Lesson video

Hello, there.

My name is Mr. Goldie, and welcome to today's maths lesson.

Our lesson outcome is, "I can add two numbers by bridging through ten." And let's have a look at those keywords for today.

So, two keywords today, I'm gonna say the word.

I'd like you to repeat the word back.

The first word is bridge.

Can you say bridge? The second word is a bit trickier.

The word is partition.

Partition, are you ready? Can you say partition? Excellent stuff.

So, what do those words mean? Well, bridging is a mental strategy, which means you can do it in your head, which uses addition or subtraction to cross a number boundary.

You can bridge 10 by adding to make a 10 and then adding whatever is left.

For example, you can add 7 and 6 together by bridging.

You could split the 6 up and do 7 + 3 = 10, and then 10 + 3 = 13.

Partition means splitting a number into parts.

8 can be partitioned into 4 and 4, or it could be partitioned into 6 and 2.

So, it's just a way of breaking numbers up into smaller parts.

And here's our lesson outline.

In the first part of the lesson, we're going to be using 10s frames to bridge 10s.

And in the second part of the lesson, we're going to be using number lines to bridge 10s, so two different strategies we're going to be using today.

Let's start off by using 10s frames to bridge 10s.

In this lesson, you will meet Izzy and Alex.

And here's Izzy, and Izzy's saying, "Number pairs for 10 will be really important in today's lesson." So, hopefully, you know those number pairs that total 10.

For example, you should know that 7 + 3 = 10.

Alex is asking, "Do you know all the number pairs that total 10?" Let's go on to our first problem.

Izzy collects conkers.

Izzy really, really likes conkers.

She has eight.

Then, she finds another four.

Here are the eight conkers she started off with, and she's found another four.

How many does she have now, and will the sum be greater than 10? So, has she got more than 10 conkers altogether? Oh, Izzy says, "Yes, it will." Will the sum be greater than 10? "Yes, it will." How do you know, Izzy? And Izzy says, "8 + 2 = 10, so 8 + 4 must be greater than 10." Izzy thinks about how to find the answer, so she's got to find the answer to 8 + 4.

How could Izzy add 4? She's starting with 8.

How could she add 4? "It helps to make 10," says Izzy.

"I know 8 + 2 = 10." Izzy partitions 4 to help her bridge 10.

Remember, partition means breaking numbers into smaller parts and bridging means crossing over those 10s boundaries.

How should she partition 4? What do you think? How would she break 4 up into smaller parts? What would Izzy do? First, Izzy partitions 4 into 2 and 2.

Okay, there's our 4, and Izzy's broken them up into 2 and 2.

Then, Izzy adds 2.

You can see there, adding the 2 to 8 fills our 10s frame.

8 + 2 = 10.

Then, she adds two more.

"10 + 2 = 12," says Izzy.

So, 8 + 2 + 2 = 12, 8 + 4 = 12.

So, Izzy has partitioned 4, broken it into smaller parts to help her bridge through 10.

And Alex is calculating a different sum.

Alex is calculating the sum of 8 and 6.

He's trying to do 8 + 6.

First, Alex partitions 6.

Now, think carefully about what Alex would need to do.

How would he bridge through that 10? "8 + 2 = 10," says Alex, "So, I'm going to partition 6 into 2 and 4." Very sensible, Alex.

Then he adds 2 to make 10, then he adds 4 more.

Altogether, 8 + 6 is the same as 8 + 2 + 4.

And 8 + 2 + 4 = 14, 8 + 6 = 14.

Izzy is calculating the sum of 9 and 6.

She's trying to do 9 + 6.

How's Izzy gonna break up that 6, I wonder? What's she going to do? First, Izzy partitions 6.

"9 + 1 = 10," says Izzy, "So, I'm going to partition 6 into 1 and 5." Remember, it's all about bridging through that 10.

Be looking for those number pairs that total ten.

9 + 1 = 10, so Izzy can break up that 6 into 1 and 5.

Then, she adds 1, so 9 + 1 makes 10.

Then, she adds 5 more.

The sum of 9 + 1 + 5 = 15.

9 + 6 = 15.

Well done, Izzy.

Alex is calculating the sum of 5 + 7.

He's trying to do 5 + 7.

"5 + 5 = 10," says Alex, "So, I'm going to partition 7 into 5 and 2." Is Alex right? "Alex is right," says Izzy, "But it's easier to start with 7 and partition 5." Normally, in a calculation, it's easier to start with the biggest number.

It's not always, and sometimes you might spot something else about the numbers.

You might spot other things, like doubles or near doubles or number pairs that total 10.

But quite often, it's most sensible to start with a bigger number because it's easier to add a smaller number.

Alex is calculating the sum of 7 + 5, so he's trying to work out 7 + 5.

It's going to be the same sum as 5 + 7 because addition is commutative.

Doesn't matter what order we have the numbers in.

5 + 7 = 7 + 5.

How will Alex partition 5? How is he going to break up that 5 to bridge through to the 10? "I'm going to partition 5 into 3 and 2," says Alex.

Again, very sensible work, there, Alex.

Alex adds 3 to the 7 to get to 10, then he adds 2 more, and that gives him altogether 7 + 3 + 2 = 12, 7 + 5 = 12.

Now, here's one to have a think about on your own.

Calculate the sum of 8 and 5.

How would you add together 8 and 5? First, partition 5 into two numbers.

What are the two numbers going to be? How are you gonna break up that 5? What are you going to add first? What are you going to add afterwards? Pause the video.

Have a think about how you could add together 8 to 5 in the most efficient and quickest way possible.

And welcome back.

Let's see if you got it right.

First of all, what would you partition 5 into? Well, here's Izzy.

Izzy says, "8 + what = 10." 8 + what = 10? 2, so we should have partitioned 5 into 2 and 3.

And then, add 2, so add the 2 first to get to 10.

It's all about making that 10, all about bridging through that 10.

And then, add 3.

And the answer would be 8 + 2 + 3 = 13, 8 + 5 = 13.

Very well done if you managed to get that one right.

And here is our first task.

Use 10s frames and counters to represent, so use 10s frames and counters to help you work out the answers to these questions.

Think about which number to put first and how to partition the second number.

You'll see there's two number sentences for each calculation.

The first one tells you what numbers you're adding together.

The second one, you're gonna have to think very carefully about how you're going to break up that number.

The first one says 7 + 4.

How would you add the 4? What would you break that 4 up into? Think about using, remember, your number pairs that total 10.

They're going to be really, really helpful for this.

Pause the video, and there's four calculations for you to have a go at.

See if you can get the right answers.

Good luck.

And welcome back.

Let's see how you got on.

That first one, 7 + 4 = 11.

How would we have broken up that 4? Well, we should have done 7 + 3, that makes 10.

Add the 1 makes 11.

Underneath that, we've got 6 + 5.

How would you add 5? You should have broken it up into 4 and 1 because 6 + 4 = 10.

6 + 4 = 10, add 1 more = 11.

That's brilliant work, absolutely fantastic.

And on to our second part of the lesson.

Our second part of the lesson, we are using number lines to bridge 10s, so we're not going to be using 10s frames anymore for a bit.

We're going to use number lines instead.

How many children are on both buses? Have a good look at the two buses.

Well, on the bus at the back, the second bus, there are 10 windows, and one of them is empty.

So, how many children on that bus, do you think? On the bus in front, the bus that's leading the way, see if you can work out how many children on that bus.

There's 3 at the top and 2 on the bottom deck.

How many children would that be all together? What calculation would you do to work out the answer? Hopefully, you worked out the calculation was 9 + 5.

Number lines can also show the process of bridging 10.

I love number lines.

Number lines are brilliant.

Here's our calculation.

9 + 5 = what number? What's the sum of 9 + 5? And how should Izzy partition 5? Well, first, Izzy partitions 5 into 1 and 4.

Then, she adds 1 to 9, so 9 + 1 = 10.

Then, she adds 4 more all the way to 14.

So, the answer is 14.

Alex calculates 8 + 5.

"How should I partition 5?" says Alex.

We've done a lot of adding to 8 already, haven't we? So, what number do you have to add to 8 to get to 10? Alex partitions 5 into 2 and 3.

Then, he adds 2 to 8.

There's 8 + 2.

That equals 10.

Then, he adds 3 more, so 10 + 3 = 13.

The answer is 13.

8 + 5 = 13.

And here's one to try on your own.

Calculate 9 + 7.

First, partition 7 into, what two numbers? How are you going to break up that 7? Then, add what number first, and then add how many more? And here's Alex just with a bit of a helpful hint.

He says, "9 + what number = 10." Pause the video and see if you can work out how to do that calculation.

Welcome back.

Let's see how you got on.

First of all, what should you partition 7 into? You should've partitioned 7 into 1 and 6.

9 + 1 = 10, so break up that 7 into 1 and 6.

Then, add 1.

And then, add how many more? 6 more, so altogether, you've added 7, so 10 + 6.

Nice, easy calculation as well.

10 + 6 = 16.

Very well done if you got that answer and very well done if you broke up 7 into 1 and 6.

Next, Izzy wants to solve this problem.

Izzy wants to solve 8 + something = 14.

First, she adds to get to 10.

What does Izzy have to add to 8 to get to 10? She has to add on 2.

8 + 2 = 10.

Then, she adds to get to 14.

Izzy's now on 10.

What does Izzy have to add to get to 14? She adds on 4.

10 + 4 = 14.

Izzy's worked out what she has to add to 8 to get all the way to 14.

Then, she works out how much she has added.

"I added 2, then I added 4," says Izzy.

2 + 4 = 6.

Altogether, Izzy added 6, so the missing number is 6.

8 + 6 = 14.

Alex wants to solve this calculation.

Again, it's a missing number calculation.

Something + 5 = 12.

Alex says, "I need to work out the missing number by adding to get to 12." First, Alex adds 2 to get from 10 to 12.

Alex adds on 2.

Remember, we're trying to get to 12.

Alex knows he's added on 5 to get to 12.

He's trying to work out what number he started from.

Then, he adds 3 to get from 7 to 10.

Altogether, Alex has added on 5, he's added 3, then he's added 2 more, and ended on the sum of the two answers, 12.

Alex now knows the missing number.

What is the missing number? The missing number is 7.

7 + 5 = 12.

That's a bit of a tricky one, 'cause you have to work backwards a little bit to work out the answer.

And here's one to try on your own.

Solve 8 + something = 15.

Again, we're looking for a missing number.

First, add what to get to 10? Then, add something else to get to 15.

What have you added altogether to start from 8? What do you have to add to get to 15? Don't forget to bridge through that 10 and then work out when you've added it all together.

Pause the video, have a go at that calculation, and we'll see whether you've got it right in just a few minutes' time.

Okay, let's see if you've got it right.

Solve 8 + something = 15.

Well, first, we add 2 to get to 10.

We start from 8 and we add on 2 to get to ten.

8 + 2 = 10.

Then, add 5 to get to 15.

Add 5 and that jumps us all the way to 15.

What have you added altogether? You've added a two, then you added a 5.

Altogether, you've added 2 + 5 = 7.

So, the missing number is 7.

8 + 7 = 15.

Excellent work if you managed to find the answer.

And if you didn't quite get it right, very well done for trying.

You can also bridge through other 10s numbers, too.

Alex calculates 9 + 6.

Alex is going to start from 9.

He's going to add on 1 to get to 10.

Then, he's going to add on 5 to get to 15.

Altogether, he's added 6.

Our answer is 15.

Alex then calculates 19 + 6.

This time, he starts from 19.

Alex adds on 1 to get to 20 and then adds on 5 more to get to 25.

Again, altogether, Alex has added 6.

1 + 5 = 6.

The answer is 25.

Alex says, "I partitioned 6 in the same way for both calculations." And you might have spotted something.

9 + 6 = 15.

19 + 6 = 25.

When one of the numbers is 10 bigger, the answer, the sum, is also 10 bigger.

9 + 6 = 15.

19, which is 10 bigger than 9, + 6 = 25, and 25 is 10 bigger, 10 greater than 15.

Alex calculates 18 + 5.

"How should I partition 5?" asks Alex.

First, Alex partitions 5 into 2 and 3.

Rather than bridging through 10 this time, we're bridging through 20.

Then, he adds 2.

18 + 2 = 20.

Then, he adds 3 more.

20 + 3 = 23.

So, you can bridge through other 10s numbers as well.

Alex gives Izzy a challenge.

"What is 17 + 8?" says Alex.

"How will I partition 8?" asks Izzy.

What do you think? How would Izzy break up that 8? Here's our number line.

First, Izzy adds 3 to get to 20.

She starts from 17, she adds 3 to get 20.

Now, she's got to add on 8 altogether.

She's added 3.

What other number added to 3 makes 8? 3 + 5 = 8.

So, Izzy adds 5 more and gets to our answer, 25.

17 + 8 = 25.

You can use number facts to help you solve other problems, too.

"I know that 7 + 5 = 12," says Alex.

"Can you solve these equations by using Alex's number fact?" asks Izzy.

If 7 + 5 = 12, what would 17 + 5 be? Could you work out the answer? What do you think? The answer would be 22.

17 is 10 bigger than 7, so our answer must also be 10 bigger.

What about 27 + 5? What do you think the answer would be? The answer would be 32.

What about 37 + 5? The answer would be 42.

Again, we're bridging through a 10s.

This time it's 40 and we're breaking up that 5 to add it on.

One of the addends is getting 10 bigger, so our sum is also getting 10 bigger, too.

Can you calculate 16 + 7? Now, again, this is one for you to try on your own.

"How will you partition 7?" asks Izzy.

Again, pause the video.

How could you work out the answer to 16 + 7? And let's have a look.

Let's see whether you managed to get that one right.

First, add 4 to get to 20.

Remember, we're breaking up that 7, so we've gotta break that 7 up into 4 and 3.

So, 16 + 4 = 20.

Then, all you've got to do is add 3 more.

20 + 3 = 23.

There's our answer.

16 + 7 = 23.

Very well done if you got that one right.

And here are your tasks for today.

Task number 1, you're going to use number lines to find the sum.

Look carefully at the calculation you've got to do.

Think about how you're gonna break up one of those addends and how you're gonna add it on easily.

Be careful as well, 'cause sometimes you might need to change the numbers around.

Sometimes you might wanna think carefully about whether you start with a bigger number or not.

Your second task is you've got to use number lines to find the missing numbers.

This time, look carefully at the number you're starting with.

What have you got to add on to get to our sum? What do you have to add altogether? And then, task number 3, you're going to use each number card once to make the equations correct.

There are six equations, there.

Which number card fits into each equation? Have a good look at that one, see if you can work out the answer.

And again, you might want to use number lines to show your thinking to help you get to the right answer.

So, pause the video and have a go at those tasks.

And very good luck.

Take your time, don't rush.

Think very carefully about how you're going to partition those numbers.

How are you gonna bridge through those 10s numbers? And welcome back.

Let's see how you got on.

First task, here are the answers.

That shows you how you should've bridged through those 10s, how you should've broken up one of those addends.

And look careful at that second one, there, 5 + 8.

We'd have to change it around.

Start with the 8 to make it slightly easier.

Could've started with 5.

You'll still get the same answer, but it's usually easier to start with the bigger number.

And here are the answers for task 2, and hopefully you managed to find those missing addends.

And then, our last task, there are the solutions.

You have those six number cards, and that's how they fit into the calculations.

That's the correct answer.

Very well done for your hard work today.

And if you managed to get to task number 3 and managed to solve that one, you have done brilliantly, 'cause of course, all of those were crossing through 20.

Excellent work today, really well done.

Here is our lesson summary to addition by bridging through 10.

Normally, start with the largest number.

Start with the bigger number and add on the smaller number.

And remember, you've gotta break up that smaller number sometimes to help you bridge through the 10.

Sometimes you don't have to bridge through a 10, but if you do have to bridge through a 10, it's nearly always best to break up that smaller number.

Use number pairs that total 10 to help you bridge 10, and that's whether you're bridging 10 or 20 or 30 or 40.

It's the same skill you can be using.