Lesson video

Hi, I'm Mr. Tazzyman.

Today I'm gonna teach you a lesson from a unit that's all about multiplying and dividing by two digit numbers.

There might be lots of steps that you encounter here, but it's really important for you to understand not just the steps but the maths behind those steps as well.

So sit back.

Listen well.

It's time to learn.

Here's the outcome for today's lesson then.

By the end, we want you to be able to say, "I can divide numbers with up to 4 digits by multiples of 10." These are the key words that you might expect to hear during the lesson.

We need to know how to say them and to understand them in order to help your learning.

I'm gonna say the word and I want you to repeat it back to me.

I'll say my turn, say it, and then I'll say your turn, and you can repeat it back.

Ready? My turn.

Dividend.

Your turn.

My turn.

Divisor.

Your turn.

My turn.

Multiple.

Your turn My turn.

Quotient.

Your turn.

So that's how you say those words.

Well done, but let's see what each of them means.

The dividend is the amount that you want to divide.

A divisor is the number we divide by.

A multiple is the result of multiplying a number by another whole number.

A quotient is the result after division has taken place.

This is the outline for the lesson today then.

We're gonna start dividing by multiples of 10.

Then we're gonna look at solving measurement problems. Sam and Andeep are gonna help us today.

Hi, Sam.

Hi, Andeep.

They're gonna be discussing some of the maths problems to give us a clue about their thinking and that's gonna help us to think as well.

Okay, ready to start? Let's go for it.

Andeep and Sam are dividing by multiples of 10.

"Let's start by dividing 1,240 by 40." They've written out the division expression there and they've got an equal sign next to it.

"We can divide both the dividend and divisor by 10 and the quotient doesn't change." So now, we've got 124 divided by 4.

The quotient will still remain the same.

"We could skip count in multiples of 4 to divide 124 by 4." "30 groups of 4 is close.

We need one more group of 4." 31 multiplied by 4 is equal to 124.

124 divided by 4 then is equal to 31.

So that means that 1,240 divided by 40 is also equal to 31 because if you divide both the dividend and divisor by the same amount, then the quotient remains unchanged.

Andeep and Sam try a different strategy.

"Let's start by dividing 1,240 by 40." "We can scale down the dividend and divisor again to make a simpler calculation." You can see that they've done that.

They've divided both the dividend and divisor by 10.

That creates a new division expression of 124 divided by 4, next to which they've written the equal sign ready to put the quotient in once they've worked it out.

It's all about trying to make the division simpler because otherwise it can look intimidating to begin with.

"They're both multiples of 2." That's a good spot from Andeep.

124 and 4 are both even numbers, so they must be multiples of 2.

So now, they can divide them both by 2.

Again, the quotient will remain the same because they've divided both the dividend and divisor by 2.

Now, they've got 62 divided by 2.

62 divided by 2 is the same as half of 62 and that's 31.

That's a nice simple equation to calculate.

And of course, because 62 divided by 2 is equal to 31, so is 124 divided by 4, and so is 1,240 divided by 40.

Sam notices something.

"This strategy reminds me of simplifying fractions.

I can write the division as a fraction." 1,240/40.

"I can divide the numerator and denominator by 10 to make an equivalent fraction," is equal to 124 quarters.

"They're both multiples of 4 so I can divide by 4." That is equal to 31 wholes.

I know a fraction over one is the same as a whole number.

This is 31.

Andeep and Sam are dividing by multiples of 10 again.

"Let's start by dividing 1,320 by 60." "We can divide both the dividend and divisor by 10 and the quotient doesn't change." We've now got 132 divided by 6.

"We could skip count multiples of 6 to divide 132 by 6." "60 groups of 6 is close.

We need two more groups of 6." 22 multiplied by 6 is equal to 132.

That means that 132 divided by 6 is equal to 22.

They're using their understanding of the inverse.

And ultimately, that also then means that 1,320 divided by 60 is also equal to 22.

Because remember, the quotient remains unchanged if you divide both the dividend and divisor by the same amount.

Okay, it's your turn.

Let's check your understanding so far.

Try and put into good practise some of the strategies you've just been learning about.

You've got to calculate 960 divided by 30.

Pause the video and give it a go.

Welcome back.

Sam says, "You can divide both the dividend and divisor by 10 and the quotient doesn't change." So that's a good first step.

We're trying to make this calculation easier.

We've now got 96 divided by 3.

You could skip count in multiples of 3 to calculate 96 divided by 3.

10 lots of 3 are 30.

20 lots of 3 are 60.

30 lots of 3 are 90.

32 lots of 3 then are 96.

That means 96 divided by 3 is equal to 32, and also 960 divided by 30 is equal to 32.

Is that what you got? Hope so.

Okay, let's move on.

Andeep and Sam tried to find the missing divisor.

We've got 1,250 divided by an unknown is equal to 50.

"We can change around the divisor and quotient." Can you see they've swapped them over in the equation? 1,250 divided by 50 is equal to the unknown.

"We can divide both the dividend and divisor by 10 and the quotient doesn't change." Same trick as usual then, making that calculation simpler to work out.

Now, we've got 125 divided by 5.

The quotient will be the same.

We could then skip count in multiples of 5.

Another 5 multiplied by 5 is equal to 25.

So 25 multiplied by 5 is equal to 125.

So we know that 125 divided by 5 is equal to 25.

That means 1,250 divided by 50 is also equal to 25, but that's not quite the finish.

We also then need to put that unknown, which we found out the value of into the initial equation because there it was the divisor and not the quotient.

Andeep says, "1,250 divided by 25 is equal to 50." Andeep and Sam tried to find the missing dividend again, but we've got a different equation this time.

An unknown divided by 90 is equal to 15.

"We can use multiplication to solve this problem," says Andeep.

"We can divide both the dividend and divisor by 10 and the quotient doesn't change." Same trick again.

The difficulty here is that one of them is an unknown.

So now, we've got an unknown divided by 9 is equal to 15.

There are 15 groups of 9 in the dividend.

So we need to calculate 15 multiplied by 9.

Andeep is talking about using the inverse here.

15 multiplied by 9 is equal to.

Well, let's work it out.

10 multiplied by 9 is equal to 90.

5 multiplied by 9 is equal to 45.

15 multiplied by 9 is equal to 90 plus 45, which is equal to 135.

135 divided by 9 is equal to 15.

Now, can we put 135 in our initial equation? No, because we know that we divided a number by 10 to give us 135.

So it must be 1,350 divided by 90 is also equal to 15.

1,350 is the missing dividend.

Okay, it's your turn then.

Let's check your understanding so far.

You've got to find the missing dividend in this equation.

An unknown divided by 60 is equal to 16.

Andeep gives us a tip here, says, "You can use multiplication to solve this problem." And Sam reminds us of a good way to start.

"You can divide both the dividend and divisor by 10 and the quotient doesn't change." So there's your introductory steps to help you along the way.

Pause the video and give this a go.

Good luck.

Welcome back.

So, if we had divided, even though it was an unknown, the dividend and divisor by 10, we ended up with an unknown divided by 6 is equal to 16.

There are 16 groups of 6 in the dividend.

So you need to calculate 16 multiplied by 6.

We can do that by firstly calculating 10 multiplied by 6, which is equal to 60, and then 6 multiplied by 6, which is equal to 36.

And adding those two together, we get 96.

96 divided by 6 is equal to 16.

There it is.

We've got the first unknown, but we need to know what the initial unknown was.

And of course it was divided by 10 to get 96.

That means that it was 960.

"960 divided by 60 is also equal to 16." "960 is the missing dividend." Did you manage to get it? Hope so.

Okay.

It's your first practise task now.

I'd like you to calculate each missing quotient from A to F.

"You can divide both the dividend and divisor by 10 and the quotient doesn't change." "Skip counting multiples of the divisor to work out the quotient." For number two, calculate each missing dividend or divisor.

"You can change around the divisor and quotient." That's a good tip.

"Use multiplication to solve problems with missing dividends." All right, pause the video here and give that a really good go.

Good luck.

Okay, here are the answers then.

Let's just look at 1A to begin with.

The answer was 16, but how might you have got there? Well, Sam did this.

"800 divided by 50 is equivalent to 80 divided by 5." So dividing the dividend and divisor by 10 means that the quotient will remain the same, but it's an easier calculation to make.

"10 multiplied by 5 is equal to 50.

6 multiplied by 5 is equal to 30.

So 16 multiplied by 5 is equal to 80." That means that 80 divided by 5 is equal to 16.

So 800 divided by 50 is also equal to 16.

Now, for the rest of the answers, I will read out what the missing quotient was.

For B, it was 16.

For C, it was 25.

For D, it was 24.

For E, it was 24.

And for F it was 22.

Pause the video if you need some extra time to catch up with the marking.

Let's look at number two, then.

Here are the answers and we'll look at 2A to begin with.

"To answer A, you could calculate 1,020 divided by 60 or 102 divided by 6." "10 multiplied by 6 is equal to 60.

7 multiplied by 6 is equal to 42.

So 17 multiplied by 6 is equal to 102." That meant that 102 divided by 6 was equal to 17.

And of course 17 in the initial equation is appearing in the divisor position.

But you can swap around the divisor and the quotient to help.

Okay, here are the answers for the rest, then.

I'll read out the missing numbers only.

For B, it was 880.

For C, it was 690.

For D it was 9 and then the quotient was 90.

For E it was 1,500.

And for F it was 1,850.

Pause the video here if you need some extra time to mark.

Let's go to the second part of the lesson now.

We're gonna solve some measurement problems. Andeep walks 70 metres in one minute.

"How long would it take me to walk? 1.

4 kilometres?" "1.

4 kilometres is equal to 1,400 metres." Really good conversion, Sam.

Well done.

You know your conversion facts.

"I need to divide 1,400 by 70.

I can divide both the dividend and divisor by 10." Great start.

Now, we've got 140 divided by 7.

That's an easier calculation.

10 multiplied by 7 is equal to 70.

20 multiplied by 7 is equal to 140.

Aha.

That means that 140 divided by 7 is equal to 20.

So 1,400 divided by 70 is equal to 20 as well.

"It takes me 20 minutes to walk 1.

4 kilometres." A class of children are making flapjacks.

Mm, flapjacks.

"Each child needs 80 grammes of oats.

A bag contains 2 kilogrammes of oats." "How many portions of 80 grammes will the bag of oats provide? 2 kilogrammes is equal to 2,000 grammes." Again, well done, Sam.

You've got your conversion facts sorted.

2,000 divided by 80.

"I can divide both the dividend and divisor by 10 to get 200 divided by 8." Quotient remains the same, but it's an easier calculation to make.

"Then I can divide 200 and 8 by 4 to make a simpler calculation." So this time we've not finished dividing the divisor and dividend.

Divide them both by 4.

Now, we've got 50 divided by 2.

Even simpler still.

"Half of 50 is much easier than dividing 2,000 into groups of 80." It's 25.

"There are enough oats in the bag for 25 children." Okay, it's your turn.

Let's check your understanding.

A class of children are making flapjacks.

"Each child needs 40 grammes of sugar.

A bag contains 1 kilogrammes of sugar." "How many portions of 40 grammes will the bag of sugar provide? You could divide both the dividend and divisor by 10." All right, pause the video here and give that a go.

Good luck.

Welcome back.

You might have started with this.

"1 kilogramme is equal to 1,000 grammes." 1000 divided by 40 is what we need to work out.

Divide both the dividend and divisor by 10 and we get 100 divided by 4.

25 multiplied by 4 is equal to 100.

100 is composed of 4 groups of 25.

"There is enough sugar in the bag for 25 children." Did you get that? Hopefully.

Andeep has spotted a connection.

Oh, good.

I like connections.

They help us to learn.

"Do you notice anything, Sam?" We've got two equations here.

2,000 divided by 80 is equal to 25.

1,000 divided by 40 is equal to 25.

Hmm.

Wonder what Andeep is getting at here.

Sam says, "I noticed that 2,000 divided by 80 is equivalent to 1,000 divided by 40." "I can halve the dividend and divisor and the quotient remains the same." Sam's mum takes part in a swimming race.

"Sam's mum has to swim 2.

1 kilometres." "My mum swims 60 metres in a minute.

How long will it take her to complete the race?" "2.

1 kilometres is equivalent to 2,100 metres." 2,100 divided by 60.

That's what we need to calculate.

"I can divide both the dividend and divisor by 10." Now, we've got 210 divided by 6.

A simpler calculation.

10 multiplied by 6 is equal to 60.

20 multiplied by 6 is equal to 120.

30 multiplied by 6 is equal to 180.

5 multiplied by 6 is equal to 30.

So 35 multiplied by 6 is equal to 210.

So the answer is 35.

"It takes Sam's mum 35 minutes to complete the race." The tomatoes have a total mass of 3.

36 kilogrammes.

"Each tomato has a mass of 80 grammes.

How many tomatoes are there altogether?" "3.

36 kilogrammes is equal to 3,360 grammes." 3,360 divided by 80 is equal to.

That's what we need to work out.

"I can divide both the dividend and divisor by 10." Now, I've got 336 divided by 8.

10 lots of 8 are equal to 80.

20 lots of 8 are equal to 160.

40 lots of 8 then are equal to 320.

So we had some doubling there.

2 lots of 8 is equal to 16.

So 42 multiplied by 8 equals 336.

The answer then is 42.

"There are 42 tomatoes in total." Okay, let's check your understanding so far.

Andeep walks 70 metres in one minute.

"How long would it take me to walk 3.

5 kilometres?" He asks.

Pause the video and give that a go.

Welcome back.

Well, Sam starts by saying this, "3.

5 kilometres is equal to 3,500 metres.

I need to divide 3,500 by 70.

I can divide both the dividend and divisor by 10." Making that calculation simpler, that's now 350 divided by 7.

You might start to see something in those digits that links the two numbers together.

10 multiplied by 7 equals 70.

20 multiplied by 7 equals 140.

30 multiplied by 7 equals 210.

40 multiplied by 7 equals 280.

And of course, 50 multiplied by 7 equals 350.

You might have known that already because you knew your 7 times table, and 5 multiplied by 7 equals 35.

So the answer was 50.

"Takes me 50 minutes to walk 3.

5 kilometres." Okay, it's time for your second practise task.

You've got to find the answer to each problem.

Some frogs have a total mass of of 2.

97 kilogrammes.

How many frogs are there altogether? Some frogs have a total mass of 3.

33 kilogrammes.

How many frogs are there altogether? Some frogs have a total mass of 4.

41 kilogrammes.

How many frogs are there altogether? Each frog has a mass of 90 grammes.

You'll need to convert kilogrammes into grammes.

You can divide both the dividend and divisor by 10.

I'm glad Andeep told us how much each frog weighs, otherwise it would've been a very tricky question indeed.

Here's number two.

Three athletes swim at different speeds.

Athlete A swims 60 metres in a minute.

Athlete B swims 70 metres in a minute.

And athlete C, wow, swims 80 metres in a minute.

For A, which athlete swims exactly 1,840 metres in 23 minutes? For B, which athlete swims exactly 2.

52 kilometres in 42 minutes? For C, which athlete swims exactly 4,080 metres in 51 minutes? And for D, which athlete swims exactly 3.

85 kilometres in 55 minutes.

Okay, so good questions there to really help you to practise what you've learned today.

Andeep helps us with the tip here.

He says you might need to use trial and improvement to work out each answer.

Thanks, Andeep.

Okay, pause the video here and give those questions a good go.

Welcome back.

Here are the answers, but remember, a frog has a mass of 90 grammes.

297 divided by 9 is equal to 33.

So 2,970 divided by 90 is also equal to 33.

33 frogs have a mass of 2.

97 kilogrammes.

For B, 333 divided by 9 is equal to 37.

So 3,330 divided by 90 is also equal to 37.

That means 37 frogs have a mass of 3.

33 kilogrammes.

For C, 441 divided by 9 is equal to 49.

So 4,410 divided by 90 is equal to 49.

49 frogs have a mass of 4.

41 kilogrammes.

Here's number two then.

For A, 184 divided by 8 is equal to 23.

So 1,840 divided by 80 is equal to 23 as well.

Athlete C swims 1,840 metres in 23 minutes.

For B, 252 divided by 6 is equal to 42.

So 2,520 divided by 60 is also equal to 42.

Athlete A swims 2,520 metres in 42 minutes.

Let's look at C then.

408 divided by 8 is equal to 51.

So 4,080 divided by 80 is also equal to 51.

Athlete C swims 4,080 metres in 51 minutes.

And lastly, D, 385 divided by 7 is equal to 55.

So 3,850 divided by 70 is equal to 55 as well.

Athlete B swims 3,850 metres in 55 minutes.

Pause the video here if you need any more time to mark those carefully.

That brings us to the end of the lesson, and here's a summary of all of our learning.

If the dividend and divisor are both scaled by the same amount, the quotient will remain the same.

If you divide the dividend and the divisor by 10, the quotient will remain the same.

Skip counting in multiples of the divisor can help you solve the problems. My name's Mr. Tazzyman.

I enjoyed that.

Hope you did as well.

Maybe I'll see you again soon.

Bye for now.