Lesson video

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

This lesson comes from the unit on "Addition and subtraction of two-digit numbers." Is this new for you? Have you done anything like this before? I'm sure you've got lots of skills about numbers and addition and subtraction that you're going to be able to bring to this lesson.

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

In this lesson, we're going to be solving problems involving subtraction of two-digit numbers that do not cross the tens boundary.

So you might have been doing some subtraction of two-digit numbers.

Have you been doing some partitioning, thinking about bar models and maybe number lines as well? Let's see if we can put that all into practise to solve some problems today.

There are two keywords in our lesson.

We've got partition and parts.

So I'll take my turn to say them and then it'll be yours.

So my turn, partition.

Your turn.

My turn, parts.

Your turn.

I'm sure they're words you're very familiar with, but we're going to be doing some partitioning in this lesson and we're going to be thinking about parts and wholes as well.

So look out for those keywords as we go through the lesson.

There are two parts to our lesson today.

In the first, we're going to be solving problems where we subtract two parts.

And in the second, we're going to be solving problems where we partition one part.

So let's make a start on the first part of our lesson.

And we've got Andeep and Izzy helping us today.

Izzy is watching the birds in the garden.

Do you watch the birds sometimes? Maybe you've got a window you can see birds from.

I'll tell you what, there aren't going to be many birds around here today.

It's pouring with rain.

Izzy counted 87 birds sitting on the fence.

30 flew away, then another six flew away.

How many birds were left sitting on the fence? Wow, Izzy! What a lot of birds you've got around you! 87 birds.

That's a lot! So Izzy's going to draw a bar model to solve this problem.

You're going to spot her mistake though.

Not sure she's got this one right.

So 87 birds were sitting on the fence, 30 flew away, and then another six flew away.

Is that right? She says, "There were 87 birds altogether.

This is the whole." That's right.

Yes, Izzy.

"One part is 30 and the other part is six.

To find the missing part, I will subtract the known parts from the whole." Well, that's right, Izzy, but.

"Oops!" she says.

"There's no missing part in my bar model.

It should have three parts." That's right.

There were 87 birds.

30 flew away and then six flew away, and there were still birds sitting on the fence.

So there need to be three parts in Izzy's bar model.

That looks better, Izzy! So we need to calculate 87, subtract 30, and subtract six.

Let's use a number line to help us.

87 subtract 30.

So we're taking away three tens.

So that's going to leave us with 57.

And then we've got to take away six.

And seven take away six is equal to one.

So 57 take away six must be equal to 51.

So the missing part was 51.

"There were 51 birds left sitting on the fence." Well done, Izzy, and well done for spotting your mistake and correcting your bar model.

So time to check your understanding.

Which bar model correctly represents this problem? There were 59 minibeasts in the garden.

20 crawled away, then another four crawled off.

How many minibeasts were left? Think about what Izzy did and how she learned from her mistake.

Pause the video, have a go, and decide whether it's A, B, or C, and come back when you're ready for the answer and some feedback.

So how did you get on? So we had a whole and how many parts? 59 minibeasts was our whole.

So that means, oh, C can't be right, can it? Well, there weren't 83 minibeasts as our whole.

There were 59 as our whole, 20 crawled away, and then four crawled off and then there were some left.

So we need three parts.

So it must be A that's correct.

59 representing the whole and the 20 and the four representing the minibeasts that crawled away.

And then we've got our missing part for the minibeasts that were left.

Well done if you spotted that.

Here's another problem to think about.

There was 36 grammes of bird seed in the bird feeder.

The birds ate 20 grammes in the morning and another three grammes in the afternoon.

How much bird seed was left in the bird feeder? So again, can you visualise this bar model? What's our whole and how many parts have we got? So there was 36 grammes of bird seed to start with.

That's our whole.

And then what was eaten? Well, first, 20 grammes was eaten.

This is the first part to be subtracted.

And then three grammes was eaten.

That's the second part to be subtracted.

But we know that there was some left in the bird seeder.

So that's our missing part.

That's the bit we're going to calculate.

And Andeep says, "To find the missing part, I must subtract the known parts from the whole." So 36 subtract 20 subtract three.

So let's draw a number line to help us.

36 subtract 20.

I'm taking away two tens from the three tens in 36.

So I've got one 10 and six ones left.

16.

And then we're going to subtract three.

16 subtract three is equal to 13.

So 36 subtract 20 subtract three is equal to 13.

Our missing part was 13.

So there was 13 grammes of seed left in the bird feeder.

Time to check your understanding.

Can you draw a bar model to represent the problem? Then, write the equation to solve it.

You could use a number line to help you.

Here's the problem.

There was 47 grammes of seed in a packet.

Andeep poured out 10 grammes and then spilt another four grammes.

How much seed was left in the packet? So draw a bar model and then maybe use a number line to help solve the equation.

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

How did you get on? So there's our bar model.

Our whole is 47.

And the parts that we were subtracting were 10 grammes that were poured out and the four grammes that were spilt.

How much seed was left in the packet? That's our third part.

So we need to calculate 47 subtract 10 subtract four.

So our whole is 47.

47 subtract 10.

We'll take away 10.

That's one 10 less, so that's 37.

But then what have we got to subtract? We've got another four to subtract.

37 subtract four is equal to 33.

So the answer to our subtraction is 33.

There was 33 grammes of seed left in the packet.

Izzy says she can write this equation to represent the same problem that she did before when she was solving a problem with bird seed.

Is she right? Before, we did 36 subtract 20 subtract three.

This time, she said 36 subtract three subtract 20 is equal to 13.

Can she re-write it this way? So there was 36 grammes of bird seed in the feeder.

The birds ate 20 grammes in the morning and another three grammes in the afternoon.

How much bird seed was left in the feeder? Well, if she writes it that way, she's subtracting the three grammes which was in the afternoon first.

Is that okay? Ah, she says, "We know we can subtract the tens and ones in any order and we will still have subtracted the same amount." You're right, Izzy.

It doesn't quite match the problem because they ate 20 grammes in the morning and then three grammes.

But if we're subtracting 20 and three, it doesn't matter which order we subtracted in.

The answer will be the same.

There'll always be 13 grammes of bird seed left.

So these number lines will give the same answer and we can see, subtract three subtract 20.

We land on 13.

Subtract 20 and then subtract three, and we still land on 13.

"I was right!" says Izzy.

You were, Izzy, and well remembered.

That's a useful thing to remember.

Sometimes, you might prefer to subtract the tens first.

Sometimes, you might prefer to subtract the ones first.

It doesn't matter which way.

You don't have to follow the same order as in the problem.

So over to you.

Which number line would you use to solve this problem? There were 76 apples in the shop.

Two were sold in the morning.

30 were sold in the afternoon.

How many apples were left in the shop? Which number line would you use? Pause the video, have a think, and when you're ready for some feedback, press play.

I wonder which one you chose.

Well, you could have chosen this one.

Although the two apples were sold first, we can still subtract the 30 apples first if we want to.

But we could also have chosen that one.

This one follows the pattern of the story.

Two sold in the morning and 30 in the afternoon.

But you can see that there were always going to be 44 apples left.

You might decide that you prefer to subtract the tens first.

I think that's what I'd probably do.

Both number lines start with the same whole amount and subtract one part of 30 and one part of two.

So either could be used to solve the problem.

You can decide whether you prefer to subtract the tens first or the ones.

This time, the children have three packets of seeds to feed the birds.

When they weigh the packets, the total mass is 98 grammes.

Izzy knows one packet has a mass of five grammes.

Andeep knows another has a mass of 50 grammes.

What is the mass of the third packet? So the whole is 98 grammes.

So we can put that in our bar model.

One part is five grammes.

And another part is 50 grammes.

And the other part is the bit we don't know.

Andeep says, "To find the missing parts, I will subtract the known parts from the whole." So 98 subtract five subtract 50.

Is that the way you'd do it? 98 subtract five.

Well, eight subtract five is equal to three.

So 98 subtract five will be equal to 93.

And then we're going to subtract 50.

Nine tens subtract five tens is equal to four tens.

So 93 subtract 50 will be equal to 43.

So the final packet has a mass of 43 grammes.

As Andeep says.

Izzy notices that this is a partitioning problem.

She wonders if the order that she subtracts matters in this problem.

She says, "I prefer to subtract the tens first." Do you know what, Izzy? I think I'm with you.

"I will subtract 50 and then five." So 98 subtract 50.

Or nine tens subtract five tens is equal to four tens.

48.

And 48 subtract five.

Well, we're just looking at the ones here.

Eight ones subtract five ones is equal to three ones.

48 subtract five is equal to 43.

So our missing part is still 43.

The final packet is 43 grammes.

And Izzy says, "The parts can be subtracted in any order because we are still subtracting the same amount in total." Well done, Izzy.

Time to check your understanding.

Is this true or false? This says this problem can be solved with either of the two equations.

Izzy's piece of string was 65-centimeters long.

She cuts it into three parts.

One part was 20 centimetres.

One part was five centimetres.

How long was the last part? So here are the two equations.

Can they both be used to solve the problem? Is that true or false? And why? Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

What did you think? It's true, isn't it? It's what Izzy was talking about.

20 and five combine to make 25, so we can subtract the tens and ones in any order and we will still have subtracted the same amount altogether.

So it was true.

Well done if you spotted that, and it's a really useful one to remember.

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

There are three problems here.

Can you draw a bar model to represent each problem and then write the equation and draw the number line to solve it? So A, there were 37 children in the park.

20 were playing football, five were on the roundabout, and the rest were having races.

How many were having races? In B, there were 49 children on the playground.

First, three went into the classroom and then 20 went into the hall.

How many were left on the playground? And in C, a packet had 86 grammes of seeds.

Izzy spilt three grammes and poured out 40 grammes for the birds.

What was the mass of seeds left in the packet? Pause the video, have a go at solving those problems using a bar model and a number line, and when you're ready for the answers and some feedback, press play.

So in A, there were 37 children in the park.

20 were playing football, five were on the roundabout, and the rest were having races.

So we needed to work out how many children were having races? So our bar model would look like this.

37 is the whole.

20 children playing football.

Five children on the roundabout.

And the rest of them having races.

Three parts.

So we need to do 37 subtract 20 subtract five.

Or you may have decided to subtract the five first.

It's entirely up to you.

We're going to subtract the tens first.

37 subtract 20.

Three tens subtract two tens is equal to one 10.

So 37 subtract 20 is equal to 17.

Now we've got to subtract five.

And 17 subtract five.

Well, seven subtract five is equal to two.

So 17 subtract five will be equal to 12.

So there were 12 children having races.

You may have subtracted the ones first and then the tens.

You can subtract the parts in any order because you are subtracting the same amount in total.

20 and five or five and 20.

We're subtracting 25 altogether.

So for B, there were 49 children on the playground.

That's our whole.

First, three went into the classroom.

One part.

Then 20 went into the hall.

Another part.

How many were left on the playground? That's our third part.

So we need to subtract three and 20 from 49.

So 49 subtract three subtract 20.

So we could do it subtracting the ones first.

49 subtract three.

Well, nine subtract three is equal to six.

So 49 subtract three is equal to 46.

And then we're going to subtract the 20.

46 subtract 20.

Four tens subtract two tens is two tens, so we've still got our six, is 26.

So there were 26 children left on the playground.

And you could have subtracted the tens first and then the ones because we know that we can subtract them in any order because we are subtracting the same amount in total.

And for C, this was the bird seed.

So the packet was 86 grammes.

That's our whole.

Izzy spilt three grammes.

Whoops! I hope the birds find those three grammes.

And then she poured out another 40 grammes for the birds.

What was the mass of seeds left in the packet? So we've got to do 86 subtract three subtract 40.

So I wonder which way around you did it.

Let's do it the way it is in the story.

Subtract three first.

86 subtract three is equal to 83.

And then subtract 40.

83 subtract 40 is equal to 43.

So the mass of seeds left in the packet was 43 grammes.

And again, you might have subtracted the tens first because you know that you can subtract the parts in any order because you're subtracting the same amount in total.

And on into the second part of our lesson.

This is problems where we partition one part.

Andeep is looking after the school rabbits.

Oh, lucky Andeep! He has 76 p to spend.

He buys them a carrot.

How much does he have left? So 76 p and he's going to subtract 25 p.

So let's use the coins to find this out.

76 subtract 25 is equal to something.

So there's his 76 p.

Can you see it's a 50 p and two 10 p? So 50, 60, 70, and then six.

76 p.

And he's going to spend 25 p.

How could we make the 25 p? He says, "I can remove coins that have a value of 25 p.

I can subtract 20 and then five." So he's subtracted 25 p.

What's he got left? He says, "I have 51 p left!" So with the coins, it's quite easy to work out, isn't it? Izzy had 47 p and she spent 24 p.

How much does she have left? Can you write an equation to solve the problem and then solve it this time? You could use coins to help you.

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

How did you get on? So we've got 47 subtract 24.

So there's 40 p and two, four, six, 7 p, 47 p.

And we're subtracting 24 p.

Two 10 ps and two 2 ps.

What's Izzy got left? She's got two 10 ps, 20, and a two and a one, 23.

So she's got 23 p left.

We've removed coins to the value of 24 p by subtracting 20 p and then 4 p.

And she's got 23 p left.

Here's another problem.

Izzy had 68 grammes of pellets and vegetables for the rabbits.

So rabbit food.

24 grammes of the food was pellets.

How much of the food was vegetables? So the 68 grammes was pellets and vegetables.

24 grammes of the food was pellets.

How much was vegetables? So the whole amount of food was 68 grammes.

So there's our bar model.

24 grammes was pellets.

So this was one part.

So we need to subtract that part to work out how much was vegetables.

So 68 subtract 24 will find us the other part.

We've got no money to help us this time.

So we need to think about these numbers.

And Izzy says, "I will partition 24 into 20 and four, and then subtract the tens and the ones separately." Can you see a link to what we were doing in part one? We were subtracting tens and then ones, weren't we? Now we're going to create those tens and ones by partitioning the number we're subtracting.

So 68 subtract 24, we can partition the 24 into 20 and four.

68 subtract 20 is equal to 48.

And 48 subtract four is equal to 44, or we can use our known facts to work those out.

So 68 subtract 24 is equal to 44.

So the other part, the vegetables, have a mass of 44 grammes.

Time to check your understanding.

Can you partition the known parts into tens and ones to solve the problem? There were 58 minibeasts in the garden.

23 were ladybirds and the rest were ants.

How many ants were there? So you might want to draw a bar model and think about partitioning the part that you're taking away.

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

How did you get on? So our whole was 58, 58 minibeasts.

There were 23 ladybirds.

That's our known part.

How many ants were there? Because the rest were ants.

That's our unknown part.

So what's our equation? We're going to subtract the part we know from the whole.

58 subtract 23 is equal to our missing part, the number of ants.

So we can partition the parts into 20 and three.

So we can do 58 subtract 20 and then subtract three.

58 subtract 20, we're taking away two tens.

So we're going to have three tens and eight ones.

38.

And then 38 subtract three.

Eight subtract three is equal to five.

So 38 subtract three is equal to 35.

You can subtract 23 by partitioning it into tens and ones, and then subtracting 20 and then three.

So there were 35 ants in the garden.

Andeep wanted to tie the rabbits' water bottle to the hutch.

He had 70 centimetres of string and he used 28 centimetres to tie the bottle.

How much string did he have left? Hmm.

We've got a ruler there.

Do you know what a ruler looks a bit like? Looks a bit like a number line, doesn't it? Andeep says, "The whole amount of string was 70 centimetres." So that's our whole.

28 centimetres was cut off.

This was one part.

"To find the other part," he says, "I must subtract 28 from 70." So 70 subtract 28 is going to tell us how much string was left.

"28 partitions into 20 and eight, so I can subtract 20 and then eight or," he says, "I could subtract eight and then 20." So 70 subtract eight is equal to 62.

We know that 10 subtract eight is equal to two.

So a multiple of 10 subtract eight will give us a two in the ones.

So 70 subtract eight is equal to 62.

And then we've got to subtract 20.

62 subtract 20, we're taking away two tens.

So 42.

So the amount of string left over is 42-centimeters long, and we can see that on the ruler as well.

There was 42 centimetres of string left.

Time to check your understanding.

Can you solve this problem by subtracting the ones first? Izzy had 68 centimetres of string and she cut off 43 centimetres.

How much string did she have left? Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

How did you get on? So our whole is 68.

And we cut off 43.

That was our known part.

So we must subtract the part we know from the whole to work out the missing part.

68 subtract 43.

But this time, you were asked to subtract the ones first.

So we can partition our 43 into 40 and three.

But this time, we're going to subtract the ones first.

68 subtract three is equal to 65.

65 subtract 40 is equal to 25.

So 68 subtract 43 is equal to 25.

So there was 25 centimetres of string left.

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

You're going to draw a bar model to represent each problem and then write the equation and draw the number line to solve it.

So for A, there were 76 animals at the farm.

35 were cows and the rest were sheep.

How many sheep were there? For B, there were 58 sweets in the shop.

25 were red, and the rest were yellow.

How many yellow sweets were there? And in C, a packet had 86 grammes of seeds.

Andeep spilt 43 grammes.

Oh dear.

What was the mass of seeds left in the packet? Pause the video, have a go at representing those problems with a bar model and using a number line to solve them, and when you're ready for the answers and some feedback, press play.

How did you get on? So for A, we were thinking about the animals.

So 76 was the whole number of animals.

35 was the number of cows.

The rest are sheep.

We don't how many sheep there are.

So we've got to calculate 76 subtract 35, and we can partition that into 30 and five.

76 subtract 30 is equal to 46.

And 46 subtract five is equal to 41.

We can use our known facts there.

So there were 41 sheep at the farm.

What about B? This was about the sweets.

58 sweets in the shop.

That's our whole.

24 were red.

That's one part.

And the rest were yellow.

That's the part we don't know.

We need to find out how many yellow sweets there were.

So we're going to subtract the part we know from the whole, and we're going to partition it to help us.

So we're going to do 58 subtract 24, but we're going to subtract 20 and then subtract four.

And here's our number line.

58 subtract 20.

We're taking away two tens.

Five tens subtract two tens is equal to three tens.

So that must be 38.

And then we're subtracting four.

38 subtract four.

Well, eight subtract four is four.

So 38 subtract four must be equal to 34.

So there were 34 yellow sweets.

That's our missing part.

And finally, this is about a packet of seeds, and Andeep spilt 43 grammes.

Our whole, though, is 86 grammes.

That was what was in the packet to start with.

Andeep spilt part of it, 43.

What mass of seeds was left in the packet? So we can subtract the part we know from the whole.

86 subtract 43.

This time, we've partitioned it into three and then 40.

So we're going to subtract the ones first.

86 subtract three.

Well, six subtract three is equal to three.

So that will be 83.

And then we're going to subtract 40.

83 subtract 40 is equal to 43.

We've subtracted four of the tens.

So our missing part is 43, and that means that there were 43 grammes left in the packet.

Oh! He spilt half of it, didn't he? 43 and 43.

Two equal parts.

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

We've been solving problems involving subtraction of two-digit numbers.

So what have we learned about? Well, we've learned that when subtracting two-digit numbers, it's important to partition the known part of the whole, and then partition it further to subtract the tens and the ones.

When subtracting, we do not partition both the whole and the part because this does not give the correct answer when the ones digits bridge 10.

And that's going to be something that's very important as we go on with our subtraction.

And we can subtract the tens and the ones in any order and the remaining part will stay the same.

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

And I hope I get to work with you in a lesson again soon.

Bye-bye!.