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.

Let's go.

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

By the end, we want you to be able to say I can solve a problem, making appropriate use of the remainder.

The keywords that you might expect to hear are long division and remainder.

I'll say them, and I want you to repeat them back to me.

My turn, long division, your turn.

My turn, remainder, your turn.

Here's the definitions for those keywords then.

Long division is a method used for dividing large numbers by breaking the number down into smaller groups.

A remainder is an amount left after a division.

This is the outline for today's lesson.

We're gonna start by finding the remainder, then we're going to move on to what to do with the remainder.

Sam and Andeep are going to join us today.

They'll be discussing some of the maths prompts that they see on screen and giving us an insight into their thinking.

That's going to help us to learn.

Okay, are you ready to learn? Let's go.

Sam and Andeep are thinking about this division: 248 divided by 24.

This looks like a long division to me.

It could be, but let's have a think about it first.

The numbers look quite friendly to me.

Do you think there will be a remainder? 24 multiplied by 10 is equal to 240, so it must be 10 remainder 8.

He thought about the numbers and got the answer.

No long division needed.

Really important point that you don't always have to go straight to long division.

Sam and Andeep are thinking about how to express the remainder.

248 divided by 24 is equal to 10 remainder 8.

What do we do with the remainder, says Sam? We could write it as a fraction.

248 divided by 24 is equal to 10 and 8/24.

As Sam says, we have 8 out of the next group of 24, so 8 24ths.

8 and 24 share a factor of 8, so it can be simplified to one third.

That's equal to 10 and one third.

Could you express the remainder as a decimal? This is a check of your understanding.

We know so far that 248 divided by 24 is equal to 10 remainder 8.

We also know that 248 divided by 24 is equal to 10 and 8/24, which is also equal to 10 and one third.

Can you express that as a decimal? Pause the video and give it a go.

Welcome back.

1/3 as a decimal is interesting as 3 is not a factor of 100.

1/3 as a decimal is equal to 0.

33333333, with the 3s going on forever.

You can see it written there.

Let's move on.

Sam and Andeep are thinking about this division: 900 divided by 24.

This looks like a long division to me.

It could be, but let's have a think about it first.

These numbers don't look as friendly.

No, they don't.

We need to think about the 24 times table.

Andeep and Sam think about multiples of 24 to help them estimate.

We've got the first 10 multiples listed down there, but we've got some empty spots that we need to fill.

These multiples are useful and easy to calculate using mental strategies.

Let's add in 3 multiplied by 24 by adding 24 and 48, 72, which is most useful to estimate 900 divided by 24.

Well, 30 multiplied by 24 is equal to 720.

40 multiplied by 24 is equal to 960, which is over 900.

A reasonable estimate for 900 divided by 24 is 35 then.

Andeep and Sam calculate 900 divided by 24 using long division.

Their estimate was 35.

We start with the hundreds.

900 divided by 24 is equal to zero hundreds.

Zero is written in the hundreds column of the answer.

We look at the tens next.

90 tens divided by 24 is equal to three tens plus a remainder.

Three tens multiplied by 24 is equal to 72 tens.

We subtract 72 tens from 90 tens to find the remainder.

We get a remainder of 180.

Three is written in the tens column of the answer.

And now it's going to be your turn to check your understanding because you've got to complete the long division from where we got to.

Pause the video here then and have a go.

Welcome back.

We have 12 ones left.

We cannot make any groups of 24 ones.

900 is equal to 37 groups of 24 with a remainder of 12.

37 remainder 12 is close to our estimate of 35.

Is that what you managed to get? Hope so.

Okay, let's check your understanding further.

How do you express the remainder as a fraction and a decimal? So, we know that 900 divided by 24 is equal to 37 remainder 12.

What is the fraction, and what is the decimal remainder? Okay, pause the video and give that a go.

Welcome back.

As a fraction, it is 12/24, which simplifies to 1/2.

1/2 as a decimal is equal to 0.

5.

So, 900 divided by 24 is equal to 37.

5.

Okay, it's time for your first practise task then.

Solve these using long division or an informal method.

Remember to estimate your answer first and express your remainder as a fraction and as a decimal.

For number four, I'm going to read it to you.

It says you've got to complete the division.

Can you do it more than one way? How could you find lots of different solutions? All right, pause the video here.

I'll be back soon with some feedback.

Enjoy and good luck.

Welcome back.

Here's the marking then for the first set of questions one to three.

You could have solved these using long division, but Andeep found a way to solve them mentally.

He says I know that there are four 25s in 100, so there must be 28 in 700 and a remainder of 5.

You can see there that a remainder of 5 becomes 5/25, which is equivalent to 1/5, which gives a decimal remainder of 0.

2.

For the second one, I know that there are four 25s in 100, so there must be 28 in 720 and a remainder of 20.

20/25 can be simplified to four fifths and is equivalent to 0.

8, so you might have ended up with 28.

8.

Lastly, I know that there are four 25s in 100, so there must be 29 in 745 and a remainder of 20.

If you took the fraction remainder, that would be 20/25.

Simplified is 4/15, and it gives 29.

8 using decimal fractions.

Here's number four, then.

0.

25 is equal to one quarter.

As a fraction out of 64, that would be 16/64.

So, the number we are dividing must be 16 more than a three-digit multiple of 64.

So, you could have had 10 multiplied by 64 plus 16 is equal to 656 up to 15 multiplied by 64 added to 16 is equal to 976.

Pause the video here if you need some extra time to check your solutions.

Okay, let's move on to the second part of the lesson.

What to do with the remainder? Sam and Andeep are thinking about what the remainder would mean in different contexts for this problem.

248 divided by 24 is equal to 10 remainder 8.

What different problems could we write? Let's think about treats for the school trip.

A local bakery had 248 cupcakes to give away in boxes of 24.

How many boxes could they fill? There would be 10 full boxes, and some cakes left over.

For this problem, you can ignore the remainder and just give the whole number quotient.

A local bakery had 248 cupcakes to give away in boxes of 24.

How many boxes did they need for all the cupcakes? Isn't that the same as the last question? Not quite.

Last time we wanted full boxes, this time all the cupcakes need to be in a box.

We need to round the answer up from 10.

333 forever to 11, even though the last box is not full.

They would need 11 boxes for all the cupcakes.

They shared them between 24 families.

How many cupcakes did each family get? It must be 10 again.

What about the 8 left over? Can't we cut them up? Oh yes, each family can have 10 and 1/3 cupcakes.

Okay, let's check your understanding so far then.

There is a remainder for this division.

Would you need to round up, ignore the remainder, or use a decimal to answer the question? 248 children are going on the trip.

They need one adult for every group of six children.

How many adults do they need to take? Pause the video and have a go at that.

Welcome back.

Andeep says you would have to round up the answer as you can't take a fraction of an adult for the extra children.

Okay, let's try this one.

Same question, but this time we've got this context.

248 children are going on the trip.

They have lunch at tables of six.

How many full tables will there be at lunchtime? Again, pause the video and have a think about that.

Welcome back.

Andeep says you would ignore the extra children this time as the question asks for the number of full tables.

The children will all get to eat lunch, though.

Of course, really important.

Have a look at this context then.

13.

64 metres of tape has been bought to stick onto the 248 children's bag, so they don't get lost.

How many centimetres of tape will each child get? Pause the video and have a think.

Welcome back.

So Andeep says you would calculate the length exactly and use a decimal.

Money and measures are where decimal answers are particularly useful.

All right then, it's time for your second practise task.

You've got to match each problem to a statement about what to do with the remainder to give an accurate answer.

So, I'll read what's on the screen here.

260 apples are put into bags of 16.

How many bags can be filled? A roll of ribbon is 4.

5 metres long.

24 children need ribbon to tie to their bags.

How long is each piece of ribbon? Five pounds are shared equally between four friends.

How much do they each get? Five children can sit at each table.

248 children need to sit down to eat lunch.

How many tables will be needed? You've got to categorise each of those into the following groups.

Round the remainder up, ignore the remainder, express the remainder exactly as a decimal.

Okay, for number two it says solve the problems. Think about the most efficient strategy to use.

Can you use a mental method? A.

260 apples are put into bags of 16.

How many bags can be filled? B.

A roll of ribbon is 4.

5 metres long.

24 children need ribbon to tie to their bags.

How long is each piece of ribbon? C.

31 pounds 50 is shared equally between 14 children to buy items for the school tuck shop.

How much do they each get in pounds? D.

12 children can sit at each table.

248 children need to sit down to eat lunch.

How many tables will be needed? Finally, we have number three.

The coach company is putting up their prices next year.

How much more will it cost for each person next year? So, Elm coaches did have 56 seats at 700 pounds per day.

Now the new price is the same: Elm coaches 56 seats but 742 pounds a day.

Can you calculate how much more it will cost each person next year? Okay, some really good questions for you to tackle there.

Good luck, I'll be back in a while with some feedback, so pause the video here.

Welcome back, here's the answers to number one.

260 apples are put into bags of 16.

How many bags can be filled? You need to ignore the remainder there because we were looking for full bags.

A roll of ribbon is 4.

5 metres long.

24 children need ribbon to tie to their bags.

How long is each piece of ribbon? You need to express the remainder exactly as a decimal.

It's a question that involves measures.

5 pounds is shared equally between four friends.

How much do they each get? Again, the remainder needs to be expressed exactly as a decimal because we're using money here.

Lastly, five children can sit at each table.

248 children need to sit down to eat lunch.

How many tables will be needed? Here we need to round the remainder up otherwise, we'd end up with three children stood eating lunch, and that's not fair.

We were simply looking at the number of tables needed, not the number of full tables.

Let's mark number two then.

For A, we had 16.

25, so only 16 bags can be filled because we needed to ignore the remainder.

We were looking for full bags.

For B, 18.

75 centimetres, so each child will have 18.

75 centimetres of ribbon.

For C, we had 3150 divided by 14 is equal to 225, which is 225 pence, so each child will get two pounds, 25.

You needed to make sure that you converted 225 pence into pounds because that's what the question asked you to do.

For D, well 248 divided by 12 is equal to 20.

667, so 21 tables will be needed for all the children to sit down and eat.

We had to round up the remainder there; otherwise, we'd still have some children standing up.

For number three, it actually would cost 75p more per person next year.

That's because the new cost was 13.

25 and the old cost was 12.

50 per person.

That's a difference of 75 pence.

All right, we've come to the end of the lesson.

Here's a summary.

The remainder can be rounded up or down depending on the context.

Some problems require the remainder being given as a fraction or a decimal.

My name's Mr. Tazzyman.

Hope you enjoyed the lesson today.

I know I did.

Maybe I'll see you again soon.

Bye for now.