Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in this lesson.

Are you ready to do some maths? This lesson comes from the unit Division With Remainders.

So we're going to be thinking a bit more about division, how we can represent it, how we can record it, and what it means to have remainders.

So if you're ready to make a start, let's get going.

In this lesson, we're going to use knowledge of division to solve problems. Have you been learning about division recently? We're going to bring all of that together and solve lots of different problems. So let's have a look and see what we're going to be doing.

We've just got one keyword in our lesson today.

It's an important one though.

It's remainder.

I'll take my turn then it'll be your turn.

My turn, remainder.

Your turn.

Well done.

I'm sure you've learned lots of words to do with division, but remainder's a really important one.

We've got to think carefully about what we do with a remainder.

Let's just check.

We know exactly what it means.

A remainder is the amount left over after division when the dividend does not exactly divide by the divisor.

Hmm.

Let's have a think.

The dividend is the number we start with and the divisor is the number we are dividing by.

And we can use our times table knowledge.

If the dividend is a multiple of the divisor, there'll be no remainder.

But if the dividend, the number we start with, is not a multiple of the divisor, then we will have a remainder.

So there are two parts to our lesson today.

In the first part, we're going to be solving division problems, and in the second part, we're going to have a go at creating some division problems ourselves.

So let's make a start on part one.

And we've got Jun and Sofia in our lesson with us today.

The children are going on a school trip to the farm.

There are 67 children going.

I like going on school trips.

Do you? Have you been on one to a farm, I wonder? Each minibus can hold 12 children.

How many minibuses are needed to take all the children to the farm? So 67 children going and 12 minibuses.

Sofia says, "Let's decide how we will write the equation." Jun says, "There are 67 children going on the trip.

So this is the whole amount." "Each minibus can hold 12 children," says Sofia.

"So we are grouping the children into twelves." Hmm.

Does that give you a clue as to what the equation's going to look like? Jun says, "So the equation will be.

." 67 divided by 12.

67 divided into groups of 12.

Well, Jun says, "5 times 12 is equal to 60.

So there are five groups of 12 and a remainder of seven." So we can use our known multiplication facts to help us to solve division problems. 67 divided into groups of 12, there'll be five whole groups and there'll be seven left over.

So five groups of 12 and seven remaining.

Oh, now we must decide what to do with that remainder.

"We must decide if, to answer the question, we ignore the remainder or include the remainder," says Sofia.

What did the question actually ask us? Ah, Jun says, "The problem asks how many minibuses are needed for all of the children?" So can we leave seven children behind? We can't, can we? This means we must include the remainder.

So six minibuses are needed to take all the children to the farm.

Five will be full and one will only have seven children in it.

When they reach the farm, there are 80 bags of different animal feed, which are shared equally between seven of the groups of children.

How many whole bags does each group receive? "Let's write the equation to represent this," says Sofia.

"There are 80 bags of animal feed.

So this is the whole amount." "80 bags are shared equally between seven groups.

So the equation will be.

." Can you think what it'll be? That's right.

80 divided by 7.

This time we are sharing the 80 bags between seven groups.

We still need to find out how many groups of seven, but each group of seven will be one bag for each of the groups of children.

Well, Jun says, "7 times 11 is equal to 77.

So there are 11 groups of seven and a remainder of three." So the answer to our equation is 11 remainder three.

But as Sofia says, "We must decide if, to answer the question, we need to ignore the remainder or include the remainder." The problem asks how many whole bags each group receives when it's shared out equally.

We can't share out the remainder equally as whole bags.

So this means we must ignore the remainder.

So each group receives 11 bags of animal feed.

So this time we can ignore the remainder.

Our answer is 11.

It's time to check your understanding.

You are going to write and solve the equation for the following problem: It's snack time on the trip.

The teachers share out 75 pieces of fruit.

Each group of children is given eight whole pieces of fruit.

How many groups of children are there? Think carefully about what the question's asking you.

Write and solve the equation.

Pause the video, have a go, and when you're ready for some feedback, press play.

How did you get on? Well, Jun says, "There are 75 pieces of fruit, so this is the whole amount." Eight pieces of fruit are given to each group.

So we are grouping the pieces of fruit into eights.

Eight pieces of fruit means one group of children.

So the equation will be 75 divided into groups of eight.

What do we know about the eight times table? Well, 9 times 8 is equal to 72.

So there are nine groups of eight and a remainder of three.

So what does that mean? We've taken 75 pieces of fruit and we've put it into groups of eight.

So there are nine groups of eight and three pieces of fruit remaining.

Time to check your understanding now.

Now decide whether to ignore or include the remainder to answer the problem.

So remember, each group of children is given eight whole pieces of fruit.

How many groups of children are there? Pause the video, have a think about what to do with that remainder, and when you're ready for some feedback, press play.

What did you think? What does that all mean, that equation? Well, each group receives eight whole pieces of fruit.

Okay, so we were dividing into groups of eight.

And the problem asks, how many groups of children are there? There are nine groups of children altogether because we can make nine groups of eight whole pieces of fruit.

The remaining three pieces of fruit are not given to a group.

So this means we ignore the remainder.

There are nine groups of children.

And it's time for you to do some practise.

You are going to write the equation to solve each problem and then decide whether to ignore or include the remainder to answer the problem.

So in A, Jun and his friends stroked 27 rabbits and guinea pigs.

There are four animals in each hutch.

How many hutches do they visit? In B, at feeding time, the farmer shares 39 carrots equally between seven rabbits.

How many whole carrots does each rabbit receive? And in C, the farmer gives trailer rides around the farm.

Each trailer has room for seven children.

How many trailers are needed for 48 children to ride? Pause the video, have a go at A, B, and C, and when you're ready for the answers and some feedback, press play.

How did you get on? Let's have a look at A.

Jun and his friends stroked 27 rabbits and guinea pigs.

Oh, lucky them.

I do like guinea pigs, I must say.

There are four animals in each hutch.

How many hutches do they visit? So our equation must be 27, that's our whole number of animals, divided into groups of four.

Well, 4 times 6 is equal to 24, and 24 plus 3 is equal to 27.

So 27 divided into groups of four is six groups of four and three remaining.

Now, what do we do with that remainder? So we need to look at the number of groups and decide if we need an extra group or if we can ignore the remainder.

The problem asks us how many hutches they visited.

They have to stroke all 27 animals.

So this means that we must have stroked the animals in the extra hutch as well.

So seven hutches must have been visited to stroke 27 different animals.

So we need to round our answer up from six remainder three to seven hutches, even though there were only three animals in the last hutch.

And in B, at lunchtime, the farmer shares 39 carrots equally between seven rabbits.

There they are waiting patiently.

How many whole carrots does each rabbit receive? So 39 divided by 7, shared this time.

So how many groups of seven? Each group of seven is one carrot for each rabbit.

39 divided by 7 is equal to 5 remainder four.

5 times 7 is 35 plus another 4.

Again, we need to look at that remainder in the number of groups and decide whether we need to include another group.

But the problem asks us how many whole carrots each rabbit receives when they're shared equally.

The remainder can't be shared equally as whole carrots.

So we must ignore the remainder this time.

Maybe the farmer can put the carrots away till next time.

So each rabbit gets five carrots.

And in C, the farmer gives trailer rides around the farm.

Each trailer has room for seven children.

How many trailers are needed for 48 children to ride? So we're taking our whole number of 48 children and dividing it into groups of seven.

So 48 divided by 7.

Well, six groups of seven is 42.

And that will give us a remainder of six.

So six whole groups of seven and a remainder of six.

Do we need to include the remainder or can we ignore it? The problem asks how many trailers are needed for all the children.

So this means we must include the remainder.

So seven trailers are needed for all the children to ride.

I hope you were able to decide what to do with your remainders in those questions.

And we're onto part two of our lesson.

We are creating division problems. Let's revisit this problem with the minibuses.

There are 67 children going on a trip to the farm.

Each minibus can hold 12 children.

How many minibuses are needed to take all the children to the farm? So this was our answer, and when we answered this before, we included the remainder because we had to take all the children.

So we took six minibuses, but one of them wasn't full.

Jun says, "I wonder if we can change the problem so that we ignore the remainder." Hmm.

Can you have a think? What would that look like? Sofia says, "We will need to ask a different question." Jun says, "Instead of asking how many minibuses are needed for all of the children, we could ask how many minibuses will be full." Ah.

So now what happens? There are 67 children going on a school trip to the farm.

Each minibus can hold 12 children.

How many minibuses will be full of children? "Good thinking," says Sofia.

"The minibus for the seven children that were left over was not full, "so we ignore the remainder this time." Don't worry, seven children aren't being left behind.

But our question is just asking us about how many minibuses will be full.

So there are five full minibuses.

Here's part of a different problem.

Each child completes it using a different question.

Which child's question requires you to include the remainder? So we're thinking about the question where we'd need to include the remainder.

So far, the children have spent 58 minutes at animal feeding sessions.

Each session lasts for 11 minutes.

Sofia says, "How many different sessions have they attended?" And Jun says, "How many full sessions have they attended?" Hmm.

I wonder if you can think.

Which question will require you to include the remainder? You might want to pause and have a think before Sofia and Jun share their ideas.

I wonder what you thought.

Well, there's our equation.

58 divided by 11.

Each session lasts for 11 minutes.

So 58 divided into groups of 11.

Well, 5 times 11 is 55, plus 3 is 58.

So our answer to our division, our quotient, is five remainder three.

Five whole groups of 11 minutes plus three minutes.

What about those two questions though? How many different sessions have they attended, and how many full sessions have they attended? Which of those would mean that we had to include the remainder? Ah, it's Sofia's, isn't it? Jun asked how many full sessions they've attended.

So that three minutes at another session wouldn't be included in Jun's answer.

But Sofia says, "How many different sessions have they attended?" So they've not finished the last session, but they've attended it.

So it's six sessions.

Five full sessions lasts for 55 minutes, but they've spent 58 minutes at the sessions.

So they need an extra session to include the remainder.

They attended six different sessions altogether.

Well done if you spotted that.

And it's time to check your understanding.

Here is a problem that requires you to include the remainder.

Change the question asked so that the problem requires you to ignore the remainder.

So at the moment the problem says, there is a quiz trail around the farm.

Nine clues must be solved at each animal enclosure to move on to the next enclosure.

Sofia finds 67 clues altogether.

How many animal enclosures has she visited? So this problem means we have to include the remainder.

Can you change the problem so that you would ignore the remainder? Pause the video, have a go, and when you're ready to share your ideas and hear some feedback, press play.

How did you get on? How do you think you could change the problem? Well, to ignore the remainder, we must ask a question that only includes the animal enclosures with nine clues.

67 is not a multiple of nine, is it? So we know that she hasn't found all the clues in all the enclosures.

So we must think about the enclosures where she has found nine clues.

So for example, in how many animal enclosures did Sofia find all nine clues? 'Cause we know that there's one where she didn't, because 67 is not a multiple of nine.

Well done if you were able to change the question.

Here's another problem.

There are 47 children waiting to go in to see the pigs.

Only eight children are allowed to go into the barn at a time.

So our equation is 47 divided by 8.

Well, 8 times 5 is equal to 40, and 40 plus 7 is equal to 47.

So 47 divided into groups of eight is five groups of eight and a remainder of seven.

Jun says, "I've started to write a problem.

I wonder what question I could ask at the end." Hmm, I wonder.

Sofia says, "Let's think of a question where we ignore the remainder." So how could we ask a question based on that information where we ignore that remainder of seven? Jun says, "To ignore the remainder, we need to ask only about the complete groups." So those five complete groups we can make.

So what would the question be, do you think? Sofia says, "We could ask how many groups of eight children went in to see the pigs?" Yeah, that would do it, wouldn't it? Then we would ignore the group of seven children.

Now let's think of a question where we include the remainder.

So again, we're still thinking about the children going to see the pigs and eight children are allowed into the barn at a time.

Jun says, "To include the remainder, we need to ask a question where an extra group is made.

We could ask how many groups of children go in to see the pigs altogether?" "Ah," says Sofia, "There are five groups of eight and a remainder of seven.

So for all the children to see the pigs, there must have been six groups of children." Well done to you two.

You've asked two different questions.

One where we ignore the remainder and one where we include the remainder.

And it's time for you to have a go at creating some problems. Here are some incomplete problems. You are going to write two questions to complete each one.

One where the remainder must be ignored and one where it must be included.

And you might be able to give the problems to your friend to solve and you might be able to solve somebody else's.

So in A, the information we have is that Sofia feeds 43 different cows on the farm.

There are six cows in each stall.

Can you finish that and write two problems? One where the remainder would be included and one where it would be ignored.

And then the same for B, there are 70 stickers.

At lunchtime, the teacher puts them in packs of nine to hand out.

In C, there are 45 children in the play area.

Each giant swing has room for eight children.

And in D, the farmer has 78 maps.

And each pack can hold 12 maps.

So have a go at creating the finishing touches to those problems so that we have a problem where we ignore the remainder and a problem where we include the remainder for each of those scenarios.

Pause the video, have a go, and when you're ready for some feedback, press play.

How did you get on? So there's lots of different things you might have asked, but they were probably along the lines of this: So Sofia feeds 43 different cows on the farm.

There are six cows in each stall.

43 divided by 6.

Well, 6 times 7 is 42 and there's one left over.

So what problem could we ask? So we could ask a question that requires you to ignore the remainder.

So we could ask, in how many stalls did she feed all of the cows? And that would be seven because there are seven lots of six.

In the remaining stalls, she only fed one cow, so she didn't feed them all.

So seven stalls was where she fed all of the cows.

We ignore the remainder.

We could ask a question that requires you to include the remainder.

How many stalls did she visit to feed 43 different cows? This time we need to account for all of the cows.

So she visited eight stalls to feed the 43 different cows, but in the last stall she only fed one cow.

For B, there are 70 stickers, and at lunchtime the teacher puts them in packs of nine to hand out.

So 70 divided into groups of nine.

Well, 9 times 7 is equal to 63, plus another 7.

So 7 remainder 7 is the answer to our division.

So we're going to ask a question that requires you to ignore the remainder.

How many full packs did she make? So she made seven full packs of nine stickers and there were seven left over.

What about a question to include the remainder? I wonder what you wrote.

This was what we wrote.

How many packs were needed to hand out all of the stickers? So if she was going to put all of the stickers into a pack, she'd make seven complete packs and one incomplete pack.

She would make eight packs to hand out all the stickers.

But one of them would only have seven stickers in.

For C, we were thinking about the giant swings.

45 children are in the play area.

Each giant swing has room for eight children.

Hmm.

So 45 divided into groups of eight.

Well, 8 times 5 is equal to 40 and five left over.

So we can make five complete groups of eight and there'll be five children left over.

So what about a question to ignore the remainder? How many full swings are there? That would work, wouldn't it? That would be five full swings.

But one swing wouldn't be full because there'd only be five children in it.

So there are five full swings.

What about if we wanted to include the remainder? Ah, there we go.

We'd have to ask something that meant we had to give an answer that worked for all of the children.

So how many swings are needed for all of the children? Six swings are needed for all of the children, but the sixth swing will only have five children in it.

And finally, D, the farmer has 78 maps and each pack can hold 12 maps.

So 78 divided into groups of 12.

Well, 6 times 12 is equal to 72 and a remainder of six.

So six packs of 12 and six maps left over.

So we're going to write a question that requires you to ignore the remainder.

So how many full packs of maps can be made? Six full packs can be made and there'll be six maps left over.

But we are ignoring those because they're not in a full pack.

What about a question to include the remainder? Well, this is something that involves all of the maps, isn't it? So how many packs are needed to hold all of the maps? So seven packs are needed to hold all of the maps.

There'll be six that have all 12 in, and there'll be one, the seventh pack, will only have six maps in it, but we will need seven packs all together.

Well done, I hope you had fun thinking about how you could write problems to use the remainder in a different way each time.

And we've come to the end of our lesson.

We've been using knowledge of division to solve problems. What have we been thinking about? Well, when solving division problems, sometimes the remainder is recorded as the number left over.

Sometimes the remainder can be ignored and sometimes an extra group is made to include the remainder.

It's really important to think carefully about what a question or problem is asking you.

And when you're thinking about the remainder, make sure that you've made the right decision as to whether to ignore it or include it.

Thank you for all your hard work and your mathematical thinking today.

I hope you've enjoyed exploring remainders and I hope I get to work with you again soon.

Bye-bye.