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I can add and subtract to and from a 3-digit number bridging 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

Addition and subtraction calculations can represent counting on and back over the 100s boundary.
When you count on in tens, sometimes the 10s digit only changes and sometimes the 100s digit changes.
When you count back in tens, sometimes the 10s digit only changes and sometimes the 100s digit changes.

Common misconception

Pupils may partition numbers incorrectly when adding or subtracting across a 100s boundary.

Encourage pupils to add or subtract to first the 100s number, using number pairs that total 10 or 100.

Keywords

Bridging - A mental strategy which uses addition or subtraction to cross a number boundary.
Partition - Splitting an object or value down into smaller parts.
100s boundary - The point at which numbers change into 100s numbers, or from one set of hundreds to another.

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Hello there.

My name is Ms. Combe.

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.

By the end of this lesson, you'll be able to say that you can add to and subtract from a three-digit number bridging 100.

Let's get going.

We have three keywords for this lesson today.

Bridge or bridging, partition and 100s boundary.

I'm going to say them and I would like you to say them back to me.

My turn, bridge.

Your turn.

My turn, partition.

Your turn.

My turn, 100s boundary.

Your turn.

Well done.

Let's take a look at what those words mean.

Bridging is a strategy which can use addition or subtraction to cross a numbers boundary.

You can also bridge 100 by adding to make 100 and then adding whatever is left and we're going to be looking at that in today's lesson.

When we partition, we split an object or a value down into smaller parts.

So six could be partitioned into three and three or four and two.

The 100s boundary is the points at which the numbers change into hundreds numbers.

So if we count 98, 99, 100, 101, 102, we have crossed the 100s boundary.

There are going to be two parts to our lesson today.

We are going to first look at adding and subtracting single-digit numbers and then we're going to add and subtract multiples of 10.

Remember we're talking about bridging 100.

So let's get started with the first part of our lesson.

In this lesson you're going to meet Sofia and Andeep and they're going to be helping you with your learning and doing lots of representations to support you.

So Andeep and Sofia think about ways to partition seven into two parts.

Andeep says that seven can be partitioned into six and one, and he shows that with cubes.

Sofia says that we can partition seven into five and two.

How else can we partition seven? Hopefully you're very familiar with the fact that we can also partition seven into four and three, three and four, two and five and one and six.

Those partitions are going to be helpful in this part of the lesson.

So Andeep and Sofia add seven to three-digit numbers.

What is 297 plus seven, asks Andeep.

Sofia is going to partition seven into three and four to help her calculate.

Sofia is going to add three to bridge the 100s boundary.

Sofia knew that seven plus three made 10, so 297 plus three made 300.

Now remember she hasn't finished here.

She needs to add four more.

So there we go, we've added four more and we can see that 297 plus seven is equal to 304.

They continue to add seven to three-digit numbers, so this time Andeep is asking what is 399 plus seven? Now this time Sofia is going to partition seven into one and six.

Sofia knows that nine plus one is equal to 10, so 399 plus one more is going to bridge that 100s boundary.

She adds one more to get to 400 and adds six more.

399 plus seven is equal to 406.

Time for a quick check of your understanding.

Calculate 498 plus seven.

Think about how you're going to partition seven to bridge the 100s boundary.

Pause the video here and have a go.

And welcome back.

So you could partition seven into two and five because adding two more to eight makes 10.

So we can bridge that 100s boundary.

We're going to add two to bridge the 100s boundary and then we're going to add five more.

498 plus seven is equal to 505.

So well done if that's what you got.

So this time I am going to talk you through an example and then I'd like you to have a go.

What is 395 plus seven? Sofia thinks about how to partition seven to bridge the 100s boundary.

First, Sofia is going to add five and then she's going to add two.

Sofia knows that five plus five makes 10, so 395 plus five would bridge that 100s boundary.

Now it's your turn.

Think about 598 plus seven.

Think about how you're going to partition seven to bridge the 100s boundary.

Pause the video here and have a go.

Welcome back.

How did you get on? So we can use the sentence here.

First add Mm, then add Mm.

First we're going to add two and then we're going to add five.

Well done have you said you were going to partition seven into two and five.

This time Andeep uses the number line to represent the calculation 395 plus seven.

So we're still thinking about partitioning seven and Andeep is going to partition seven into five and two.

He's going to find 395 on the number line and add five to bridge the 100s boundary and then he's going to add two more.

395 plus seven is equal to 402.

Time for a check of your understanding.

Use a number line this time to represent the calculation 598 plus seven.

Think about how you're going to partition seven to bridge the a 100s boundary.

Pause the video here.

How did you get on? So I would've partitioned seven into two and five.

I would've found 598 on the number line, added two and added five more.

598 plus seven is equal to 605.

Well done if that's the answer you got.

Andeep and Sofia move on to think about partitioning six into two parts and I'm sure you can think of the partitions for six.

Six can be partitioned into five and one it can also be partitioned into four and two.

How else can you partition six? Well hopefully you spotted that you can have three and three, two and four or one and five and these are going to be useful to Sofia and Andeep for their calculating.

Andeep and Sofia, subtract six from three-digit numbers.

What is 204 subtract six, asks Andeep.

So here we have 204 and Sofia is going to partition six into four and two to help us bridge the 100s boundary.

First she's going to subtract four.

So you can see there if we subtract four from 204, we get back to 200, so we're bridging the boundary, and then she's going to subtract two more.

So think about what happens when you subtract a one-digit number from a three-digit number? 204 subtract six is equal to 198.

This time Andeep asks, what is 403, subtract six? Think about how you might partition six.

Sofia is going to partition six into three and three to bridge the 100s boundary.

She's going to subtract three first and then she's going to subtract three more.

We can see that 403 subtract six is equal to 397.

Time to check your understanding.

Calculate 302 subtract six.

Here's 302.

Think about how you're going to partition six to bridge the 100s boundary.

Pause the video here and have a go.

And welcome back.

How did you get on? So 302 is two away from 300.

So we could first partition six into two and four.

We subtract two first and then we subtract four more.

302 subtract six is equal to 296.

Well done if you said that.

So now I'm going to go through an example and then I'm going to ask you to have a go.

What is 601 subtract six? Sofia is thinking about how she would partition six to bridge the 100s boundary.

She says, \"First I'll subtract one, then I'll subtract five.\" So she's taking away one to get back to 600 and then taking away five more.

Now it's your turn.

I'd like you to think about 605 subtract six.

How should you partition six to bridge the 100s boundary? I'd like you to say the sentence, first subtract Mm, then subtract Mm.

Pause the video and have a go.

Welcome back.

Now this time I would subtract five and then one.

So, let's say that sentence together.

Are you ready? First subtract five, then subtract one.

Great job.

This time Andeep uses the number line to represent the calculation 601 subtract six.

He says he's going to partition six into one and five.

He's going to subtract one to bridge the 100s boundary.

So he's going to find 601 and subtract one, and then he's going to subtract five more and we can see that 601 subtract five is equal to 595.

Time to check your understanding.

This time I'd like you to use a number line to represent the calculation 605, subtract six.

Think about how you're going to partition six to bridge the 100s boundary.

Pause the video here.

Welcome back.

How did you get on? So if we position 605 on the number line, we can see that it's five away from 600.

So we can partition six into five and one, we're going to subtract five, and then we're going to subtract one more.

605 subtract six is equal to 599.

Well done if your number line looked like that.

Now on to our first task.

For part one, this should be quite straightforward.

You're going to find all the ways of partitioning eight into two parts.

So think about how you're going to partition eight and that will be useful for your next task.

For task two, I wait to think about how you'd partition eight to bridge the 100s boundary to calculate.

So for example, 304, subtract eight, what are you going to partition eight into? Subtract Mm, then subtract Mm.

Now remember some of these are subtraction and some are addition.

And then for part three I'd like to calculate the answers.

If you need to use base 10 blocks or a number line to help you, that's absolutely fine.

Pause the video here, have a go at these three tasks and I'll see you shortly for some feedback.

Welcome back.

Let's see how you got on.

So first of all, these are all the ways of partitioning eight into two parts and hopefully you used these when you were calculating.

For question two, these are the partitions that you should have got.

Let's look at a couple of examples.

304, subtract eight and I'm subtracting, so I want to get back to the next 100 to bridge the 100s boundary.

304 is four away from eight, so I can partition eight into four and four.

If I look at the last example, 295 plus 8, 295 is five away from 300.

So to bridge the boundary I'm going to partition eight into five and three.

Well done if you've got those answers.

And here are the answers for question three.

Pause the video here to mark your work.

And let's move on to part two of our lesson where we're going to be thinking about adding and subtracting multiples of 10.

So this time Andeep and Sofia are thinking about ways to partition 70 into two multiples of 10.

Remember, multiples is one of our key words.

70 can be partitioned into 60 and 10.

So if we show seven 10s, remember 70 is seven 10s, we can partition that into six 10s and one 10 or 60 and 10.

Sofia says that 70 can be partitioned into 50 and 20.

How else can we partition 70 into two multiples of 10? Well we can also have 40 and 30, 30 and 40, 20 and 50, and 10 and 60 and Sofia and Andeep are going to use these to calculate.

Andeep and Sofia add 70 to three-digit numbers.

What is 290 plus 70, asks Andeep.

So here is 290 and we're going to be adding 70.

We can still use partitioning to bridge the 100s boundary.

Sofia is going to partition 70 into 10 and 60.

We can see that 290 is one 10 away from 300.

So we're going to add 10 to bridge the 100s boundary.

Now remember Sofia needs to add 70 altogether, so she's going to add 60 more.

Think about what happens when we add a multiple of 10 to a three-digit number.

290 plus 70 is equal to 360.

Let's look at another example.

What is 270 plus 70, asks Andeep.

This time Sofia is going to partition 70 into 30 and 40.

We can see from the model that 270 is three 10s or 30 away from 300.

So she's going to add 30 to bridge the 100s boundary and then she has to add 40 more.

So we've got 300 plus 40, 270 plus 70 is equal to 340.

Time to check your understanding.

Calculate 380 plus 70.

Here's 380, and Sofia is reminding you to think about how you're going to partition 70.

Pause the video here and have a go.

And welcome back.

How did you get on? So I can see that 380 is two 10s away from the next multiple of 100.

So I'm going to partition 70 into 20 and 50.

I'm going to add 20 and then I'm going to add 50 more.

So 380 plus 70 is equal to 450.

Well done if you've got that.

I'm going to have a go and then I'm going to ask you to have a go.

What is 360 plus 70? Sofia thinks about how she would partition 70 to bridge the 100s boundary.

She says, first she's going to add 40, then she's going to add 30.

I want you to have a think what is 440 plus 70? How should you partition 70 to bridge the 100s boundary? I'd like you to say the sentence, first add Mm, then add Mm.

Pause the video here.

And welcome back.

How did you get on? Well, I know that 40 plus 60 makes 100, so I'm going to partition 70 into 60 and 10.

Let's say that sentence together.

Are you ready? First add 60, then add 10.

Well done if that's what you said.

Andeep uses a number line to represent the calculation 360 plus 70.

So we're still going to be partitioning and this time Andeep is going to partition 70 into 40 and 30.

He's going to add 40.

So he finds 360 on the number line adds 40 to get to 400.

We're bridging that a 100s boundary and then adds 30 more.

360 plus 70 is equal to 430.

Time to check your understanding.

Use a number line to represent the calculation 440 plus 70.

Think about how you're going to partition 70.

Pause the video here.

And how did you get on? First we're going to partition 70 into 60 and 10 and then we're going to add 60 and add 10 more.

Well done, if your number line looked like that and you knew that 440 plus 70 was equal to 510.

So Andeep and Sofia move on to think about ways to partition 80 into multiples of 10.

We can partition 80 into 70 and 10, says Andeep, and we can also partition it into 60 and 20 says Sofia.

How else can we partition 80 into two multiples of 10? Well, we can also have 40 and 40, 30 and 50, 20 and 60, 10 and 70.

So Andeep and Sofia subtract 80 from three-digit numbers.

What is 330 subtract 80, asks Andeep.

So here is 330.

Sofia is going to partition 80 into 30 and 50.

330 is 30 away from our 100s boundary.

So, we're going to subtract 30 to get to 300.

Then remember we need to subtract 80 altogether, so we're going to subtract 50 more.

Think about what happens when we subtract a 10s number from a 100s number.

330 subtract 80 is equal to 250.

This time we're going to subtract 80 from 370.

Think about how you might partition 80 into two parts.

Sofia is going to partition 80 into 70 and 10.

We're going to subtract 70 to get to our 100s boundary and then subtract 10 more.

370 subtract 80 is equal to 290.

Time to check your understanding.

Calculate 440 subtract 80.

Here's 440.

And Sofia is reminding you to think about how you're going to partition 80.

Pause the video here to have a go.

Welcome back.

How did you get on? First we partition 80 into 40 and 40.

We're going to subtract 40 and then another 40.

So, 440 subtract 40 is equal to 360.

Well done if that's what you got.

So my turn.

What is 530 subtract 80? Sofia is thinking about how she's going to partition 80 to bridge the 100s boundary.

\"First I'll subtract 30, then I'll subtract 50\", she says.

So we're going to take away the 30 to get back to our 100s boundary and then subtract 50 more.

Your turn.

What is 520 subtract 80? How are you going to partition 80? I'd like you to say the sentence, first subtract Mm, then subtract Mm.

Pause the video here to have a go.

Welcome back.

How did you get on? Let's say the sentence together.

First subtract 20, then subtract 60.

Well done if that's what you said.

So this time Andeep is going to use a number line to represent the calculation 530 subtract 80.

Here's our number line.

He's going to partition 80 into 30 and 50.

So he's going to find 530 and subtract 30.

And we can see there we're getting back to that a 100s boundary.

Then he subtracts 50 more.

530 subtract 80 is equal to 450.

Time to check your understanding.

Use a number line to represent the calculation 520 subtract 80.

Remember to think about how you're going to partition 80.

Pause the video here.

Welcome back.

How did you get on? So we're going to partition 80 into 20 and 60.

We're going to find 520 and subtract 20.

Then we're going to subtract 60 more.

Well done if your number line looked like that.

520 subtract 80 is equal to 440.

Time for your second practise tasks.

First of all, find all the ways of partitioning 70 into two multiples of 10.

They're going to help you with your next calculations.

For question two, think about how you'd partition 70 to bridge the 100s boundary.

So for example, 410 subtract 70, subtract Mm, then subtract Mm.

How are you going to partition 70 to bridge that boundary? For question three, you can use base 10 blocks or a number line to help you calculate the answers.

Now be careful, because there's a mix of addition and subtraction here.

Have a go and I'll see you shortly for some feedback.

Welcome back.

How did you get on? So these are all the ways that you could partition 70 into two multiples of 10.

Well done if you spotted all of those and used them in your calculations.

For question two, we can partition 70 in lots of different ways, but we need to think about how we're being efficient.

So 410 subtract 70, I can see that 410 is 10 away from 400.

So I'm going to subtract 10 first.

So I'm partitioning 70 into 10 and 60.

For 370 plus 70, I can see that 370 is 30 away from the next multiple of 100.

So I'm going to partition 70 into 30 and 40, add 30, then add 40.

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

And here are the answers for question three.

Pause the video here and mark your work.

So, we've come to the end of the lesson and I know you've worked incredibly hard to think about bridging 100.

Let's summarise our learning.

We can partition numbers in order to bridge a 100s boundary and we can count on or back to that 100s number in order to bridge through the 100s boundary.

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

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" }, "questionType": "Multiple choice", "correct": [ { "text": "subtract 5 then subtract 2" } ], "choices": [ { "text": "subtract 2 then subtract 5" }, { "text": "subtract 3 then subtract 4" }, { "text": "subtract 4 then subtract 3" }, { "text": "subtract 5 then subtract 2" } ], "id": "87eee4e4-32e4-b7cc-3bbe-193e4d634127", "lessonId": "021d37ed-ff0c-98eb-acf8-a47ff2d60e06" }, { "type": "Question", "question": { "text": "Which calculations cross a 100s boundary? " }, "questionType": "Multiple choice", "correct": [ { "text": "90 + 20" }, { "text": "220 − 30" } ], "choices": [ { "text": "90 + 20" }, { "text": "120 + 30" }, { "text": "190 − 20" }, { "text": "220 − 30" } ], "id": "5b3779c1-e0fc-610f-59ca-095ed71fa066", "lessonId": "021d37ed-ff0c-98eb-acf8-a47ff2d60e06" }, { "type": "Question", "question": { "text": "220 − 30 = ______ " }, "questionType": "Short answer", "correct": [ { "text": "190" } ], "id": "d4ec6fbd-f110-74e5-02c6-92a2c8c54b84", "lessonId": "021d37ed-ff0c-98eb-acf8-a47ff2d60e06" }, { "type": "Question", "question": { "text": "Use the number line to complete the calculation. 370 + ______ = 420", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703060435%2Fic5v5jecu6tn61ugpsxc.png&w=828&q=75", "imageKey": "5ecbccec-19fe-137f-9526-d3fc6d5ad859/question/e5ad9f71041788611a1b20573aa4482a.png" }, "questionType": "Short answer", "correct": [ { "text": "50" }, { "text": "fifty" } ], "id": "cb73de8e-f93f-f324-94a1-2a60bc5e8520", "lessonId": "021d37ed-ff0c-98eb-acf8-a47ff2d60e06" }, { "type": "Question", "question": { "text": "Use the number line to complete the calculation. 550 − ______ = 480", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1703060436%2Fdfg8pqrq4g6bftcgt5yb.png&w=1200&q=75", "imageKey": "5ecbccec-19fe-137f-9526-d3fc6d5ad859/question/19192ccb5a662903559ab2f6f45956df.png" }, "questionType": "Short answer", "correct": [ { "text": "70" }, { "text": "seventy" } ], "id": "20177a12-d7e8-ec3e-0268-13e5e6ce290a", "lessonId": "021d37ed-ff0c-98eb-acf8-a47ff2d60e06" } ], "lessonId": "021d37ed-ff0c-98eb-acf8-a47ff2d60e06", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "Representing 3-digit numbers, comparing and positioning on number lines", "lessonCount": "15", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Add and subtract to and from a 3-digit number bridging 100" } } ] }