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I can subtract 2 or 3-digit numbers using partitioning and bridging a multiple of 10

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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

By looking at the minuend and subtrahend we know if we will have to bridge 10 or 100
If the ones digit of the subtrahend is greater than the ones digit of the minuend then we will have to bridge through 10
If the 10s digit of the subtrahend is greater than the 10s digit of the minuend then we will have to bridge through 100

Common misconception

Pupils will often try to use a written method/algorithm which they know gives an accurate answer but don't understand why it works.

Encourage the pupils to be brave and remind them that this is about mental subtraction so, with practice, will be quicker than any written methods.

Keywords

Minuend - The minuend is the number being subtracted from.
Subtrahend - A subtrahend is a number subtracted from another.
Difference - The difference is the result after subtracting one number from another.
Partition - Partition is the act of splitting an object or value down into smaller parts.

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Hello, my name is Mr. Tazzyman, and I'm really excited to be working with you on this lesson today.

If you are ready, let's get started.

It's time to get going.

The outcome of today's lesson is for you to be able to say, \"I can subtract 2 and 3-digit numbers using partitioning and bridging a multiple of 10.\" Here are the key words that you're going to be facing during this lesson.

I'm gonna say them and then I want you to repeat them back to me.

So I'll say my turn and say the word, and then I'll say your turn and you say it back.

My turn, minuend.

Your turn.

My turn, subtrahend.

Your turn.

My turn, difference.

Your turn.

My turn, partition.

Your turn.

Here's an explanation of some of these keywords.

The minuend is the number being subtracted from.

A subtrahend is a number subtracted from another.

The difference is the result after subtracting one number from another.

You can see below that there's an equation there.

7 subtract 3 = 4, and labelled on that equation are the minuend, which in this case is 7, the subtrahend, which has been subtracted, and in this case is 3, and that equals 4, which is the difference.

Hopefully that helps you.

Partition is the act of splitting an object or value down into smaller parts.

Here's the outline of today's lesson.

We'll start by doing some partitioning without bridging, and then we'll look at how to partition with bridging.

Let's get started.

In this lesson, there's a couple of people who you will be meeting, Sam and Laura, and they're here to help us with some of the answers to help us with some of the discussions, and to respond to some of the prompts that you'll see on the screen.

Okay.

Guinea pigs.

Guinea pigs can live in large herds.

In a herd of 68 guinea pigs, 26 brown and the rest are other colours.

How many guinea pigs are not brown? You can see this has been represented with a bar model at the bottom there, 68, 26, and then a question mark.

Sam says, \"We know the whole is 68 and one part is 26.\" We need to subtract to find the missing part.

The minuend is 68 and the subtrahend is 26.

You can see it's been written as an equation there.

Laura says, \"I can partition the subtrahend to subtract mentally.\" 26 can be partitioned into 20 and 6.

This makes it easier to subtract in my head.

68 subtract 20 subtract 6 gives 42.

She draws it on a number line.

\"First, I will subtract one part of 20.\" So she takes 20 away to get to 48.

\"Then I will subtract one part of 6.\" She takes that 6 away to get to 42.

Well done, Laura.

The difference is 42 so 42 guinea pigs aren't brown.

There's the answer.

Okay, it's time to check your understanding of what we've just learned.

\"What subtraction equation does this number line represent?\" So you've got to write out an equation that this number line represents.

Pause the video here, have a go at that and I'll be back in a moment to tell you what the equation was so you can see how you've got on.

Good luck.

Welcome back.

Let's see how you did.

Here's the equation represented by this number line.

86 subtract 34 equals 52.

You can see on the number line that the subtrahend has been partitioned into two parts using place value.

Firstly, 30 has been subtracted and then 4.

This is an easy way of doing that subtraction mentally, and so that's why that represents the equation you can see on your screen.

Okay, next part.

More guinea pigs, but this time there's some rabbits as well.

\"Guinea pigs can also live well with rabbits.

In a herd of 168 guinea pigs and rabbits, there are 26 rabbits.

How many guinea pigs are there?\" Well, Sam says, \"The subtrahend is the same in this problem, it is 26.\" The minuend is 100 more than 68, and we can see it's been represented there on the left hand side.

We've got 168 takeaway 26 equals something, we don't know yet it's an unknown, but we've got the bar model below to show that 168 is the total and that has two parts, 26, and again, our unknown that we don't know.

Sam says, \"I think we can use the same partitioning strategy.\" Laura steps in and she starts to draw it on the number line.

She say, \"We can partition 26 into 20 and 6 again, I can subtract 20, then subtract 6.\" The difference is 142.

So there are 142 guinea pigs.

That's a lot of guinea pigs.

\"Gertie and Gilbert are baby guinea pigs.

Together they have a mass of 680 grammes.

Gilbert has a mass of 260 grammes.

What is Gertie's mass?\" We can see the equation there below.

680 subtract 260 equals something, an unknown.

And the bar model below, again, represents this problem.

Laura says, \"This time there is a 3-digit subtrahend.\" I think we can still partition the subtrahend.

Laura shows the steps on a number line.

She says, \"I can partition 260 into 100s and 10s to subtract.

260 is 200 and 60 and I can subtract each part.\" There's the equation she's thinking about.

680 subtract 200 subtract 60 is an unknown.

She draws it on the number line and says, \"First, I will subtract 200, then I will subtract 60.

The difference is 420.

So Gertie's mass is 420 grammes.\" Well done, Laura.

The parts were bigger than before, but partitioning made it easy to subtract mentally.\" And that's what this method is all about, trying to make it as easy as possible to do mentally.

But Sam sees a different way to calculate.

\"I can unitize.

680 is the same as 68 tens.\" And this is a concept that you may have come across before.

\"260 is the same as 26 tens.

I can now subtract mentally.\" This has been written below as an equation.

68 tens subtract 20 tens subtract 6 tens equals something.

\"I subtract 20 and then 6 from 68, and I end up with a difference, which is 42 tens.

42 tens is 420.\" Now it's time to check your understanding of the things that we've just learned.

\"Complete the jumps on the number line and find the difference.\" So you can see that the number line has been started.

In fact, the subtrahend has already been partitioned.

We've got 690 subtract 470, and that 470 has been partitioned into 400 and 70.

Can you complete the number line? Pause the video here, have a go, and I'll be back in a moment to show you the answer.

Welcome back.

Let's finish off this number line.

We can see that 400 has already been subtracted, so from our partitioning, 70 is left over to subtract.

If we subtract that 70, we finish on 220.

So the difference was 220.

How did you get on? I hope you got it.

Let's move on.

\"Laura makes a 3-digit number, 750.

Sam makes a smaller 3-digit number, 410.

Laura wants to know how much larger her number is compared to Sam's.\" Laura says, \"I know 750 is bigger, but how much bigger?\" And Sam replies, \"We need to find the difference between 410 and 750.\" \"Laura partitions 410 into 100s and 10s to subtract.\" Laura says, \"The minuend is 750 and the subtrahend is 410.

I will partition 410 into one part of 400 and one part of 10.

I can subtract 400 and then subtract 10.\" So she does just that.

She starts by subtracting 400 from 750 to give her 350 and then she does 350 take away 10.

\"The difference is 340.\" Well done, Laura.

\"Sam unitizes and partitions to subtract.\" Sam says, \"I can think of 750 as 75 tens and 410 as 41 tens.

I can partition 41 tens into 40 tens and 1 ten.\" 75 tens subtract 40 tens subtract 1 ten.

So we've got 75 takeaway 40, which gives us 35.

35 takeaway 1 gives us 34.

The difference is 34 tens or 340.

Great work, Sam.

Same difference.

Okay, it's time for you to have a practise now.

For number one, I want you to find the difference between each pair of numbers using partitioning.

You could unitize first.

Use a number line to show the steps if you need to.

So for a, we've got 680 and 410, b, we've got 680 and 540, and c, we've got 830 and 520.

D is 470 and 360.

Pause the video here, have a really good go at finding the difference on each of these questions, and I'll be back in a little while to give you some feedback.

Welcome back.

Let's do some feedback.

Now, the methods chosen here might be different to the ones that you chose, but let's see what the differences were.

For a, we've chosen to use partitioning and we've got a result of 270 by partitioning 410 into 400 and 10, and then subtracting both of those parts independently.

And for b, we used unitization and then partitioned it.

We took 68 tens, subtract 54 tens and partitioned the 54 tens into 50 and 4.

We ended up with 14 tens, which is, of course we know, 140.

For c, once again, we used partitioning and ended up with a difference of 310 by partitioning 520 into 500 and 20.

And for d, it was unitization again, we took 36 tens and partitioned it into 30 and 6.

The end result was 11 tens giving us a difference of 100 and 10.

How did you get on? I hope you got them.

Ready to move on? Second part of the lesson now.

We're gonna look at partitioning with bridging.

\"Laura makes a 3-digit number, 752.

Sam makes a 2-digit number, 47.

Laura wants to know how much larger her number is compared to Sam's.\" Laura says, \"I know 752 is bigger, but how much bigger?\" And again, Sam replies by saying, \"We need to find the difference between 752 and 47.\" \"Laura partitions 47 into 10s and 1s to subtract.\" She shows the steps on a number line.

\"I will partition 47 into 40 and 7 to subtract mentally.\" Well done, Laura.

That's a really good thing to do, makes it nice and easy.

I will subtract 40 from the minuend, there it goes, and she gets 712.

\"I now need to subtract 7, but that's not easy.

Well, I know.

I can partition again and bridge through 10.

I can partition 7 into 2 and 5 to help me.

This means I can bridge through 10, which is a good mental strategy.

712 subtract 2 is 710, which is an easier number to use.

710 subtract five is 705 so the difference is 705.\" Well done, Laura.

Great thinking.

\"Sometimes partitioning twice makes calculating easier.\" \"Laura makes a 3-digit number.

Sam makes a 3-digit number.

Laura wants to know how much larger her number is compared to Sam's.\" She says, \"I know 520 is bigger, but how much bigger?\" And once again, what does Sam reply? \"We need to find the difference between 520 and 470.\" \"Hmm.

I can see we might have to partition twice,\" says Laura.

I wonder why that might be.

\"Laura partitions 470 into 10s and 100s to subtract and she shows the steps on a number line.\" She starts by partitioning 470 to 400 and 70.

Then she subtracts the 400 from the minuend to give her 120.

Now she needs to subtract 70, but that's not easy.

\"I know,\" she says.

\"I can partition again and bridge through 100.\" We can see that if we took 120 and subtracted 70, we're gonna have to go past the 100s boundary.

So that's why this second partitioning's really useful.

She partitioned 70 into 20 and 50 to help her bridge.

\"120 subtract 20 is a 100, which is an easier number to use.

100 subtract 50 is 50, so the difference is 50.\" Well done, Laura.

Sometimes partitioning twice makes calculating easier.

\"Sam unitizes and partitions to subtract.\" Sam says, \"I can think of 520 as 52 tens and 470 as 47 tens.\" 52 tens subtract 47 tens is the same as 52 tens subtract 40 tens subtract 7 tens.

Sam's partition 47 into 40 and 7.

Then Sam goes on to say, \"I can subtract 40 from 52 to give 12 and then subtract 7.\" Again though Sam has the similar problem, this needs some bridging.

So Sam says, \"I think I'll need to partition again and then bridge.\" Sam partition 7 into 2 and 5, and the difference is 5 tens or 50.

Okay, it's your turn.

Let's check how well you've understood what we've just talked about.

I'd like you to finish the number line and find the difference.

You can see below we've got an equation 630 subtract 250 and 250 has already been partitioned into 200 and 50.

Your task is to finish that number line and find the difference.

Pause the video here, have a go, and I'll be back in a moment to give you the answer so you can see how you've got on.

Welcome back.

Let's see how we got on.

So we know 630 takeaway 200 is 430.

Then we're gonna subtract 30 first because we will have partitioned 50 into 30 and 20.

So then we subtract that 20 to give us 380.

Did you get it? Some of you might have tried to subtract 50 all in one go and known that 430 takeaway 50 was 380.

That's okay, but it might be a good idea to think about whether or not you need to partition twice when you're bridging.

Ready to move on? Here's your practise task.

I'd like you to find the difference between each pair of numbers using partitioning.

You could unitize first.

Use the number line to show the steps if you need to.

So for a, it's 730 and 470.

For b, it's 840 and 470.

For c, it's 710 and 390.

And for d, it's 620 and 560.

Here's number two.

You're gonna use a partitioning strategy to answer each worded problem.

And remember, you can still unitize if you'd prefer.

I'll read out the worded problems to you A, \"In a standing jump competition, Laura jumps 170 centimetres.

Sam jumps 220 centimetres.

How much further did Sam jump?\" \"Sam scores 340 points and Laura scores 190 points against each other other on a computer game.

How many points does Sam win by?\" Gosh, Sam's doing well.

\"Sam and Laura play a game on the beach.

They throw stones at a piece of driftwood and score 10 points every time they hit it.

Sam hits the driftwood 25 times and Laura hits it 32 times.

How many more points does Laura score?\" Okay, I'm gonna pause the video for you to have the chance to complete these practise questions.

I'll be back in a little while to give you some feedback.

Good luck.

Let's see how you got on in a moment.

Welcome back.

Let's see how you got on.

One a and b as shown here and we've got the workings.

This one's been done with unitization.

You should have found a difference of 26 tens, which is 260.

For b, you should have found a difference of 370.

I'll let you mark those first couple of questions and I'll be back in a moment with the rest of the answers.

Welcome back.

Let's do c and d.

For c, you could have used unitization and got 32 tens and that would've given you a final difference of 320.

And for d, the final difference was 60.

Again, pause the video here so that you can have the chance to carefully mark those.

Number two.

A, we had our standing jump.

The difference ended up being 5 tens, which is 50.

For b.

our computer game, the difference was 150.

And for c, the difference was 70.

I hope you got those.

It's time to summarise now.

Today, here's what we have learned about.

\"We can subtract by partitioning the subtrahend and subtracting this from the minuend.

Sometimes we need to bridge 10 or 100 to subtract efficiently.

In this case, we can partition the subtrahend further.

Partitioning to subtract is a mental strategy which can be effective.\" Thanks very much for learning so well today.

My name's Mr. Tazzyman, and I really hope to see you soon in another Maths lesson.

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{ "text": "10 − 4" }, { "text": "13 − 7" } ], "choices": [ { "text": "26 − 19" }, { "text": "10 − 4" }, { "text": "100 − 4" }, { "text": "27 − 10" }, { "text": "13 − 7" } ], "id": "1ff56996-8f52-fad9-734a-26cf0145b49c", "lessonId": "d240b47e-5e70-624d-9cca-415f9f042381" }, { "type": "Question", "question": { "text": "207 − 190 = ______ " }, "questionType": "Short answer", "correct": [ { "text": "17" }, { "text": "seventeen" } ], "id": "68851dad-1430-7f18-3aee-85cc87dccb6a", "lessonId": "d240b47e-5e70-624d-9cca-415f9f042381" } ], "lessonId": "d240b47e-5e70-624d-9cca-415f9f042381", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "Informal and mental strategies for adding and subtracting two 3-digit numbers", "lessonCount": "10", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Subtract 2 or 3-digit numbers using partitioning and bridging a multiple of 10" } }, { "id": "c71490c0-e58a-f724-67ce-e9a1c47a8593", "type": "Resource", "resourceType": "Quiz", "title": "Subtract 2 or 3-digit numbers using partitioning and bridging a multiple of 10", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "Which is the correct definition of difference?" }, "questionType": "Multiple choice", "correct": [ { "text": "The result after subtracting one number from another." } ], "choices": [ { "text": "The result after adding one number to another." }, { "text": "The result after multiplying two or more numbers." }, { "text": "The result after dividing one number by another." }, { "text": "The result after subtracting one number from another." } ], "id": "5cecb653-9870-8322-f984-0f4000ae1d2f", "lessonId": "d240b47e-5e70-624d-9cca-415f9f042381" }, { "type": "Question", "question": { "text": "What subtraction equation does this number line represent?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1706533496%2Frw0gi5pgw7g6zjkny4nb.png&w=1080&q=75", "imageKey": "c71490c0-e58a-f724-67ce-e9a1c47a8593/question/ec1bfa71564aa037a35c88e7d0ce6c5e.png" }, "questionType": "Multiple choice", "correct": [ { "text": "75 − 24 = 51" } ], "choices": [ { "text": "75 + 24 = 99" }, { "text": "75 − 20 = 55" }, { "text": "75 − 24 = 51" }, { "text": "75 − 51 = 24" } ], "id": "e266da63-1ed4-c1b8-130c-657c917dcee4", "lessonId": "d240b47e-5e70-624d-9cca-415f9f042381" }, { "type": "Question", "question": { "text": "Find the difference between 270 and 160 using partitioning." }, "questionType": "Short answer", "correct": [ { "text": "110" }, { "text": "one hundred and ten" } ], "id": "ce110878-f6e0-bb83-ce6f-d8883582a500", "lessonId": "d240b47e-5e70-624d-9cca-415f9f042381" }, { "type": "Question", "question": { "text": "Find the difference between 430 and 310 using partitioning." }, "questionType": "Short answer", "correct": [ { "text": "120" }, { "text": "one hundred twenty" } ], "id": "422992ff-bb51-fb1d-4c37-7e5520d6934f", "lessonId": "d240b47e-5e70-624d-9cca-415f9f042381" }, { "type": "Question", "question": { "text": "Find the difference between 540 and 360 using partitioning and bridging." }, "questionType": "Short answer", "correct": [ { "text": "180" }, { "text": "one hundred and eighty" } ], "id": "df1b0f1a-53c7-bdb2-f601-4203133c0619", "lessonId": "d240b47e-5e70-624d-9cca-415f9f042381" }, { "type": "Question", "question": { "text": "Find the difference between 670 and 490 using partitioning and bridging." }, "questionType": "Short answer", "correct": [ { "text": "280" }, { "text": "two hundred and eighty" } ], "id": "a61be753-472b-7737-3316-25e73ef565d6", "lessonId": "d240b47e-5e70-624d-9cca-415f9f042381" } ], "lessonId": "d240b47e-5e70-624d-9cca-415f9f042381", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "Informal and mental strategies for adding and subtracting two 3-digit numbers", "lessonCount": "10", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Subtract 2 or 3-digit numbers using partitioning and bridging a multiple of 10" } } ] }