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Hello everyone.

Welcome back to another maths lesson with me, Mrs. Pochciol.

As always, I can't wait to learn lots of new things and hopefully have lots of fun.

So let's get started.

This lesson is called add and subtract two numbers that bridge through 10 and it comes from the unit calculating within 20.

By the end of this lesson, you should be able to add and subtract using strategies to bridge through 10.

Let's have a look at this lesson's keywords.

Whole, part, partition, and bridging 10.

Let's practise.

My turn.

Whole.

Your turn.

My turn.

Part.

Your turn.

My turn.

Partition.

Your turn.

My turn.

Bridging 10.

Your turn.

Fantastic.

Now that we've practised these words, let's use them.

Let's have a look at our lesson outline.

The first part of our learning, we are going to be adding two addends that bridge through 10.

And in the second part of our learning, we are going to be subtracting two numbers that bridge through 10.

Are we ready to get started? Let's start with the first part, adding two addends that bridge through 10.

In this lesson, we are going to meet Laura and Andeep.

They're going to help us with our learning today.

Are we ready guys? Let's go.

Laura and Andeep are exploring an equation.

7 plus 5 is equal to something.

Hmm.

Andeep knows that the sum will be more than 10.

Laura explains that when a sum is more than 10, we use a strategy called bridging 10.

Laura and Andeep now solve this problem using this known strategy.

First we partition 5 into 3 and 2.

Remember so we can make 10 first, and we know that 7 and 3 is equal to 10.

Then we make 10.

So 7 add 3 is equal to 10 and we record that equation underneath.

Then we bridge the 10 because now we are going to add to go more than 10.

We need to add the other parts when we partition 5.

So 10 plus 2 is equal to 12.

So we now know that 7 plus 5 is equal to 12.

Did you see where we bridged 10? That simply means going over 10.

They now represent the addition on a number line.

Can you see? We are going to start with 7.

We are gonna add 3 to 7 because we want to first make 10.

Then we bridge through 10, we go past 10, and we add 2 more because that's the other part that we still need to add when we partitioned our 5, remember? We now have a three addend edition.

Look at the number line.

We now have 7 plus 3 plus 2.

We are all superstars at three addend additions now, aren't we guys? 7 add 3 is equal to 10.

10 add 2 is equal to 12.

So 7 plus 5 is equal to 12.

Wow.

How easy is it to bridge through 10 when you can see it on a number line like that.

We changed 7 plus 5 into 7 plus 3 plus 2 by partitioning the 5.

We have now recorded our strategy in one equation.

We partitioned 5 into 3 and 2, can you see that in our equation? And we added 7 and 3 to make 10.

Then we added 10 and 2 to find the sum, which was 12.

All of that information in our one equation.

Laura now shows a bridging 10 edition using this method.

She's going to do 9 plus 6.

Let's have a look at what she does.

Hmm, can you help her to create the equation to show her strategy? You can see that the equation's already been started for you.

Can you fill in the missing numbers to complete her equation? Pause this video, complete the equation, and come on back when you are ready to see how you got on.

Welcome back.

Let's have a look at how you got on.

Come on then, Laura, let's complete this equation.

First we had to partition 6 into 1 and 5.

So first we added 9 and 1 to make 10.

Can we see? We first added that 1, you can see that that adding one step is the first thing that we did.

Then 10 add 5 is equal to 15.

So the next part of our equation is plus 5 because we partitioned the 6 into 1 and 5.

We're now adding that second part and we can see that the sum will be 15.

So 9 plus 6 is equal to 15.

Wow.

Let's have a look at Laura's equation to see if yours is the same.

9 plus 6 is equal to 9 plus 1 plus 5, which is equal to 15.

Well done if you manage to get that equation.

Laura and Andeep are now finding out how much fruit is left after their snack time.

There are 8 apples in the large box and 6 apples in the small box.

How many apples do they have all together? Hmm.

Laura notices that we need to add together 8 apples and 6 apples to find out how many they have altogether.

Andeep says that they're experts at bridging 10 now.

So let's do this.

They represent the addition as an equation and show their working out on the number line.

So we're going to start on 8.

What are we going to have to do first? We need to make 10 first, remember? So how are we going to partition our 6? Ooh, we know that adding 2 and 8 will make 10, so we need to partition the 6 into 2 and 4.

So 8 and 2 is equal to 10.

Then we need to add that other part which is 4.

So 10 add 4 is equal to 14.

Can you see that they've recorded that three addend addition now in their equation 8 plus 2 plus 4? And we now know that 8 plus 6 is equal to 14, so we can also add that to our equation.

Our completed equation is now 8 plus 6 is equal to 8 plus 2 plus 4 because we partitioned that 6, which is equal to 14.

So we can now confidently say that 8 plus 6 is equal to 14.

Well done guys.

A really good use of that bridging 10 strategy there.

So can we retell our story now then, guys? There were 8 apples in the large box and 6 apples in the small box.

There are now 14 apples all together.

Wow, well done guys.

You really are experts at this now.

Should we have another go? Andeep now finds out how many bananas they have left, but he needs a little bit of help because there's a part of his equation missing.

Laura notices that Andeep is adding 6 again just like they just did, but this time they're going to have to partition it differently.

We know that 7 and 3 pair to make 10, so he's going to need to partition his 6 into 3 and 3 this time, whereas remember before they did 2 and 4.

This time it's 3 and 3.

Now we need to add the other 3 because that's the other part, so that's the bit that you missed, Andeep.

We need to add 3.

We know that 10 add 3 is equal to 13, so Andeep must have had 13 bananas left.

Well done if you spotted that.

Over to you then.

They finally calculate how many oranges there are.

There are 5 oranges in the small box and 8 oranges in the large box.

How many oranges do they have altogether? Can you complete the equation to calculate how many oranges there are? Pause this video.

Have a think about how you might partition 8 to help you with this calculation and find the sum of how many oranges altogether.

Come on back once you've got an answer.

Welcome back.

I hope you enjoyed there calculating those oranges.

Should we have a look? There are 5 oranges in the small box and 8 oranges in the large box.

How many oranges do they have altogether? We know that 5 and 5 is equal to 10, so we need to partition 8 into 5 and 3.

Once we've added our 5 and 5 to make 10, we're going to add the 3, which we know 10 add 3 is equal to 13.

So we can now confidently say that there are 13 oranges altogether.

Well done to you if you manage to complete that equation correctly.

Over to you then for task A, let's keep practising this bridging 10 strategy.

Fill in the missing numbers to find the sum of the equation.

So you will see that A and B, you are finding that other part that you need to add to find the sum.

In C and D, you have to partition the second addend to complete the equation and find the sum.

And in E, you have to show all of that second expression to find the sum.

Pause this video, have a go at completing those equations and finding the sums and come on back to see how you get on.

Welcome back.

I hope like Laura and Andeep, you're now thinking that you are experts at this bridging 10 strategy.

Let's have a look at how we got on.

7 plus 6, we can see that we've already done the first part.

We know that 7 and 3 make 10, so what's the other part that we partition 6 into? Hmm, 3 and 3.

So now we know that 10 plus 3 is equal to 13.

Well done if you've got that one.

Let's have a look at 8 and 6.

You can already see that we've partitioned the 6 into 2 and something, what's the other part? We know that 2 and 4 make 6.

So 8 plus 2 is equal to 10 plus 4 more is 14.

So we can say that 8 plus 6 is equal to 14.

Well done if you've got that one right.

This next one then we need to partition the 6 by ourself.

So we know that we've got 5 as our first addend, so how do we need to partition 6? Well I know that 5 plus 5 is equal to 10 and 5 and 1 make 6.

So now we can see that it's 5 plus 5 plus 1.

5 and 5 make 10 plus 1 more, we know is 11.

Well done to you, if you got 11.

D then, 9 plus 6.

Oh we're adding 6 again, but this time I'm going to have to partition it differently because I've got 9 as my first addend.

I know that 9 and 1 make 10, so this time I'm going to have to partition 6 into 1 and 5.

9 and 1 are equal to 10, plus 5 is equal to 15.

And finally, 8 plus 8.

We need to do this whole second expression.

So we know we are going to start with 8 because that's our first addend, and 8 and 2 make 10.

So we've partitioned that second addend into 2 and 6.

So 8 plus 2 is equal to 10, plus 6 is equal to 16.

So 8 plus 8 must be equal to 16.

Welcome to you if you got those correct.

Oh, did you notice that 6 had to be partitioned in different ways each time to bridge through 10? Look, A, B, C, and D, all were adding 6 and each time we partitioned it differently to help us bridge through 10.

A good spot there Laura.

Oh, and Andeep noticed that actually in E, he didn't need to bridge through 10 because he could have just used his doubling knowledge.

8 plus 8 is equal to 16.

Well done to you if you spotted that.

Let's move on then to the second part of our learning.

In the first part, we've been practising adding two addends that bridge through 10.

Now we're going to apply our learning into subtracting to bridge through 10.

Are we ready? Let's go.

There are 13 children on the bus.

5 children gets off the bus.

Hmm.

There are now 8 children on the bus.

Can we see? 13 subtract 5 is equal to 8.

Now let's have a look at this.

Andeep notices that we have just bridged through 10 just like we did when we were adding, but this time we're subtracting.

3 children have to go from the top deck, which leaves 10 children altogether.

Then 2 children leave from the bottom deck, which leaves us with 8.

Can you see how first the 3 children got off and then 2 children got off? Let's represent this on our 10 frame to have a look.

There were 13 children on the bus and 5 got off, 3 children got off the top deck, which leaves us with 10 children, and 2 children get off from the bottom deck, which leaves us with 8 children.

There are now 8 children on the bus.

Ooh, can we see our written strategy on the right-hand side there? It looks very similar to when we were adding weren't we? Should we have a look then? First we took away 3 counters to make 10.

Then we took away another 2 counters to make 8 because we partitioned 5 into 3 and 2.

We are still making 10 and then subtracting the other part.

Let's have a look on our number line.

We know that subtracting 3 from 13 is equal to 10.

We have partitioned the minuend 5 into 3 and 2.

So now we need to subtract 2, which is the other part.

If we subtract 2 from 10, that leaves us with 8.

So 13 subtract 5 is equal to 8.

Can you see how it's the same bridging strategy that we use when we were adding, but this time we are subtracting? This is a really great strategy to help us subtract through 10.

Let's have a practise then.

The next day on snack duty, Laura and Andeep handout the daily fruit.

There are 15 apples in the box.

They give out 8 apples.

How many apples are left in the box? We need to subtract 8 from 15.

Andeep thinks that we can do this.

Let's get our 10 frames out.

Let's represent 15 subtract 8 on our 10 frame and complete our written strategy at the same time.

We need to subtract 5 ones to equal to 10 because we had 15 remember? So we're gonna subtract to 10, which is 5.

So first we partition 8 into 5 and 3.

Can you see that there on our written strategy? First we're going to subtract the 5 from 15 to leave us with 10.

Can we see? Then we're going to subtract the other 3 because that's the other part from 10 which will leave us with 7.

So we know that 15 subtract 8 is equal to 7.

Can we see all of our steps there on our written method? First we partitioned the 8 into 5 and 3, we subtracted the 5 to make 10, and then we subtracted the other part which was 3, which left us with 7.

So we now know that 15 subtract 8 is equal to 7.

Let's have a practise of this then over to you.

Can you use Andeep stem sentence to help you to complete this problem? 13 subtract 6.

Use your 10 frame to help you and complete the stem sentence and the written strategy to show what you've done.

Pause this video, have a go at finding an answer, and come on back once you're ready to see how you got on.

Welcome back.

I'm hoping you enjoyed practising that strategy there.

Shall we see how you get on? So 13 subtract 6.

Hmm, 13, if I want to make 10, that means I need to subtract 3.

So first I'm going to have to partition 6 into 3 and 3.

Then we're going to subtract 3 from 13, which will give us 10.

There we go.

And then we need to subtract the other part which is 3.

So 10 subtract 3 is equal to 7.

So we can now say that 13 subtract 6 is equal to 7.

Well done to you if you completed that strategy and found that the missing answer was 7.

Laura now shows the apple subtraction on a number line.

So we're gonna start with the number 15.

And what we're going to do first, Laura? We partitioned 8 into 5 and 3.

So first we had to subtract 5 to get to 10.

Then we subtracted 3 because that's the other part that we partitioned 8 into.

This has led us to 7.

So 15 subtract 8 is equal to 7.

Can you see those two steps there to bridge 10? Over to you then.

Can you now represent your strategy on a number line? Remember, what number do we start on? What do we subtract first to make 10? Then what do we subtract the other part? And what number do we finally end up on? Pause this video, complete your number line, and come on back to see how you get on.

Welcome back.

Let's have a look at what our number line should have looked like then.

So we are going to start with 13 because that was our starting number.

Then we had to subtract 3 to get to 10.

There's the first step.

I now need to subtract the other part.

So 10 subtract 3 is equal to 7.

We can now show that 13 subtract 6 is equal to 7.

So well done to you if your number line looks like mine.

Laura and Andeep now both apply their learning to solve a missing number problem.

Ooh.

Laura's got a bar model and Andeep's got a part-part-whole model.

Laura notices that her missing number is a part, so she needs to subtract the other part from the whole to find the missing number.

We need to solve 11 subtract 5.

We can see that that's going to bridge 10, can't we? Because 1 is a smaller ones number than 5, so that's definitely going to bridge 10.

Andeep has both of his parts but not the whole.

So he knows that he needs to add the two parts together to find the whole.

He's going to solve 5 plus 6.

Hmm, is that going to bridge 10? I think it might do.

Let's have a look at then Laura.

Laura is going to solve 11 subtract 5.

She partitions her 5 into 1 and 4 because remember we need to subtract that 1 first to make 10.

11 subtract 1 will make 10.

And 10 subtract 4, the other part from where we partitioned 5 will leave us with 6.

So Laura's missing part is 6.

Andeep partitions 6 into 5 and 1.

5 plus 5 is equal to 10 and 10 plus 1 is equal to 11.

Andeep's missing whole is 11 because 5 plus 6 is equal to 11.

Hmm, do we notice something there? Laura and Andeep noticed something about their missing number problems. Laura notices that the parts and the wholes are the same, but Andeep did an addition and Laura did a subtraction.

That's because subtraction and addition can undo each other, remember? They are inverse operations.

If we know that 5 plus 6 is equal to 11, then we know that 11 subtract 5 is equal to 6 and vice versa.

Oh, so remember, when we are thinking about missing number problems, we can use this knowledge of addition or subtraction to help us.

So let's have a practise of this then.

What is the missing number in this equation? 14 subtract something is equal to 8.

We're going to show this as a part-part-whole model because that's going to help us to visualise this problem.

We know that 14 is the whole and subtracting something is equal to 8.

So one part must be 8 and the other part is the unknown part.

What are we going to have to do to find the missing part? Pause this video, do some calculations to find my missing number, and come on back to see how you get on.

Welcome back.

I hope you managed to find my missing number.

Shall we see how Andeep solved it? We know that a whole subtracts the known part is equal to the unknown part.

So we can partition 8 into 4 and 4.

14 subtract 4 is equal to 10.

And 10 subtract 4 is equal to 6.

So we know that the missing part must be 6.

So 14 subtract 6 is equal to 8.

Well done to you if you found that missing number.

Andeep now checks his answer using this knowledge.

If we know that 14 subtract 6 is equal to 8, then 8 plus 6 should be equal to 14.

We can partition 6 into 2 and 4 because 8 and 2 make 10.

Then we add 10 plus 4, which is equal to 14.

So was Andeep correct? Was 6 the missing number? Yes, because look, 8 plus 6 is equal to 14, which is agreeing with our part-part-whole model.

So 14 subtract 6 must be equal to 8.

Wow, using an addition to check your subtraction Andeep, that's a really good way to check your working.

And well done to you if you also did this to check your working.

Over to you then for task B.

Part one, use your 10 frames to solve these problems and fill in the missing numbers.

So you'll see that slowly the models start losing some of the parts for you to complete more of them.

So have a go at A, B, and C, and then move on to question two.

Part two is to use bridging 10 strategies for addition and subtraction to find the missing numbers.

So you can see we've got some bar models and some part-part-wholes in A, B, and C.

And D, E, and F are all equations.

So you might want to draw your part-part-whole because remember that's going to help you to visualise the maths.

Pause this video, have a go at part one and part two, and come on back when you're ready to see how you got on.

Welcome back.

Should we see how you got on? Let's fill in the missing numbers then.

We can see that we've partitioned 8 into 5 and 3.

First step subtract the 5 to make 10, then subtract the 3, which leaves us with 7.

So 15 subtract 8 is equal to 7.

B, let's have a look then.

I know that I'm gonna have to subtract 1 to make 10 from 11.

So 1 must be one of my parts, so the other part is 2.

The first step is 11 subtract 1 will leave me with 10.

Then I need to subtract the other part from 10, which is 2.

10 subtract 2 is equal to 8.

So 11 subtract 3 is equal to 8.

And C, let's have a look.

So they haven't given me anything on this model here.

So 12 subtract 5.

I can see that I need to subtract 2 from 12 to make 10.

So that's going to be my part, 2 and 3.

12 subtract 2 is equal to 10.

And 10 subtract 3 is equal to 7.

So 12 subtract 5 is equal to 7.

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

Let's have a look at part two then, bridging 10 strategies for addition and subtraction to find the missing numbers.

I can see that I've got 14 as my whole and 5 as a part, so to find the other part, I would've had to complete 14 subtract 5.

And I know that 14 subtract 5 is equal to 9.

Well done if you've got that one.

B then, 13 is my hole and 6 is a part, so I'm going to have to do 13 subtract 6, which will leave me with 7.

C, again, we have our whole and a part, so we are going to subtract 9 from 6, which will leave us with 7.

Let's have a look then.

17 subtract something is equal to 9.

Hmm.

If I visualise my bar model, I know that I've got a whole and a part there.

So if I do 17 subtract 9, that will give me the missing part.

17 subtract 9 is equal to 8.

So I know that 17 subtract 8 will be equal to 9 because that's the other part.

Well done if you got that one.

Oh, now E, what have I got here then? I can see that something subtract 4 is equal to 9.

Hmm, I know that when we are subtracting, we start with the whole so the whole is missing.

So to find the whole, I'm gonna have to add 4 and 9 together to find the starting number of the subtraction.

9 plus 4 is equal to, so 1 more makes 10 plus 3 more, so that's 13.

13 was the missing number for E.

And let's have a look at F.

8 plus something is equal to 15.

So I can see here that I've got the whole and I've got a part.

So if I did 15 subtract 8, that would leave me the missing part.

15 subtract 8.

So I'm gonna subtract the 5, then subtract the 3, which would leave me with 7.

Welcome to you if you've got those correct.

Let's have a look at what we've learned today.

Partition the addend so that you can make a number pair to 10.

The remaining part can then be added onto 10.

Partition the subtrahend so that one of the parts is equal to the ones digit to make 10 when subtracted.

The remaining part can then be subtracted from 10.

Bridging through 10 can be represented on a number line.

So we can show this using addition or subtraction.

Well done for all of your hard work today.

Remember, keep practising and you'll become so much more confident at this bridging through 10 strategy.

I hope to see you all again soon for some more maths learning.

See you soon.