives you 0.

85 kilometers.

Either way, we can see that Lucas traveled further.

Okay, similar question.

Can this kettle of 1.

85 liters fill four 400 milliliter cups? We can convert both values as before, but I'm just going to convert once, converting the 1.

85 liters.

Remember, milliliter means 1/1,000 of a liter.

By converting 1.

85 liters, we will avoid decimals, which is why it's my preferred method.

1,000 lots of 1.

85 is 1,850 milliliters and that is the capacity of the kettle.

Right, if we focus on the four cups, four lots of 400 multiplied together is 1,600 milliliters.

The kettle has a bigger capacity and so it can fill all the cups with water to spare.

Okay, check time.

Which bottle contains the most liquid? Pause and figure that out.

Ah, both are equal because 0.

82 liters is equal to 820 milliliters, so they are exactly the same capacity.

We can find out values bigger or smaller than a measurement by converting the measures first.

So, Laura asks to find three different distances with three different units that are all longer than 20 meters.

My advice is to convert 20 meters into the other units of distance.

These are kilometers, centimeters, and millimeters.

Before attempting to find the distances that are longer, I want to focus on the conversions first.

20 meters is equal to 0.

02 kilometers, 2,000 centimeters, and 20,000 millimeters.

And so that conversion has basically done the whole job for us.

Any number bigger than those three values will be a suitable answer.

Here are some examples.

0.

03 kilometers is bigger than 0.

02 kilometers, 2,500 centimeters is bigger than 2,000 centimeters, and 20,001 millimeters is bigger than 20,000 millimeters.

Right, next few checks.

Select all the capacities that are bigger than 1.

04 liters.

Remember, you will have to convert the 1.

04 liters first.

There may be more than one correct answer.

Pause and give it a go.

1.

04 liters is equal to 1,040 milliliters.

So the only correct value is D.

Onto independent practice.

By converting the units of every animal first, find out which cat is longest, for question one, and which dog is heaviest, for question two.

Pause the video and good luck.

Convert these values first to answer the questions.

There are multiple, multiple correct answers for each.

Pause the video and good luck.

For question five, place these distances in order of size, smallest first.

It might help to convert them all into a common unit.

Which unit you choose is up to you.

Take your time, pause, and good luck.

By converting all of the cats to millimeters, we see that the first cat is the longest at 1,070 millimeters.

Converting all of the dogs to grams, we can see the second dog is the heaviest or has the greatest mass.

For question number three, 1.

3 liters is the same as 1,300 milliliters, so any number less than 1,300 milliliters is correct.

Careful on question four though, 2,300 kilograms becomes 2,300,000 grams. So any number bigger than that 2,300,000 is correct.

Question number five, I converted all of those into meters.

Do not worry though if you converted into a different unit, like centimeters or kilometers.

Regardless of the unit, the correct order is the same.

F is the shortest, then D.

B and E are equal in size.

Very well done if you spotted that.

Then C, and then A is the longest.

Now that you're hopefully familiar with converting and comparing, let's check if the conversions people make are sensible, especially when comparing to real-world things.

Right, starting with Jun, who says his mum drove 16 kilometers to work.

Well, 16 kilometers is reasonable for someone who travels to work in a different but nearby city or town.

But Jun says that this is equal to 160 meters.

Is Jun correct? Well, 16 kilometers is equal to 16,000 meters.

Jun's thought is 100 times too small to be correct.

How do I know instantly without converting that Jun's thought was not sensible? Well, 160 meters is a short walk down the road, not a drive to work.

Okay, final check.

This small aircraft is 13 meters long.

This is the same as 13,000, what? Which answers, if any, look sensible? You can also convert 13 meters to confirm your answer.

Pause and give it a go.

Right, 13,000 millimeters is the correct answer as there are 1,000 millimeters in a meter.

Let's look at the other options.

13,000 kilometers is far too big.

In fact, it is the distance that nearly gets you to Australia.

13,000 centimeters is ambiguous.

You can't tell instantly if it's correct or incorrect, so it is sensible to do the mathematical conversion to check it wasn't the correct answer.

And now onto the final few independent practice tasks.

For questions one and two, using either understanding of real-world measurements or by converting, I do not mind which, figure out which of these values are correct conversions for the mass of the bike and the water capacity of a full bathtub.

There may be more than one correct answer for either question.

Pause and give these questions a go.

Right, a cruise ship is huge.

This one is 0.

29 kilometers long and has a mass of 113 million kilograms. By converting these values into different units, think about what missing units would go with the 290 and the 29,000, and what number goes before the grams. Take some time to think.

Pause the video and off you go.

And the last question.

The value on the left of each pair is shorter.

The value of the right of each pair is either longer or taller.

Come up with a number to make these descriptions correct.

Again, you'll have to do some conversions first.

Pause and good luck.

Onto the answers.

For question number one, 1.

457 kilograms is too light.

It's the mass of a small watermelon.

145.

7 kilograms is far too heavy.

It's the mass of a lion.

And so 14.

57 kilograms is correct.

Question number two, there are two answers here.

182 liters, which is found by dividing 182,000 by 1,000.

This might seem quite high, but remember you rarely fill a bathtub all the way to the top.

The other answer is 18,200 centiliters, an uncommon but still used unit of capacity.

We get this by dividing 182,000 by 10, as centi is 10 times bigger than milli.

Okay, onto question three.

First, let's convert 0.

29 kilometers into meters.

This gives us 290 meters.

Converting from meters to centimeters gives us 29,000 centimeters.

And converting from kilograms to grams means multiplying, multiplying by 1,000.

So 130 million multiplied by 1,000 is 113 billion.

Yes, that is nine zeros after the 113.

Right.

And last question, question four.

24,400 centimeters is the same as 244 meters.

Since 225 meters is still too small, the missing unit must be kilometers.

And for Izzy's height, 0.

0017 kilometers is the same as either 1.

7 meters or 170 centimeters.

Since 16.

5 meters is too big, it must be centimeters.

And if centimeters is correct and millimeters is a smaller unit, millimeters must also be correct.

Mark your answers, and very well done for all the questions you've completed today.

And that concludes our lesson on metric units.

Today we have covered converting using place value charts and converting using prefixes.

We have also compared two or more measures using conversion and checked whether those conversions make sense in a real-world context.

Right, that is all for today.

Thank you so much for joining me, and I hope to see you soon for some more maths.