Lesson video

Hello there.

My name is Ms. Coe.

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 welcome to this lesson as part of the unit looking at three digit numbers.

The learning outcome for this lesson today is that by the end of the lesson, you will be able to solve problems by adding to and subtracting from three digit numbers.

We have some important keywords in this lesson.

Let's have a go at saying them together in my turn, your turn.

Are you ready? My turn, bridge.

Your turn.

My turn, partition.

Your turn.

My turn, 100s boundary.

Your turn.

Excellent work.

Let's have a look at what all those words mean.

Bridging is a strategy which uses addition or subtraction to cross a number boundary.

For example, you can bridge 100 by adding to make 100 and then adding whatever is left.

And we're going to be looking at that in our lesson today.

Partitioning is when we split an object or value down into smaller parts.

Six could be partitioned into three and three or four and two.

The 100s boundary is the point at which the numbers change into 100s numbers or from one set of 100s to another.

So for example, when we're counting 98, 99, 100, 101, 102, we cross the 100s boundary when we say 100.

Our lesson today has two parts.

First, we're going to be looking at adding and subtracting 10s numbers, and then we'll be looking at adding and subtracting with any three digit number.

Let's get started in our first cycle.

In this lesson today, you are going to meet Sophia and Andeep.

They're going to be helping you with your learning and asking you some questions to deepen your understanding.

So we're going to start by thinking about Colin the cat.

Colin the cat sits in a tree.

He starts off by being 360 centimetres high.

He climbs up another 70 centimetres.

How high is he now? So let's visualise that problem.

Colin starts off being 360 centimetres high in a tree.

Now that sounds quite high, but cats are brilliant at climbing.

Colin then climbs up another 70 centimetres.

We need to work out how high is he now.

Andeep is asking us, how would we work that out? So what calculation do we need to do? Well, Sophia helps us out here and says that we need to add together 360 centimetres and 70 centimetres.

Let's look at how we might do that.

So Andeep calculates 360 centimetres plus 70 centimetres using a number line.

He partitions 70 to bridge the 100s boundary.

So he's going to partition 70 into 40 and 30.

He's going to add 40 because he knows that 60 plus 40 is 100, so 360 plus 40 is 400.

Then he's going to add 30.

So we can see that as a second jump on our number line.

So Sophia knows that Colin is now 430 centimetres high.

We've calculated how high Colin is in his tree.

So Colin is now 430 centimetres high in his tree, very high up, but remember he's a very good climber.

He climbs up another 90 centimetres.

How high is he now? Andeep is asking us, well how would work out how high Colin is now? Hmm, I think we can use a similar strategy.

Sophia is reminding us that we can add 430 centimetres and 90 centimetres together and we can do that by partitioning 90 to bridge the 100s boundary.

Think about how you might partition 90 to bridge that 100s boundary.

Andeep says he's going to partition 90 into 70 and 20.

Andeep knows that 30 plus 70 is 100, so 430 plus 70 makes 500.

We've bridged that 100s boundary.

Now remember we haven't finished here because we need to add 90 altogether.

We've added 70, so Andeep needs to add 20 more and shows that on his number line.

So we can now see that Colin is now 520 centimetres high in the tree.

Time to check your understanding.

Colin is now 520 centimetres high in the tree.

He climbs up another 90 centimetres, very brave Colin.

Andeep is asking you to work out how high Colin is now in the tree.

Think about how you partition 90.

You can use the number line to help you.

Pause the video here and work out the answer.

Welcome back.

How did you get get on? How did you partition 90 centimetres to bridge the 100s boundary? Well I know that 20 plus 80 is equal to 100.

So 520 plus 80 is 600.

Now I have to add 90 altogether of added 80, so I'm going to add 10 more.

So Colin is now 610 centimetres in the tree.

Well done if you've got that answer.

So back to Colin.

He is 610 centimetres high in the tree.

He decides he's a bit high, so he climbs down 60 centimetres.

How high is he now? Andeep is asking, well how can we now work out how high Colin is? Do we need to do the same calculation as before? Hmm.

Sophia says we need to subtract 60 centimetres from 610 centimetres and she's right because he's climbing down, so the new height is going to be lower or less than 610.

Let's think about how we're going to do that.

Andeep calculates 610 centimetres subtract 60 centimetres.

He's going to partition 60 to bridge the 100s boundary.

So think about how he could partition 60.

What could we do? Andeep says that he's going to partition 60 into 10 and 50, because if he subtracts 10 from 610 he gets to 600.

He's bridging the 100s boundary and we always need to look out for that when we subtract.

Now remember Andeep isn't finished.

He subtracted 10 but he needs to subtract 60 altogether.

So he subtracts 50 and he shows that on the number line.

So he can see that Colin is now 550 centimetres high.

He's 60 centimetres lower than he was, which is 550 centimetres.

So Colin is now 550 centimetres high in the tree and he climbs down another 80 centimetres.

I think you can predict what calculation we're going to have to do.

How high is he now? Andeep is asking, well how are we going to work that out? So he's 550 centimetres high in the tree, he climbs down 80 centimetres.

Sophia is reminding us that we need to subtract again because Colin is going to be lower in the tree.

So we need to subtract 80 from 550 centimetres.

Andeep is going to calculate that again and he knows that he needs to partition 80 to bridge the 100s boundary.

Think about how you would partition 80.

Andeep says he's going to partition 80 into 50 and 30.

Can you think about why he might have partitioned the number in that way? So first he's going to subtract 50.

So he's going to show that on his number line and hopefully you can see that by subtracting 50 we've got to 500.

We are bridging the 100s boundary.

He's now going to subtract 30, that's the rest of the 80, so we can show that on the number line.

And we can see now that Colin is 470 centimetres high.

Time to check your understanding.

Colin is now 470 centimetres high in a tree.

He climbs down 80 centimetres.

Andeep is asking you to work out how high Colin is now.

Sophia is reminding you to think about how you're going to partition 80 to bridge that 100s boundary.

Pause the video here, use the number line to help you if you need it.

And welcome back.

How did you get on? So remember Colin is climbing down so we need to subtract 80 from 470.

I can see that 470 is 70 away from 400.

So I'm going to partition 80 into 70 and 10.

I'm going to subtract 70 first to get to 400 and then I'm going to subtract 10 more.

So I can see that Colin is now 390 centimetres high in the tree.

Well done if you've got that.

This time, Katya the cat is sitting in a tree.

It's a different cat, same problem.

Katya climbs up another 80 centimetres.

She is now 320 centimetres high.

How high did she start? Hmm.

So let's see if we can visualise that problem.

Katya the cat is in a tree.

We don't know to start with how high she's in the tree, but we know she climbs up another 80 centimetres and after doing that she's at 320 centimetres high.

We need to know how high she was when she started.

So Andeep is saying that the answer add 80 centimetres is equal to 320 centimetres, so something plus 80 is equal to 320.

And Sophia is reminding us that when we have a problem like that we can subtract.

So we can subtract 80 centimetres from 320 centimetres to find the answer.

Let's have a look at how we might do that.

Andeep calculates 320 centimetres subtract 80 centimetres.

Now as always, he is going to partition 80 to bridge the 100s boundary.

Think about how you might partition 80.

He's going to partition 80 into 20 and 60 because if we subtract 20 from 320, we bridge that 100s boundary.

So we're going to subtract 20, which gives us 300.

And remember we have to subtract both of the partition parts.

So now he subtracts 60 and shows that's on the number line.

300 subtract 60 is 240.

So therefore Katya started 240 centimetres high in the tree.

Time to check your understanding.

Katya is sitting in a tree again.

She climbs down 90 centimetres.

She is now 350 centimetres high.

How high did she start? How would you calculate the answer? Pause the video here and have a think about what you would do to find the answer.

And welcome back.

What did you say? Andeep says that the answer subtract 90 centimetres is equal to 350 centimetres.

So something subtract 90 is equal to 350.

So Sophia says that to find the answer we need to add together 90 and 350 centimetres.

Well done if you said that.

So carrying on from that, I would now like you to work out well what is 350 centimetres plus 90 centimetres? Andeep is reminding us to think about how we're going to partition 90 to bridge the 100s boundary.

Pause the video here and have a go.

And welcome back.

How did you get on? So we could partition 90 into 50 and 40.

So remember we're adding 90 to 350.

We're going to add 50.

So 350 plus 50 is equal to 400.

We're bridging that 100s boundary.

Then we're going to add 40.

So 400 plus 40 is 440.

So we know the answer is 440 centimetres.

Well done if you've got that.

Time for your first practise task.

Question one, you need to work out how high Colin is in the tree each time.

So he starts out at 380 centimetres high.

First he climbs up 80 centimetres.

How high is Colin? So the tricky bit here is that your answer to A will start the answer to B.

So once you've worked out A, use the height of Colin in the tree to answer B, which is he climbs up another 70 centimetres.

And then continue to follow that through C and D.

You can use a number line to help you calculate the answer if you need to, but remember to think about partitioning.

For question two, you need to calculate how high the cats were to start with.

So A, Katya sits in a tree.

She climbs up another 70 centimetres, she's now 250 centimetres high.

How high did she start? And Clive the cat sits in the tree.

He climbs down 90 centimetres.

He's now 250 centimetres high.

How high did he start? Pause the video here and I'll see you shortly for some feedback.

Welcome back.

How did you get on with those two tasks? Let's think about number one.

Colin started at 380 centimetres high.

He climbed up 80 centimetres.

So hopefully you added 80 to 380 and got 460 centimetres, because we then use that information for B.

So we know that Colin is now at 460 centimetres high.

He climbs up another 70 centimetres.

So for B, the calculation we needed to do was 460 plus 70, which is 530 centimetres.

Well done if you've got those two right so far.

So he is now at 530 centimetres high.

He climbs down 60 centimetres.

How high is he now? Well he's climbing down so he's going to be lower.

So we had to do 530 subtract 60, which is 470 centimetres.

And then finally he climbed down another 90 centimetres.

So how high does he end up? So we had to do 470 centimetres subtract 90 centimetres, which was 380 centimetres.

Well done if you managed to get to the end of that because it was really tricky keeping track of all of those answers.

For question two, Katya was sitting in a tree and she climbed up another 70 centimetres.

Now we didn't know where she started off, so we had to do 250 subtract 70, which is 180 centimetres.

So she started at the height of 180 centimetres.

For the second question, Clive started at a height, he climbed down 90 centimetres and then he was also 250 centimetres high.

But to work out his starting position, we had to add together 250 and 90, which is 340.

So Clive started at 340 centimetres high.

Well done if you solve both of those tricky problems. Let's now move on to the second part of our lesson where we're adding and subtracting with any three digit number.

So we're still thinking about our cat problems. Carlos is sitting in a tree.

He starts off at 362 centimetres high.

He climbs up another 70 centimetres.

How high is he now? Andeep is asking us, well how could we work out how high Colin is? I think we can use some of what we already know to do this.

Sophia is saying that we can add together 362 centimetres and 70 centimetres.

Let's have a look at how that might work.

We can do this on a number line and we can use the same strategy that we've been using already.

We're going to partition 70 into 40 and 30 because I know that 60 plus 40 makes 100.

So 360 plus 40 makes 400.

Now it doesn't matter that we have an extra two there.

The idea of bridging the 100s boundary remains the same.

So we're going to start on 362 and add 40.

Here's 362 on my number line and if I add 40, I get to 402, so I've bridged the 100s boundary.

Now remember I need to add 30.

When we add a multiple of 10 to a three digit number, the 10s digit changes.

So we have 402 plus 30 makes 432.

Remember that extra two.

So Carlos is now 432 centimetres high.

Remember the ones digit doesn't change when we add a multiple of 10.

So we've added 40 and 30, which are both multiples of 10 and that ones digit, the two at the end of our three digit number hasn't changed at all.

That'll be really useful for when you are calculating yourself.

Carlos is now 432 centimetres high in a tree.

He climbs up another 90 centimetres.

How could you work that out? I think you know how you'd work that out.

But Sophia is reminding us that we can add together 432 and 90 and hopefully by now you know that we are going to be partitioning 90 into two parts to help us do that.

Andeep is going to show us how that works on a number line.

So he's going to partition 90 into 70 and 20.

Think about why he's chosen 70 and 20.

Think about that 10s digit in 432.

He's going to start on 432 and add 70.

So he finds 432 and adds 70, which makes 502.

Remember that ones digit not changing.

He's added 70.

He now adds 20.

502 plus 20 is 522.

So we have 522 altogether, so Carlos is now 522 centimetres high.

Time to check your understanding.

Carlos is now 522 centimetres high in a tree.

He climbs up another 90 centimetres.

Very brave, but remember cats are excellent climbers.

How could you work out how high Carlos is now? Think about how you're going to partition 90.

Pause the video here, use the number line if you need to.

And welcome back.

How did you get on? So first we're going to find 522 on our number line and we're going to partition 90 into 80 and 10 because 522 plus 80 gives me 602.

Then I'm going to add 10 more, so 602 plus 10 is 612.

So Carlos is now 612 centimetres up in the tree.

Well done if that was your answer.

So Carlos is 627 centimetres high in a tree.

He climbs down 70 centimetres.

How high is Carlos now? How are we going to work out how high Carlos is? Think about what we know in this question.

He's climbing down.

So this time, well done if you said we need to subtract 70 from 627.

Now we should be super familiar with this by now, but we're going to partition 70.

Andeep is going to partition it into 20 and 50.

Then we're going to subtract 20.

So we're going to find 627 on our number line and we're going to subtract 20.

Remember the ones digit doesn't change, so we have 607.

We've partitioned into 20 and 50, so now we need to subtract 50.

So 607 subtract 50 is equal to 557.

So Carlos is now 557 centimetres high in his tree.

Remember, Andeep is reminding us again, when we subtract the ones digit doesn't change.

So you can see that we have 627 then 607 then 557.

So good check, make sure your ones digit is the same in your answer.

Carlos is 557 centimetres high in the tree.

He climbs down 80 centimetres.

How high is he now? How could you work out how high Carlos is? I'm hoping you are telling me really loudly that we need to subtract 80 centimetres from 557 centimetres.

Think about how you are going to partition 80 to help you bridge that 100s boundary.

Andeep is going to do the calculating again and this time is he's going to partition 80 into 50 and 30.

He's going to subtract 50.

So we're finding 557 subtracting 50, which makes 507.

Then we're going to subtract 30 more.

Remember that ones digit isn't changing.

507 subtract 30 is 477.

Carlos is now 477 centimetres high.

Time to check your understanding.

Carlos is 477 centimetres high in a tree.

He climbs down 90 centimetres.

You need to work out how high Carlos is now.

And again, another reminder, think about how you're going to partition 90 to bridge that 100s boundary.

Pause the video here and have a go.

And welcome back.

How did you get on? So I would partition 90 into 70 and 20.

I'd subtract my 70 first to get to 407 and then I would subtract 20 more.

So hopefully you said that he is now 387 centimetres high in the tree.

Well done if that's what you got.

Cassie the cat is sitting in a tree.

She climbs up another 60 centimetres and she's now 445 centimetres high.

How high did she start? So we've seen these problems before, but let's visualise it.

Cassie's in a tree.

We don't know where she's starting in the tree, but we know she climbs up 60 centimetres and at the end of that she's 445 centimetres high.

So we know that the answer add 60 centimetres is equal to 445 centimetres.

How are we going to work that out? Can you remember? Well done if you've remembered that we need to subtract 60 from 445 centimetres to find the answer.

So let's do that.

Andeep calculates 445 centimetres subtract 60 centimetres.

Hopefully you can see how we're going to partition 60.

We're going to partition 60 into 40 and 20 says Andeep, and we're going to show that on a number line.

So we're going to find 445 and subtract 40, which gives us 405.

And then we're going to subtract 20 more, which gives us 385.

So our missing number, Cassie started 380 centimetres high in the tree.

Well done if you were thinking that.

Time to check your understanding.

Katya is sitting in a tree.

She climbs down 70 centimetres and she's now 440 centimetres high in the tree.

How high did she start? How would you calculate the answer? Pause the video here and think about what calculation you need to do.

Welcome back.

How did you get on? Andeep is saying that the answer subtract 70 centimetres is equal to 444 centimetres.

And if that's the case, hopefully you said that to calculate the answer, we need to do 70 centimetres plus 444 centimetres or the other way round.

Well done if that's what you said.

So this means I would like you to add those together.

I would like you to find out what is 444 centimetres plus 70 centimetres.

Think about how you're going to partition 70 to bridge the 100s boundary.

Pause the video here and have a go.

Welcome back.

How did you get on? I partitioned 70 into 60 and 10.

Remember, I'm adding this time, so I want to bridge that 100s boundary.

I know that 40 plus 60 is a 100, so that's gonna help me.

I'm going to add 60.

So 444 plus 60 is 504, then I'm going to add 10 more to get to 514.

Notice how my ones digit did not change.

So our answer is 514 centimetres.

Well done if that's what you got.

Time for your second practise task.

For question one, you need to work out how high Colin is in his tree again.

Be careful with the numbers this time.

He starts at 456 centimetres high.

This is similar to what you did earlier where the answer to one starts the next question.

So he starts off at 456 centimetres.

He climbs up 90 centimetres.

Think about the calculation we're doing, he climbs up.

Then you'll use the answer to A to answer B, C, and D.

Remember, you can use number lines to help you calculate the answers if you need to.

For question two, you need to calculate how high the cats were to start with.

So Cassie is sitting in a tree.

She climbs up 80 centimetres, she's now 421 centimetres high.

How high did she start? Carly sits in a tree.

She climbs down 90 centimetres.

She is now 553 centimetres high.

How high did she start? And Clive is sitting in a tree.

He climbs down 50 centimetres.

Then oh, clever Clive, then he climbs back up 80 centimetres.

He's now 339 centimetres high.

How high did he start? Now I think C's extra tricky, but I know you're going to do brilliantly.

Pause the video here and have a go at those tasks.

And welcome back.

How did you get on? So for question number one, remember all of our answers depended on the other.

So I'm hoping you were super careful with your calculation.

For our first question, we had to add together 456 and 90, which got 546 centimetres.

We then used that information because Colin climbed another 70 centimetres.

So we had to do 546 centimetres plus 70 centimetres, which was 616 centimetres.

Then he climbed down 80 centimetres.

So we had 616, subtract 80, which is 536 centimetres.

Then finally he climbed another 60 centimetres downwards.

So we had to do another subtraction.

536 subtract 60, so finally he was at 476 centimetres.

Well done if you've got all of those.

For question two, Cassie started at a position.

She climbed up 80 centimetres, was now at 421 centimetres, so we had to subtract.

Cassie started 341 centimetres high.

For B, this time we had to add.

And so Carly started at 643 centimetres high.

So for question C, it was extra tricky because there were lots of steps to think about.

So we could have done 339 subtract 80 is 259 centimetres and then added 50 centimetres.

So Clive started 309 centimetres high.

Extra well done if you got that one correct.

We've come to the end of our lesson and I have really enjoyed learning with you today.

Let's summarise our learning.

We can partition numbers to help us bridge through a 100s boundary and calculate.

Remember that when we add or subtract a multiple of 10, the ones digit does not change.

And we can also use number lines to record the steps in our thinking when we are partitioning to add and subtract.

Thank you so much for learning with me today and for all the effort you've put in, and I look forward to seeing you again soon.