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Hello everybody, and welcome to today's Math session.

My name is Miss Hughes, and today, we're going to be looking at adding and subtracting two 2-digit numbers and thinking about the mental strategies that we can put in place to solve it in our heads.

So let's get going.

Let's take a look at our lesson agenda for today's lesson then.

So again, we're going to be exploring strategies that we can use for addition.

Then you're going to have a talk task.

Next we'll be exploring strategies that you can use for subtraction.

And finally, it's your main task and of course the quiz at the end of the lesson.

So let's move on.

For today's lesson you are going to need a pencil and rubber and some paper.

So pause the video now to get these things if you have not got them with you already.

To start us off for today's lesson, we're going to look at these equations on the board where you are adding and subtracting a two digit number to another two digit number.

I want you to try and solve these equations by using the known fact that you have within 10 to help you solve them.

So have a think about the ones, and have a think about the tens.

And think about the number bonds you can use that will help you to solve these equations.

Off you go.

Okay, I'm going to go through those answers now then.

So let's have a think first about the ones that are in each of these equations.

So in this equation, 64 and 35, I have four ones, and I'm adding five ones to get my whole.

I know that four add five is equal to nine, so I know that I'm going to have nine ones in my whole.

In 78 takeaway 42, I have eight ones take away two ones.

I know that eight take away two is equal to six.

Therefore I know that I'm going to have six ones in my missing part of this equation.

Now that we've done our ones, we can move on to our tens.

So in 64 add 35, I know that I have six tens add three tens, and I know that six add three is equal to nine.

So I know that I'm going to have nine tens in my whole.

In this equation, I've got seven tens and I'm taking away four tens.

I know that seven take away four is equal to three.

So I know that I'm going to have three tens in this missing part here.

If I know that six add three is equal to nine, then I know that 60 at 30 is going to be 90, nine tens has the value of 90.

Seven take away four is three, I know that 70 takeaway 40 will be 30.

So I know that my three tens in my missing part here will have the value of 30.

Now what I have to do is add my nine tens, 90 and nine ones, which is 99.

And my three tens here and six ones that I had left here, which is 36.

So my answers were 99 and 36.

We're going to have a look at some word problems now and have a think about the strategies that we can put in place to solve these problems. So let's have a read of this problem here on the board.

In the morning, 45 people were on one train and 32 people were on another train.

How many people were on both trains? We want to think about which no number bonds will help us solve this.

So keep that in your head as we go forward.

Let's represent our problem in a pothole model first.

Remember when we're thinking about a pothole model and a word problem like this, we need to think about what parts we know, what values we know already, and what we are trying to find out.

I know that one of my part is 45.

So I put 45 in there.

I also know that one of my parts is 32.

And so I know now that because one of my parts is 45, and one of my parts is 32, we're still trying to find our whole, our whole is unknown.

Let's represent these parts in dims so we know pictorially what we are working with.

45 is made up of four tens and five ones.

So I've got 10, 20, 30, 40, 41, 42, 43, 44, 45 and 32 is made up of three tens, 10, 20, 30 and two ones, 31, 32.

So to work out our unknown whole, we need to do 45, which is our first part, add 32, which is our second part, and that will give us our whole.

Let's think now about the number bonds we can use to solve this equation 45 add 32.

Remember, we can partition our parts 45 and 32 into tens and ones.

So 45 has four tens, which is 40, and five ones, which is five.

32 has three tens, which is 30, and two ones, which is two.

Let's start by thinking about a number bond that can help us add our four tens in 45 to our three tens in 32.

I know that four add three is equal to seven.

Therefore I know that 40 add 30 is equal to 70.

So I know that my tens added together is going to have the value of 70.

Now we can think about our ones.

I have five ones in 45, and I'm adding two ones from that to 32.

I know that five add two is equal to seven.

So I know that I'm going to have seven ones in total.

Let's explore this on a pothole model.

So I have my 45 part here, I have my second part which is 32.

We're going to start by adding our four tens to our three tens, which is equal to seven tens.

There we go.

So now I have seven tens in my whole, which is worth 10, 20, 30, 40, 50, 60, 70.

So my tens are worth 70 now in my whole, just like we found out here.

Now I have five ones and two ones I need to add together, and we know that five and two makes seven.

So I've got my seven ones in here.

So I now know that this is my whole.

I've got 70 add seven which is 77.

So 45 and 32 is equal to 77.

We could also work it out a different way, with a new strategy.

Have a look at this new question.

What happens if I only partition the part 32 into tens and ones and add this onto 45? Will the whole have the same value? We're going to explore this question now.

So remember, my two parts were 45 and 32.

And what I'm going to do is put 45 in my whole, and partition the number 32 and add that onto what's in my whole already.

45 is the whole that we're going to have because we're adding on our partitioned number 32 to it.

So I'm going to put 45 in the whole already.

So 32 we know can be partitioned into three tens which is 30 and two ones, which is two.

I'm going to start with adding my tens first.

So I know that all together I've got 45 in here.

But more importantly, I've got four tens.

I know that I can add three tens to four tens, because the four add three is equal to seven.

So if I was to add these three tens into this whole, I'm going to have seven tens all together, and my five ones.

So I know that 45 as on three tens will give me 75.

So now we have 75 in this whole all together, and now just have these two ones left over.

I know that five ones add two ones equals seven.

So 75 add on two ones is going to give me 77.

So I can move them in there like that.

As you can see, by starting with my part 45 I'm partitioning one of my parts 32.

My whole still has the same value.

It was just a different strategy of working it out.

Okay team, it is time for your talk task.

So you have been given two equations on the board, 23 add 46, and 53 add 46.

And I want to think you to think about how many different mental strategies you can use to solve those two equations.

So pause the video now to have a go your talk task, and then play the video when you're ready to continue.

I'm going to go through a couple of strategies now for this top equation and see if you were able to find the same strategies that I did.

So I have 23 add 46, I'm not going to write out cause I've got it here.

I'm going to start off with my number bonds that are going to help me add my ones and my tens.

So I know looking at my tens I've got two tens here and four tens here.

I know that two add four equals six, therefore I know 20 add 40 is going to equal 60, like that.

Now that I've looked at my tens, I know that my value of my answer will be 60, it's going to have 60 in it.

Now I can look at my ones.

Of three add six ones.

I know that three, add six is equal to nine.

So I know that in my answer, I'm going to have nine ones.

Now all I need to do is add up my tens and my ones together.

So 60 add nine is 69.

There we go.

So that was one strategy I had.

You could have done this other strategy that we just looked at before I took the task.

Or I take one of my parts, and I'm just going to partition the other parts and add that to my whole other part.

I'm going to keep 46 as a it is, and I'm going to partition 23.

23 can be partitioned into two tens, which is 20 and three ones, which is three.

So let's start with our tens.

I've got two tens and four tens.

If I know that two add four is equal to six, then I know that 20 add 40 is equal to 60.

So therefore I also know that 20 add 46, remember, I'm keeping that 46 the same, is going to be 66, like this.

I know I'm going to have 66 because my 10 is going to stay the same and my ones I don't add anything to that.

Now I can look at my ones.

I've got three ones and I know that three ones, add six ones, is equal to nine ones.

So three add six is equal to nine.

So I know that three add 66 is going to be 69.

You can see that my whole here, and my whole here have not changed value.

All I've done is found different strategies to solve those equations.

We're going to think now about some new work problems and the strategies we can use to solve the subtraction word problems. So let's have a read of this question.

In the evening, 78 people were on a train, and then 35 people got off the train, how many people were left on the train? Remember, we need to think about our no number bonds that can help us solve this mentally.

So have that in your mind as we go forward.

We're going to represent this word problem into a pothole model so we can think about it more clearly.

Remember, when we have a word problem, we need to think carefully about what parts we know, so what information do we know? Do I know the value of my parts or my whole? And what am I trying to find out? Well, from this question, I can tell that we start off with 78 people.

And then 35 people get off the train and we want to know how many are left.

So I know that was 78 must be my whole.

So I'm going to put 78 there so I've got 70 as my whole.

If 70 is my whole, I know that 35 is my first part.

And what we don't know is this missing part.

So I'm going to hit 35 and my first part now, so I've got 35 here, that helps me to know that I've got 35 in this one part, and we don't know this part.

To work out this part, I need to do a subtraction equation.

I need to do 78, which is my whole take away my known part 35 to find out my missing unknown part.

Let's think now about the number bonds we could use to help us solve this equation, 78 take away 35.

I'm going to start by partitioning my two numbers in my whole and my first part.

My whole 78 is partitioned into tens and ones, so seven tens and eight ones.

My part 35, that I'm taking away, can be partitioned into tens and ones as well.

So three tens is 30 and five ones is five.

Let's have a think about our tens first.

And so I know I've got seven tens in my whole and I'm taking away three tens which is 30.

I'm going to put a pothole model example up as we're going through our number bond so that you can see what's happening.

Remember, 78 is our whole so I'm going to start off with 78 dims in my whole.

And we're going to think about our tens first.

So remember I start off with my whole, seven tens I'm taking away three tens.

I know that seven take away three is four.

Therefore I know that 70 take away 30 is equal to 40.

So let's take away 30, and I'm left with 40 here, we can see that.

Now that we sorted our tens, we've taken away off 30 from our 70, and we're left with 40, we can look at our ones.

I know I've got eight ones in my whole, and I'm taking away five of them.

And I know that eight takeaway five is equal to three.

So let's take this five away.

And you can see that I'm left with three.

So we'll see here in this box, all that we're left with is our missing part.

So let's put it into here now because that's where it belongs.

So I've got my four tens which is 40 and my three ones, which was three.

And now all I need to do is add them together to get my answer.

10, 20, 30, 40, 41, 42 43.

I know that 40 add three is 43, which means that my final answer to 78 takeaway 35 is 43.

It is now time for your independent task guys.

So you have been given four equations, two of them are addition, two of them subtraction.

And what I want you to do with these equations is to explore how many different mental strategies you can use to find the answer to these equations.

Remember, you're using your number bonds within 10 to help you find new facts with these different equations.

As you're going through these equations, I want you to use these sentence starters.

If I know, then I know.

Pause the video now to complete your task and resume the video once you have finished.

Okay, let's go through those answers then guys.

For the first equation 62 add 23 is equal to 85.

Second one is 53 add 45 equals 98.

In the last two you're subtracting, so 89 take away 64 is equal to 25, and 76 take away 32 is equal to 44.

Team, you have been absolutely fantastic today.

Thank you for all of your hard work.

I really look forward to seeing everything you have remembered from today's session.

So good luck in your quiz and hopefully see you soon.

Bye, bye.

If you'd like to, please ask your parent or carer to share your work on Instagram, Facebook or Twitter, tagging @OakNational and #LearnwithOak.

Okay team, it's now time to complete the quiz.

I'm really excited to see all of the fantastic learning that you've taken away from today's session.

Good luck.