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 are going to be able to bring to this lesson.

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

So in this lesson, we're going to be explaining different strategies we can use to subtract.

So we're thinking about subtraction in this lesson.

I wonder what different strategies you've used for subtracting numbers.

Let's have a look.

See what's in our lesson today.

We've got two keywords.

We've got calculate and efficiently, so I'm going to say them and then it'll be your turn.

So my turn, calculate, your turn.

My turn efficiently, your turn.

Excellent.

Those words are going to come up a lot in our lesson today.

So listen out for them and see if you can calculate efficiently as we go through today's lesson.

There are two parts in the lesson.

In the first part, we're going to be using known facts to subtract efficiently.

And in the second part, we're going to be subtracting tens and ones from an amount.

So let's make a start on part one.

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

The children go shopping, they can't write anything down, so they need to be able to calculate the cost of sets of items efficiently.

Izzy has 38 pounds and she wants to buy a car.

How much money will she have left? She says, "When I subtract two from an even number, I reach the even number before." Oh, what's she thinking about there? She's got 38 pounds and she's subtracting two pounds.

So 38 is even and she's subtracting two.

So what's the even number before going to be? Eight subtract two is equal to six.

So 38, subtract two will be equal to 36.

She says I'll have 36 pounds left.

That's right.

36 is the even number before 38.

Well done Izzy, good thinking.

Andeep has 84 pounds.

He buys a robot.

How can he calculate how much he will have left efficiently? So he has 84 pounds and the robot costs 20 pounds.

He says, "I will also use a known fact." He's partitioned his 84 into four and 80.

He says eight subtract two is equal to six.

Well that's the same fact that Izzy used, isn't it? So eight tens subtract two tens is equal to six tens.

He's applied it to his tens.

So Andeep will have 64 pounds left.

84 subtract 20 is equal to 64.

I have 64 pounds left he says.

What did you notice about this calculation about Andeep's one with the robot and Izzy's calculation where she bought the car? Can you see something there? Andeep says we both used the same known fact to help us calculate efficiently.

Izzy said I was subtracting ones, but you used the same fact to help you subtract tens.

They both used eight, subtract two, didn't they? But Andeep was able to use it to know that eight tens subtract two tens would be equal to six tens.

Izzy used it for eight subtract two is equal to six.

But it enabled them both to calculate efficiently.

They got to their answer quite easily without having to do too much work.

And it was an accurate way of working.

Time to check your understanding.

Which known fact would each child use to calculate the money they have left after buying the toy? So Andeep says, I have seven pounds and he's going to buy the pencils for three pounds.

And Izzy says I have 75 pounds and she's going to buy the dinosaur for 30 pounds.

So have a look at those choices, a, b, and c.

Which known fact would each child use? Pause the video, have a think.

And when you're ready for the answer and some feedback, press play.

What did you think? Yes, they could both use seven subtract three is equal to four, couldn't they? Seven subtract three is equal to four is a known fact and it can be used to calculate seven tens subtract three tens is equal to four tens or 40.

So that fact C could be used by both Andeep and Izzy to work out how much money they had left.

Let's look at the calculations on a 100 square.

38 subtract two is equal to 36.

Izzy's moved back two along that line of thirties.

She says I was subtracting ones.

It didn't cross the tens boundary.

So only the ones digit changed.

So Izzy's going to look at Andeep's calculation now 84 subtract 20.

Ah, she says this time I was subtracting tens.

So only the tens digit changed.

So our ones of four have stayed the same.

84 subtract 20 is equal to 64.

We can also see the pattern using base 10 blocks.

We've got 38 subtract two and 84 subtract 20.

So 38 subtract two, we are just changing our twos digits.

Eight twos have become six twos, 36.

What about 84 subtract 20? Ah, so we've done eight subtract two again, haven't we? But this time it was eight 10, subtract two tens.

So our answer is 64.

The tens change from eight to six because we subtracted two tens.

Time to check your understanding.

Can you match each equation to say which digit will change when it is solved and then fill in the missing numbers in those stem sentences.

So 76 subtract four is equal to something and 67 subtract 40 is equal to something and our stem sentences say the tens digit will change from hmm to hmm And the ones digit will change from hmm to hmm.

Which sentence matches which equation? And can you fill in the gaps? Pause the video, have a go When you're ready for the answer and some feedback, press play.

How did you get on? So 76, subtract four it's the ones digit that's changing isn't it? The ones digit will change from a six to a two because six, subtract four is equal to two and the answer will be 72.

So the other one we must be changing the tens.

That's right, 67 subtract 40.

So the tens digit will change from a six to a two because 60 subtract 40 is equal to 20.

So our answer will be 27.

67 subtract 40 is equal to 27.

We used six subtract four in both equations, but in one it was applying two the one's digits and in the other to the tens digits.

Well done if you spotted that.

The children have each saved 40 pounds and they buy these toys.

How much money does each child have left? So Andeep bought a rocket for 30 pounds and Izzy has bought a football for three pounds.

Hmm.

Can you spot something? We're going to do 40, subtract 30 and 40 subtract three.

How can they calculate this efficiently? Well they're going to represent Andeep with tens blocks.

So Andeep is subtracting tens from tens.

So he can use a known fact.

He says, "I know that four subtract three is equal to one." So four tens subtract three tens is equal to one 10 or 10.

He says "I have 10 pounds left." That was quite straightforward, wasn't it? Andeep? Well done.

What's about Izzy's 40 subtract three? I wonder if Izzy can use known facts too? She says, well 40 is four tens, so I'm going to regroup one 10 as 10 ones because she's got to subtract three ones, hasn't she? So she can regroup one of her tens as 10 ones.

So she's still got 40, but she's regrouped one into ones so she can subtract the ones.

Now she says I can use the known fact 10 subtract three is equal to seven.

So 40 subtract three will be equal to 37.

There are the three ones and she's got 37 left.

"I have 37 pounds left," she says.

So Andeep's calculation was quite easy to do, wasn't it? Izzy's took a little bit more thinking because she had to exchange one of her tens, regroup it into 10 ones and then she could bridge back through 10.

Time for you to do some practise.

Izzy has 70 pounds and she wants to find out how much money she would have left if she bought one item each time? So find out how much she will have left in each case.

So she's got 70 pounds and she buys the crayons.

How much money would she have left? She has 70 pounds and she buys the aeroplane.

How much money would she have left? So start with 70 pounds each time and work out how much money she would have left.

Andeep has 67 pounds, he wants to buy one item from the shop as well.

Find out how much money he has left after each item.

So each time he's going to test out, "If I had 67 pounds and I bought the Teddy, how much money would I have left? Or if I had 67 pounds and I bought the pencils, how much would I have left?" Pause the video, have a go.

When you're ready for the answers and some feedback, press play.

How did you get on? So let's start with Izzy.

She had 70 pounds, didn't she? So she's represented her 70 pounds with seven base 10 blocks, seven tens.

What if she bought the crayons for six pounds? 70 subtract six.

Ah, 70 is seven tens.

So we can regroup one 10 as 10 ones.

Now we can use the known fact 10 Subtract six is equal to four.

So 70 subtract six is equal to 64.

So she'd have 64 pounds left.

What if she bought the plane? Ah, this time we're subtracting two tens from seven tens.

So we can use a known fact.

We know that seven subtract two is equal to five.

So seven tens subtract two tens will be equal to five tens or 50.

So if you take away two of the tens, we've got five tens left, 50.

Izzy would have 50 pounds left.

What if she bought the teddy? Well again, that's going to be quite straightforward, isn't it? We're subtracting three tens from seven tens, so we can use known facts.

Seven subtract three is equal to four.

So seven tens subtract three tens is equal to four tens or 40.

So Izzy would have 40 pounds left.

What if she bought the pencils? Ah, we've got to regroup again because she's taking away four one pounds, isn't she? So we can regroup one 10 as 10 ones and now we can use a known fact of our factor to 10.

10 subtract four is equal to six.

So 70 subtract four will be equal to 66.

So she'd have 66 pounds left.

And on into question two.

Andeep had 67 pounds to start with.

What would he have left if he bought each item? So what if he bought the crayons for six pounds? There's his 67 pounds represented as six tens and seven ones.

He's got enough ones to take away, hasn't he? So he knows seven take away six is equal to one.

So 67 take away six will be equal to 61.

So he'd have 61 pounds left.

What if he bought the aeroplane? Well this time he's spending 20 pounds, two lots of 10.

So we know that six take away two is equal to four.

So six tens take away two tens will be equal to four tens.

Our ones are going to stay the same, we're only taking away tens.

So let's take away two tens and we can see that we've got 47 left.

67 subtract 20 is equal to 47.

He'd have 47 pounds left.

If he buys the teddy, he spent 30 pounds.

And again that's taking away a number of tens.

Six take away three is three.

So six tens take away three tens is equal to three tens.

So we've taken away three of the tens, but the seven pounds is still there.

So he'd have 37 pounds left.

67 subtract 30 is equal to 37.

We've only used tens, so our ones have stayed the same.

And what about if you bought the pencils? 67 subtract four.

Well we've got plenty of ones here, haven't we? So we know that seven, subtract four is equal to three.

So 67 subtract four will be equal to 63.

So Andeep would have 63 pounds left.

Well done.

And I hope you spotted when you were taking away a number of tens and when you were taking away a number of ones.

And on into the second part of our lesson, we are going to be subtracting tens and ones from an amount.

First Izzy had 87 pounds, but then she bought a rocket and then a car.

How much money does she have left now? She says I will use base 10 blocks to represent the numbers.

So there's 87 representing the money she had to start with.

I subtract 50, then subtract two.

So 87, subtract 50, let's take away five of those tens.

She's got three tens left, but all her ones are still there, but then she's got to take away two.

So she's taken away two of her ones.

So she's got three tens and five ones left, 35 left.

Izzy wonders if she would have more money left if she bought the toys in a different order.

Hmm, what do you think this time? She's going to buy the car first and then the rocket.

So 87, subtract two for the car.

There we go.

So she's still got all eight tens and she's got her five ones.

Now she's going to buy the rocket.

So she's going to take away 50, 5 tens, and she's still got 35 left.

She says if I subtract two then 50, I will still have the same amount of money left.

She says I will still have 35 pounds left because I subtracted the same amount altogether.

Time to check your understanding.

Can you use base 10 blocks to work out how much money Andeep would have left if he bought some crayons first and then an aeroplane.

So he's got 58 pounds, he's going to buy some crayons first for six pounds and then an aeroplane for 20 pounds.

And then can you use 'em to find out how much money he would have left if he bought the aeroplane first and then the crayons.

So have a go at buying those in different order and see how much he has left.

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

How did you get on? So first he was buying the crayons and then the aeroplane.

So 58, subtract six, subtract 20.

So there's our base 10 blocks representing our 58 pounds or Andeep's 58 pounds.

He's going to spend six pounds and then 20 pounds.

And what's he got left? He's got three tens and two ones.

He's got 32 pounds left.

What if he did it the other way around? 58 subtract 20 and then subtract six.

There are his base 10 blocks again.

Can you see what's going to happen? We subtract 20 and then we subtract six and we've still got 32 pounds left, and there will still be 32 pounds because we subtracted the same amount altogether.

We subtracted six and 20 and then 20 and six.

So altogether we'd subtracted 26.

So let's show these equations on the number line.

We've got 87, subtract 50, subtract two is equal to 35.

Izzy says first I subtracted the tens; 87 subtract 50 is equal to 37.

She subtracted the five tens.

Then I subtracted the ones 37, subtract two is equal to 35 and we can sort of imagine that with the base 10 blocks being crossed out can't we? First you crossed out the five tens and then the two ones.

"I had 35 left," she says.

Let's subtract in a different order.

She says first I subtracted the ones, 87 subtract two is equal to 85.

Then I subtracted the tens; 85 subtract 50 is equal to 35.

I had 35 left.

Let's write an equation for each representation.

So we've got 87, subtract 50, subtract two is equal to 35, the top number line and 87 subtract two, subtract 50 is equal to 35 for the bottom number line.

Izzy says we can subtract the tens and ones in any order and we will be left with the same amount.

Did you spot that? It's time to check your understanding.

Write an equation for each number line and then match the subtraction equations that reach the same amount.

Pause the video, have a go.

When you're ready for the answers and some feedback, press play.

How did you get on? So this top number line on the left was representing 79, subtract two, subtract 30.

The one underneath it was representing 96, subtract five, subtract 40.

The top one on the right was representing 96, subtract 40, subtract five.

Can you see there's one similar to that already, isn't there? And the final one was representing 79, subtract 30, subtract two is equal to 47.

Can you see the ones that match? That's right.

Those were the ones that matched, weren't they? They had the same answer, 47 and then 51.

And that was because they subtracted the same amount but in a different order.

Andeep wants to write different equations using one number from each set of cards.

Let's see how many equations he can create.

So he's got 69, subtract something, subtract something, and the somethings are going to come one from the group on the left, the 30 and the 20, and one from the group on the right, the four and the six.

So he started with 69, subtract 20, subtract four.

And he knows that 69 subtract 20 would be 49 and 49 subtract four would be 45.

What else could he do? Oh, what's he done this time? Ah, he's just changed the order hasn't he? 69, subtract four would be 65 and 65 subtract 20 would be 45.

It's the same answer, it's just because we've subtracted the numbers in a different order.

What else could he do? Oh, he could do 69, subtract 20, subtract six.

And if he worked that out it would be 43 and then he could swap the order of the numbers he's subtracting and the answer, our result would stay the same.

It's still 43.

What else could he do? Well, he could do the same with the 30 and the four, couldn't he? 69 subtract 30, subtract four is equal to 35, and 69 subtract four, subtract 30 is equal to 35.

And then you could also do 69, subtract 30, subtract six is equal to 33 and 69, subtract six, subtract 30 is also equal to 33.

He says, I noticed that I could subtract the same tens and ones in any order and the missing part of the whole would be the same.

That's right because what we're left with is a missing part of our whole and the whole was 69.

Time for you to do some more practise.

So in question one, you're going to draw a number line that will help you to complete each equation.

Remember to start with the whole and subtract each part in turn.

So we've got 46, subtract two is equal to 44 and 44, subtract 30 is equal to something.

So have a go at drawing the number lines to help you to fill in those missing parts.

And then in question two, just like Andeep did, choose a card from each set to create a subtraction equation.

So our first box is going to have 78 or 97 in it.

And then we're going to decide whether to subtract 40 or 10 and then subtract two or five.

So you're going to choose one number from each set.

And remember, because we're subtracting, this time, we want to start with the largest value.

So 78 or 97, will go in our first missing box.

That's our whole.

Pause the video, have a go at questions one and two.

And when you're ready for some feedback, press play.

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

So in question one, you were drawing number lines to fill in those missing boxes.

So for A, we had 46, subtract two is equal to 44 and then 44, subtract 30 is equal to 14.

We've subtracted three of the tens from four 10, so we've got one 10 left, so 14.

For B, 68, subtract 30 is equal to 38.

38 subtract two or we're just subtracting two ones this time.

So eight, subtract two is equal to six.

So our answer is 36.

What about C? 86 subtract 20.

So this time we are working out how many we've got when we've subtracted our multiple of 10, 86 subtract 20.

So we're taking away two tens from eight tens.

So six tens left is 66, and then 66 subtract four is equal to 62.

For D 78 subtract five is equal to 73.

And then ah, we'd taken away 20 to equal 53.

So we must have had that 73 as our whole.

73 subtract 20 is equal to 53.

For E 65 subtract 30 is equal to 35, and then 35 subtract something is equal to 31 or five subtract four is equal to one.

So 35, subtract four is equal to 31.

And finally for F, 97, subtract something is equal to 37.

While our ones have stayed the same, are tens have changed.

And nine subtract six is equal to three.

So it must be 97 subtract 60 is equal to 37, and then 37 subtract three is equal to 34.

Well done if you used number lines to help you and thinking about whether you were subtracting a number of tens or a number of ones.

And for question two, there were lots of possibilities here, weren't there? So you could work systematically to try each combination of tens and ones with 97 and then 78.

Let's have a look.

So we could have 97, subtract 10, subtract two, and then we could reverse the ones with subtracting 97, subtract two, subtract 10, and they'd both be equal to 85.

Then we could have 97, subtract 10, subtract five, or 97, subtract five, subtract 10.

And that would give us an answer of 82.

97 subtract 40 subtract two would give us 55.

And so would 97 subtract two, subtract 40.

97 subtract 40 subtract five gives us an answer of 52 and 97, subtract five, subtract 40 is also equal to 52.

Gosh, what a lot of combinations we've got.

So we had eight different equations we could write down using just 97 as our start.

So then we could do the same with 78 and we'd have another eight equations.

I'll just leave them there so you could have a little look.

Did you get all of those as well? Well done if you worked systematically through those.

Systematically means organising our answers so that we can see what we've got and we can identify any that we might have missed.

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

We've been explaining different strategies used to subtract.

What have we learned about? Well, we can use number facts and strategies we already know to help us to subtract two digit numbers efficiently.

And it's really important to be able to calculate mentally so to do things in our head using known facts when beginning to subtract two digit numbers.

You've done some great partitioning and applying of number facts today.

Thank you for your hard work.

I hope you've enjoyed the lesson as much as I have and I hope I get to work with you again soon.

Bye-Bye.