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I can add to and subtract from multiples of 100.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

When you add a one-digit number and a multiple of 100, only the 1s digit changes.
When you subtract a one-digit number from a multiple of 100, the 100s, 10s and 1s digits change.
When you add a 10s number and a multiple of 100, only the 10s digit changes.
When you subtract a 10s number from a multiple of 100, the 100s and 10s digits change.

Common misconception

Pupils may need help using number pairs that total 10 to support their thinking in this lesson.

Make explicit connections between number pairs that total ten and the learning (e.g. 10 - 3 = 7 so 100 - 7 = 93 and 100 - 30 = 70).

Keywords

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

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Hello there.

My name is Ms. Ko.

I'm really excited to be learning with you today.

I know we're going to have lots of fun and I know that you are going to put loads of effort into this lesson.

If you're ready, let's get going.

So by the end of this lesson today, you'll be able to say that you can add to and subtract from multiples of 100.

Let's get going.

Our keyword today is multiple.

I'm going to say it and I'd like you to say it back.

My turn.

Multiple.

Your turn.

Well done.

Let's take a look at what that word means.

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

So 10, 20, and 30 are all multiples of 10.

2, 4, 6, and 8 are all multiples of 2.

Our lesson today is about using known facts to add and subtract from multiples of 100 and there are two parts to the lesson.

The first part will be adding and subtracting one's numbers and in the second part, we'll be adding and subtracting ten's numbers.

Let's get going with the first part of the lesson.

In this lesson today, you will meet Sofia and Andeep, and they will be helping you with your learning and asking you some tricky questions along the way to deepen your understanding.

Andeep and Sofia are adding one digit numbers and multiples of 100.

Andeep asks, what is 100 plus four? Sofia says that we can use known facts to help us.

She asks, what is 10 plus four? Now hopefully you know that if we have one 10 and we add four ones, we know that 10 plus four is equal to 14 and we can use that to find 100 plus four.

Here we have 100, and if we add four more, we have 104, so we can use that known fact to help us.

So they move on to thinking about adding four to other multiples of 100.

What is 200 plus four asks Andeep.

So here we have 200 this time and we're going to do the same thing.

We need to add four ones, and we can see that 200 plus four is equal to 204.

Can you see a pattern? Let's think about another example.

What is 300 plus four? We can share that again.

We have three hundreds and we're going to add four ones.

And so we have 304.

300 plus four is equal to 304.

I can definitely see something going on here.

Andeep and Sofia go on to use number lines to represent their calculations.

What is 400 plus four asks Sofia? Now I think you might already know the answer to this.

Let's have a look.

Here's our number line and Sofia's going to find 400 and count on four more and we can see that 400 plus four is equal to 404.

It's definitely a pattern here.

Andeep asks what is 600 plus four? So again, he's going to show that on a number line.

He's going to find 600 and count on four more and therefore 600 plus four is equal to 604.

So what happens when you add a one digit number and a multiple of 100? Well Andeep is saying that when you add a one digit number and a multiple of 100, only the ones digit changes.

And I think if we think about our examples, we can see that the tens digits and the hundreds digits don't change.

So let's check that with another example.

200 plus eight is 200 plus eight more is 208.

The ones digits changed.

The tens and hundreds stayed the same.

If we do 300 plus seven, I think you can see where this is going.

The hundreds digits and the tens digit don't change, but we are adding seven ones.

So the ones digit will change.

300 plus seven is 307.

Time to check your understanding.

I want you to calculate the answers.

What is 200 plus five asks Andeep, and there's some base 10 blocks there to help you.

And what is 400 plus three ask Sofia.

Again, there are base 10 blocks if you need them.

Pause the video here and answer those calculations.

Welcome back.

How did you get on? So hopefully you remembered that the ones digit changes but the tens and hundreds digits do not.

So 200 plus five is 205 and 400 plus three is 403.

Well done if you've got those.

This time they want to subtract a one digit number from a multiple of 100.

What is 100 subtract four asks Andeep.

Sofia is saying that actually we can also use known facts here.

What is 10 and subtract four? So here's our 10 and if we subtract four, we know that 10 subtract four is six.

We also know this because four plus six is 10.

So 10 subtract four is equal to six.

So remember you can use those addition facts to help you think about subtraction.

So if we know that 10 subtract four is equal to six, I wonder if you can think about what is 100 subtract four? So we know that 100 is 10 tens.

So in order to subtract four ones, we're going to think about subtracting four from one of the tens.

So here's our hundred, we're going to subtract four from one of our tens in 100 and therefore we have nine tens and six ones or 96.

100 subtract four is equal to 96.

Andeep and Sofia, think about subtracting four from other multiples of 100.

What is 200 subtract four? So think about what we just did with 100 subtract four.

This time we have two hundreds and we're going to subtract four from one of the tens, and we can see that 200 subtract four is 196.

Hmm, I think I've seen 96 before.

Sofia is asking what is 300 subtract four? Can you predict what the answer's going to be? Well this time I have three hundreds.

I'm going to subtract four from one of the tens in my hundred, and I can see that 300 subtract four is equal to 296.

Andeep and Sofia go on to use number lines to represent their calculations.

What is 400 subtract four asks Sofia? She's going to find 400 on the number line and count back four.

And we can see that 400 subtract four is equal to 396.

Can you see the pattern here in the answers? Andeep is asking what is 600 subtract four.

I bet you can predict the answer.

He's going to find 600 on the number line and count back four.

And we can see that 600 subtract four is equal to 596.

So what happens when you subtract a one digit number from a multiple of 100? Well in this case all of the digits change, so the hundreds, tens and ones digits change, which can feel a bit tricky but we can also use our number pairs that total 10 to help us.

So Sofia is saying she knows that 10 subtract seven is equal to three, because three plus seven makes 10.

And so if we're going to do 200 subtract seven, we know the ones digit is going to be three.

So 200 subtract seven, we're going to take seven away from one of the tens and we are left with 193.

If we think about 300 subtract seven, again, we're going to take seven away from one of the tens and we have 293.

So we can use patterns to help us even though all of the digits change.

So what happens when you subtract five from a multiple of 100? Andeep knows that 10 subtract five is equal to five because five plus five makes 10.

And so Sofia from that knows that 100 subtract five is equal to 95.

So therefore we can use those two bits of information to think about what is 300 subtract five.

Think about all the digits going to change but there's a pattern in how they're going to change.

We know that the number's going to end in five.

We're going to subtract five ones from one of the tens and we have 295.

300 subtract five is equal to 295.

What about 400 subtract five? Can you tell me the answer? We're going to subtract five ones from one of the tens and we have 395.

Time to check your understanding.

What happens when you subtract two from a multiple of 100? Andeep is helping us out a little bit and saying I know that 10 subtract two is equal to eight.

Sofia is saying she knows 100 subtract two is equal to 98.

So I'd like you to have a think about what happens when we do 300 subtract two or 400 subtract two? Pause the video here and have a go at those two calculations.

Welcome back.

How did you get on? Did you spot those patterns? Well if I know that 100 subtract two is 98, then 300 subtract two is going to be 298.

And then I can use that to find 400 subtract two because my minuend, the number I'm subtracting from is 100 greater.

So my answer, my difference is going to be 100 greater as well.

400 subtract two is equal to 398.

Well done if you've got both of those correct.

So what happens when you subtract nine from a multiple of 100? Andeep says that he knows 10 subtract nine is equal to one and therefore he knows that 100 subtract nine is equal to 91.

So Sofia is going to use that information and show on a number line what 300 subtract nine is.

So she's going to find 300 and count back nine, 300 subtract nine is 291.

So what happens when we subtract nine from other multiples of 100? What is 400 subtract nine? But hopefully you can see the pattern here.

We're going to show that on a number line, 400 subtract nine is 391.

So therefore what is 600 subtract nine? I'm sure you are shouting at the screen and telling me that 600 subtract nine is equal to 591.

Well done if you've spotted that pattern.

Time to check your understanding.

What is 500 subtract nine? So think about what is 100 subtract nine? There's a number line there if you need it.

Pause the video here.

And welcome back.

How did you get on? So if we know that 100 subtract nine is 91, we can use that to think about 500 subtract nine.

There are more hundreds there, but we can find 500.

Count back nine and we know that 500 subtract nine is 491.

Well done if you said that.

So let's take a look at this learning in a slightly different context.

We're going to complete the table.

So if we look at the first row, we can see that the number is 100 and we need to think about seven less and seven more than the number.

Andeep is thinking about seven less as a subtraction.

So we can also think about it as 100 subtract seven.

Well I know that 10 subtract seven is three, so 100 subtract seven is 93.

I can then think about seven more, and I can think about that as 100 plus seven, which is 107.

We can complete the middle row in the same way.

Seven less than 400 is 393, 7 more is 407.

That last row is a bit trickier though.

We know that seven more than something is 707.

We don't yet know what the number is, but we can do the inverse, the opposite to find out.

So if seven more than a number is 707, then the number must be seven less than that.

So the number is 700.

Once we know that, we can work out seven less by subtracting again and think about the pattern we can see here.

So we can see that seven less than 700 is 693.

Time to check your understanding, complete the table.

So you have 100,400; this time you've got five less and five more.

Pause the video here and have a go.

Welcome back.

How did you get on? Well five less than 100 is the same as thinking about 100 subtract five, and five more is the same as thinking about 100 plus five.

So five less is 95, 5 more is 105.

And then we can use that information for 400.

So five less than 400 is 395 and five more is 405.

Well done if you said that.

Time for your first practise task.

For question one, I'd like you to calculate the answers.

Be really careful because there is a mix of addition and subtraction in there.

What do you notice about them when you finish them? For question two, I'd like you to complete the table.

So the first three rows are quite straightforward, but be very careful on the fourth and the fifth row, where you are given some of the numbers but not the original number.

Welcome back.

How did you get on? Here are the answers for question one.

Pause the video here to mark your work.

Thinking about what you noticed.

Well you might have noticed lots of different things, but Andeep noticed that in E, F, G and H, the ones digit was always four, well spotted Andeep.

Now that's because 10 subtract six is four.

Therefore when we subtract six from a multiple of 100, we're going to have four as our ones digit.

He also noticed that the hundreds digits is one less than the minuend.

So let's use an example, 300 subtract six equals 294.

The minuend is 300, the value of the hundreds digit is three and in our answer, the difference the value of the hundreds digit is two.

And that works for all of them.

Well spotted Andeep, and well spotted if you said anything like that in your answers.

And here is the completed table.

You can pause the video here and check your work.

And let's look at the very last row.

So we knew that eight more than the number was 908, so we had to subtract dates to find the original number which was 900 and then we had to subtract eight more.

And again, we could have used the pattern here.

We knew the ones digit was going to be a two, so eight less than 900 was 892.

Well done if you spotted that.

Let's move on to the second part of our learning today where we're thinking about adding and subtracting tens numbers.

So Andeep and Sofia are adding tens numbers and multiples of 100 together.

Andeep asks what is 300 plus 40? Sofia is reminding him that he can use his known facts.

What is 100 plus 40? Well I know that 100 plus 40 is 140.

So we can see here 100 plus four more tens is 140.

Sofia's saying that will help Andeep.

We can see here we have 300 and if we add four more tens, we can see that 300 plus 40 is 340.

Andeep and Sofia add 40 to other multiples of 100 and they represent the calculations using number lines.

So Sofia thinks about, well what is 200 plus 40? I think you might be able to guess this before I show you.

She finds 200 on the number line, adds 40, and we can see that 200 plus 40 is equal to 240.

Andeep says what is 500 plus 40? I can see a pattern.

He finds 500 on the number line, adds 40, and finds that 500 plus 40 is 540.

So what happens when you add a tens number and a multiple of 100 together? Well Andeep says that when you add a tens number and a multiple of 100, only the tens digit changes.

The ones digit and the hundreds digit don't change.

So let's look at an example.

600 plus 40, 640.

The tens digit changed but none of the other digits did.

700 plus 40, 740; 900 plus 40, 940.

Only the tens digit changed.

Well spotted Andeep.

Time to check your understanding and you might want to use what Andeep spotted.

Calculate the answers.

What is 200 plus 50? What is 400 plus 50? You have the base 10 blocks there to help you if you need to.

Pause the video here and have a go.

Welcome back.

Hopefully, you realised and remembered that the tens digit is the only digit that changed.

So if we add 50 to 200, we get 250.

And if we add 50 to 400, we get 450.

Well done if you got those correct.

This time Andeep wants to subtract a tens number from a multiple of 100.

What is 300 subtract 40 he asks.

Sofia is reminding him again that he can use known facts.

What is 100 subtract 40? Now remember the 100 is the same as 10 tens, 40 is four tens.

So 10 tens subtract four tens is equal to six tens or 60 and we can use our pairs of 10 to help us.

So therefore what is 300 subtract 40? Well we're going to subtract 40 from that last hundred and we can see that 300 subtract 40 is 260.

Andeep and Sofia go on to subtract 40 from other multiples of 100 using number lines.

What is 500 subtract 40 says Sofia.

She's going to find 500 on the number line and subtract 40 and she can see that 500 subtract 40 is 460.

Again, I might be able to see a pattern here.

What is 800 subtract 40 asks Andeep.

And again we're going to find 800 on the number line.

Subtract 40 and we can see that 800 subtract 40 is 760.

It's definitely something in those tens numbers.

So what happens when you subtract a tens number from a multiple of 100.

Andeep is telling us that when we do this, the hundreds and tens digits change but the ones stay the same.

So if we look at these examples here, we can see that our difference, our answer, the ones stay the same, they're zero all the time, and the tens and the hundreds digits have changed.

So what happens when you subtract 30 from a multiple of 100? Sofia is reminding us of the fact that you might know that 100 subtract 30 is 70 and that's going to be quite useful.

I think seventy's going to be be an important number for their examples.

So 300 subtract 30 is going to be 270, that's 70 again, what do you think the answer will be for 700 subtract 30? Think about what changes and what stays the same.

That's right, it's going to be 670.

And what about for 900 subtract 30? I think you're seeing the pattern now.

870.

Time for a quick check for your understanding.

What happens when you subtract 20 from a multiple of 100? So here's 100 and Sofia's reminding us that she knows that 100 subtract 20 is 80.

So have a go at those three calculations.

Pause the video here.

Welcome back.

How did you get on? Hopefully you spotted a pattern.

So we have 280, 680, 880.

They all end in 80.

The ones digit stayed the same and the hundreds digit changed.

Well spotted and well done if you've got those answers, complete the table.

So this time we have a hundred and we're thinking about 70 less and 70 more.

Andeep is reminding us that we can think about 70 less as 100 subtract 70.

Now I know that 10 subtract seven is three.

So 100 subtract 70 is 30, 70 more is the same as thinking about 100 plus 70.

Remember when we add a multiple of 10 to a multiple of 100, only the 10s digit changes.

So that's 170.

We can use that to think about 70, less than 70 more than 300.

If 70 less than 100 is 30, then 70 less than 300 is 230 and 70 more than 300 is 370.

Similarly we have 500, so we have 430 and 570.

Now the last row is a little bit trickier.

We know that 70 more than a number is 770.

So to find out the original number, we need to subtract 70.

770 subtract 70 is 700.

Once I know the number, it's quite straightforward to find 70 less.

70 less than 700 is 630.

Time to check your understanding.

Complete the table.

Pause the video here.

How did you get on? I know that 10 subtract six is four.

So 100 subtract 60 is 40.

So 60 less would be 40 and 60 more is 160.

Remember the 10s digit is the only one that changes when we add a multiple of 10 to a multiple of 100.

Once I know that, I can use the same patterns and ideas for 400.

60 less is 340, 60 more is 460.

Well done if you said that.

We're now going to look at some problem solving using this idea.

Pat is a panda and he is sitting on some cardboard boxes.

The boxes are 300 centimetres high.

Now don't worry, pandas are excellent climbers.

So he's perfectly safe.

The boxes are 300 centimetres tall and Pat himself is 80 centimetres tall.

What is the total height of pat and the boxes? So Andeep is saying to solve this problem we need to add together 300 centimetres and 80 centimetres.

Now don't worry because we can still use the same ideas that we've been doing even though it's in centimetres.

So we're going to find 300 on a number line and we're going to add on 80, which gets us to 380.

So 300 centimetres plus 80 centimetres is 380 centimetres.

So Pat and the boxes are 380 centimetres tall.

Time to check your understanding, Pedro is sitting on some cardboard boxes.

Here's Pedro on his boxes.

The boxes are 200 centimetres high and Pedro is 70 centimetres tall.

What is the total height of Pedro and the boxes? Pause the video here.

Welcome back.

How did you get on? So we're thinking about 200 centimetres plus 70 centimetres.

We can show that on a number line and we can see that Pedro and the boxes are 270 centimetres tall altogether.

Well done if that's what you said.

Pia is sitting on some cardboard boxes.

There's Pia on her boxes.

Now the total height of Pia and the boxes is 500 centimetres.

Pia herself is 90 centimetres tall.

How high are the boxes? Hmm, that's a slightly different problem.

Andeep says, in order to find the answer, we need to subtract 500 centimetres, subtract 90 centimetres.

Remember what happens when we subtract a multiple of 10 from a multiple of 100, we're going to find 500 and subtract 90.

And we can see that if Pia is 90 centimetres tall and the total height is 500 centimetres tall, the boxes must be 410 centimetres tall.

Time to check your understanding.

Petra is sitting on some cardboard boxes.

The total height of Petra and the boxes is 300 centimetres and Petra herself is 60 centimetres tall.

How high are the boxes? Pause the video here and have a go.

And welcome back.

So we need to subtract again what is 300 centimetres subtract 60 centimetres.

We can find 300 on the number line.

If we count back 60, we have 240.

So the boxes are 240 centimetres tall.

Well done if you said that.

Time for your second practise task, for the first part, I would like you to calculate the answers.

Now be careful because there's a mix of addition and subtraction questions in there.

For question two, I'd like you to complete the table.

So this time you have some numbers in the middle and you have 90 less and 90 more.

Be really careful of those last two rows.

I've tried to catch you out.

For question three, we have some pandas are sitting on some boxes.

You need to calculate the answers.

So think really carefully about whether you need to add or subtract to find the answers.

Pause the video here, have a go at those tasks and come back when you're ready for some feedback.

Welcome back.

How did you get on? So here are the answers for question one.

Pause the video here and mark your work.

Here is the completed table for question two.

So if we know that 10 subtract nine is one, 100 subtract 90 is 10.

And we know that when we add a multiple of 10 to a multiple of 100, we are changing just the tens digit.

So you should be able to see some patterns there.

I know I tried to check you out with the last two.

So if we look at the very last row, we know that's 90 less than a number is 710.

So to find the number you needed to add 90 to 710, which go to 800.

And then we had to add 90 more.

So 890, well done if you got that correct, especially those last two rows.

And then for the last one, we had to do some addition and subtraction depending on the problem.

So for the first one, we had to find the height of the boxes.

So 400 subtract 90 is 310.

For the second one, we had to find the total height of panda and box.

So 400 plus 70 is 470.

And then finally again, we had to find the height of the boxes.

So 300 subtract 80 is 220.

Well done if you've got all of those correct.

We have come to the end of our lesson, and I'm really, really impressed at how hard you have worked.

Let's summarise our learning.

When you add a one digit number and add a multiple of 100, only the ones digit changes.

When you subtract a ones digit number from a multiple of 100, the one hundreds, tens, and ones digit changes, but there's some patterns to be found there.

When you add a tens number and a multiple of 100, only the tens digit changes.

When you subtract a tens number from a multiple of 100, the 100 and tens digit numbers change.

Thank you so much for learning with me today and I look forward to seeing you again soon.

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