# Lesson video

In progress...

Hello, thank you for joining me.

My name is Miss Jeremy and today's math lesson is focused on using and explaining addition and subtraction strategies.

So find yourself a quiet space for learning, and once you're ready, press play to begin the lesson.

So let's begin with our lesson agenda.

We're going to start with a warm up today where we'll be looking at some additional strategies as a recap.

We'll then some three digit addition before looking at subtraction strategies.

And we'll end with some addition pyramids before your independent task and quiz at the end of the lesson.

For today's lesson, you will need some paper and a pencil and a nice quiet space for your learning.

So go find your resources first by pausing video.

And then when you're ready, get started by pressing play.

Okay, let's begin with our warmup.

Where we're going to look at some number bonds and we're going to be thinking about which addition strategy is the best one to use in this particular case.

So we've got the equation here, 26 plus 17 plus 24.

And I'd like to know whether you think we should be using partitioning, commutativity or around an adjust approach to help us with solving this problem.

Remember, we are focusing on number bonds, so that might help you work out, which of these three would be most suitable.

I want to leave you five seconds to decide which of those strategies you'd like us to use.

Okay.

So actually any of those are absolutely fine to use, but in this case, my selection would be to use the law of commutativity.

And the reason being that I've spotted some number bonds to 10 here in this particular equation I think could help me.

But, I will need to rearrange the numbers in this equation, using the law of commutativity in order for those number bonds to work.

So reminding ourselves that the law of commutativity tells us that in an addition equation, where you've got an addition question.

You can mix up the numbers in that equation and place this numbers wherever you want them to make that equation easier to answer.

So in this case, the number of bonds is 10 that I've spotted are six here, and a four here.

So I can see that adding those together would make 10.

So actually I'd like to rearrange this equation, I'm going to make it 26 plus 24 plus 17.

And because of the law of commutativity, I can do that without any issue.

So knowing 26 plus 24, first of all, well, I know that 20 plus 20 is equal to 40 and six plus four is equal to 10.

So 40 plus 10 is equal to 50.

And then in my head very easily, I can do 50 plus 17, which is equal to 67.

So you can see that I could have used any of those strategies.

I could have rounded and adjusted.

I could have partitioned, but in this case, commutativity help me out.

Because I saw those number bonds to 10 and whenever we see number bonds to 10, we should try and maximise using those because we can use our mental arithmetic strategies rather than using a strategy, like the column method.

So moving on, let's have a look.

What I want to know is whether these three strategies that we've learned about partitioning, commutativity, rounding and adjusting can also be used when we're adding together three digit numbers.

Like you can see here.

So I've got put numbers in the hundreds.

I've also got two digit numbers as well.

And I wondered whether we could use those same strategies for these three questions.

I've laid them out in order.

So first one, I'd like us to try and use partitioning.

And I'm going to model to you how I would use partitioning.

Reminding ourselves the partitioning is breaking apart a number into its components to make adding them together easier.

I'm going to demonstrate this using writing on the screen.

But actually the great thing about partitioning is it's a mental arithmetic strategy.

So let me have a go with the first one.

It is 250 plus 132.

Now I can see straight away here.

I don't need to use regrouping.

And because I don't need to regroup in any of those columns when I add them, partitioning is ideal.

So I'm going to partition each of the numbers up.

I'm going to partition this into 200 and then 50.

I don't need to do anything with the ones there.

There are no ones.

I'm going to partition this into 100, 30 and two.

Adding together my hundreds first, I've got 200 plus 100, which is equal to 300.

Then I've got my tens, which is 50 plus 30, which is equal to 80.

And then I've just got my two ones.

I'm going to add those onto the end 382.

And as I said, once I've written that down for you, you could actually do that all in your head without needing to write anything down without needing to use the column method.

So looking at commutativity and reminding ourselves that commutativity means that we can mix up the numbers in an addition equation, because it doesn't matter which order you put those numbers.

The answer will still be the same.

So I'm looking for my number bonds to 10 here, and I can see straight away that I've got a one and a nine and both one plus nine makes 10.

So I'm going to actually rearrange this equation.

I'm going to make it 121 plus 19 plus 230.

I'd like to do it in that order, So I can maximise those number bonds to 10.

So looking at adding my 121 plus 19, what I know that one plus nine is 10, and then I've just got to add another 10.

So that's 20 and then another 20, which is 40.

So that's 140 and then I've got to add my 230.

I can do that using partitioning in my head.

So I can see we're going to have 300, and looking at my tens now, and 70, 370.

And now finally reminding ourselves the round and adjust strategy.

Now, rounding and adjusting is fantastic, when you can see a number that is really close to a number that is a multiple of 10 or 100.

Basically, if a number is a multiple of 10, 100, 1000, it's very easy for us to add.

You saw also how easily I added 114, 230 there.

In this case, I've got the number 139.

And actually that's quite difficult at 42 in my head.

But if I use rounding and adjusting, I can make that number, an easier number to add.

If I add one to that number and make it 140 and then add 42.

Now that's super simple all of a sudden.

I've rounded that 139 up to 140.

So 140 plus 42 is equal to 182, but I've got to remember to adjust.

I've done my rounding, I've got to now adjust because I added on one earlier on.

I've got to take away one now.

So I'm going to take away one from that amount.

So there's a little recap of how we can use partitioning, commutativity and rounding and adjusting in order to solve three digit addition questions.

So now you've seen me use those three strategies and we've had a practise but I'd like you to practise this independently yourself.

So you've got three questions on the board and each of those questions links to one of those strategies.

So the first one I'd like you to try and use partitioning to solve.

The second one requires commutativity.

And the third one I'd like you to use the around and adjust strategy.

Spend a bit of time working that out on some paper now or using the mental arithmetic strategies.

Pause the video and then resume it once you're finished.

Okay, let's have a look because some of the answers to see how you go on.

So as you can see the answers are on the screen now.

Have a look at your own answers and mark them, see whether you agree with what I've written and if not go back and have another look and see if you can rework where you might've gone wrong Using some of those strategies.

If you need to rewind the video to recap how we use those three strategies with equations involving three digit numbers.

So let's move on to subtraction now.

I want us to have a thing about question like we can see on the screen here.

It says, how could we complete the following equation? We've got 124 plus something is equal to 280.

Now using my inverse method and reminding myself of the inverse method.

I know that in order to solve this, I could use 280 minus 124 and find my answer that way.

That's one of the methods I could use.

There is also the find the difference by adding method.

And that's what I'm going to demonstrate to you now, how we could find the difference using adding, because as strange as it might sound, adding can actually help us when we subtracting, even though adding and subtracting inverse, they're the opposite of each other.

We can still use adding in order to help us with subtracting.

And actually some people prefer using adding.

The reason being that some people feel more confident when they're adding on rather than taking away.

And so actually use this strategy to help them rather than subtraction using the column method.

So this is how we do it.

First of all, we need to think about what the difference is between 124 and 280.

And what you can do is you can use an adding on strategy using a number line to help you work out what that difference is.

The first thing you do is draw yourself a nice number line like this.

And at the end, we've got 280, and actually doesn't matter how long it is because you are going to use it accordingly and you can make your jumps proportional.

We've got 124 on this side and we're trying to work out the difference.

What do we have to add to 124 to get to 280? So the first thing I'm going to do is make a jump to my next easy number to add on my next multiple of 10, basically.

So I'm thinking, what can I add to 124? It's going to give me a multiple of 10.

My next multiple of 10 after 124 is 130.

And in order to get from 124 to 130 using my number bond knowledge, four plus six, I know that that's going to be adding on six.

So you see number bonds come in handy, even when we're dealing with numbers way above the number 10.

So now I've got to 130.

I wonder whether I can make a really big jump and I can jump all the way to 200 next time.

So again, using my number bonds, what do I have to add to 130 to get to 200? Well, what do I add to 13 to get to 20? I add seven.

So to get from 130 to 200, I'm adding 70.

So I'm adding on 70 there, and now the next bit is fairly straight forward.

What do I add? 200 to get 280, really nice, easy numbers here.

Now that you've done that and you've added on to find the difference, we need to add together all those differences.

I need to add 80 and 70 and six.

So using my number fact, I already know 80 per 70.

Well, I know that eight plus seven is 15, 80 plus 70 must be 150 and then I put about the six.

So you can see here, lots of different ways, you could have solved this.

You could have subtracted, like we showed there, you could have used the column method to subtract there.

Partitioning would have been tricky because you would have to be doing some regrouping there.

So that might have been a bit harder.

But my preference was used this strategy called finding the difference by adding.

And the reason is that I really like adding on, I think that's a really nice, easy strategy, and it shows you what you're adding proportionally on a number line.

So now we've practised using adding on strategy in order to subtract.

Let's have a look at another strategy that you might use when subtracting.

So we've got the question here, 368 minus 124.

And straight away when I'm looking at this, I'm looking to see those columns.

In my mind I'm imagining that place by the charts, and I'm trying to work out whether there's any regrouping required in this particular question.

So I'm looking at my ones first.

I've got eight subtract four, no regrouping there.

Then I'm looking at my tens.

I've got six, subtract two, no regrouping there.

Then I'm looking at my hundreds.

I've got 300 subtract 100, again no regrouping there.

So I can see straight away that this could be a really good example of the question where I can use partitioning for subtraction.

Partitioning is a wonderful strategy to use for addition and subtracting when you don't need to regroup.

So let me show you how this might be done.

First thing I'm going to do is partition out the numbers 300 and then we've got 60 and then we've got eight then I've got 100, then I've got 20, then I got four.

We've with partitioned that into our components, just like we would do with addition, but instead of adding the numbers together this time we're subtracting them.

I'm subtracting 300 subtract 100 and that's equivalent to 200.

So I'm going to put two in my hundreds column.

Then I'm looking at my tens.

I've got 60 subtract 20, which is equivalent to 40.

I'm going to put four in my tens column.

And then I've got eight subtract four, which is equal to four.

So I'm going to put four in my ones column.

Super simple.

Again, I'm writing all of these out for you so you can see my thought process.

But essentially partitioning is something you can do really easily in your head as well.

So another quick example for us to practise.

821 minus 710.

Here's a challenge for you.

Can you solve that without writing anything down? Can you see when you can work out and partition that in your mind, focus on the ones first, then the tens and the hundreds and see whether you can partition that and work out what that would be using your partitioning strategy.

I'm going to give you 10 seconds.

Okay.

So let me see if I can do it myself.

So I know straight away that I'm partitioning out my 821 into 800, 20 and one and my 710 partitions into 700 and then 10.

I've got no ones there.

I'm focusing on my hundreds column first because there's no partitioning here, No regrouping here, sorry.

I'm doing 800 minus 700 and that's equal to 100.

So one goes in the hundreds column.

Then I'm looking at my tens column.

I've got two tens minus one ten, which is equal to one ten.

And then I've got one one minus no ones, which is equal to one one.

No writing needed all of that was a mental arithmetic strategy.

And interestingly, a lot of people might have looked at that question and thought, I'm going to write that down using the column method.

In this particular case, not necessary.

If you don't see the need for regrouping, you can use partitioning that easily.

So I'd like you to have a practise of this.

I've got two questions for you on the screen.

One of them, the first one, I'd like you to see whether you can solve using, finding the difference by adding to draw out that number line, do those jumps from 221 to 430 and see what the difference is.

And then the second one, I'd like you to have a go at partitioning that using the partitioning strategy that we've just practised.

No regrouping for that question is required.

Spend just a couple of minutes working on that.

Pause the video now to complete the task and then resume it once you've finished.

Okay.

How did you go on? Let's have a look at the answers together.

So as you can see, I've put them on screen there.

And I'm just going to show you really quickly the jumping on the finding the difference example, because that's the one that I think is slightly more challenging.

So just in case you found this one tricky, I'm drawing my number line.

I'm putting 430 at the end because that's the final, that's the final of our whole and 221 on this side, and I'm going to do my jumps all the way to 430.

I'm adding on as I go.

So the first thing I'm going to do is try and get to the next multiple of 10.

So I can see I'm going to try and get to 230 and adding on nine, plus nine there.

Next I'm going to try and get to my next multiple of 100, Ideally.

Now you can see my jumps, aren't particularly proportional.

My jumper nine and my jump is 17.

They're not particularly proportional, but the idea is that, you know what those jumps mean and what they represent.

And I need to add on a hundred to do that.

And then a slightly smaller jump of adding on 30 there.

So you can see that I've done all of my jumps, and I can see that I am going to now add 100 plus 70 that's 170, and then plus 30 that's 200 and then plus nine that's 209.

So using your adding on strategy, another really quick method for working out the difference between two numbers.

So now we've practised our strategies for addition and subtraction.

It's time to apply these to addition pyramids.

So you can see on the screen here, we've got an example of an addition pyramid, and the way that they work is this, the two numbers at the bottom of the pyramid or the bottom of another number are added together to create that top number.

So for example, if I want to work out this number up here, I would need to add the number that's in this box and this box together.

Similarly, if I want to create the number that is in this top box here, I need to add the number that's in this box and the number that's in this box together.

So we are creating pyramids, using addition and subtraction to work out those missing values.

I've highlighted two of the boxes on the screen, that I'd like to have a look at when we're identifying the missing values and both of them are going to require us looking at our subtraction strategies.

So let's have a look at the first one.

I want us to have a look at the number that should go into this box here and I can see straight away that whatever is in here would need to be added to 325 to give me 530.

And that's the same as saying 530 minus 325 is equal to my answer.

Whatever's the numbers in that box.

So having a look at that equation and what do you think I should do? Should I use a counting on number line to work out what the missing value is? Or should I use partitioning? Five seconds for you to make a decision.

So actually in this case, either of those methods works, even though this requires some regrouping, you can still use partitioning because the numbers that we're working with, are fairly easy to subtract from one another.

And that's because we've got multiple of 10 and I've got 530, which helps us out.

So if I've got 530 minus 325, instead of partitioning this fully, I could partition this into 500 and 30 and then this into 300, and instead of partitioning this all the way, I'm going to partition it into 25, because I think 25 is going to be easy to take away from 30, whereas 20 and then five might be hard.

I'm going to do 500 minus 300, that's equal to 200.

So two goes in the hundreds column, and then I'm going to do 30 minus 25.

I can really easily use my number bonds there to help me out.

And that's equal to five.

So I'm going to have no tens and it's going to be five.

So that answer, that is 205.

So you can see that even though some regrouping was required because I was able to change the way I partitioned those numbers, I was able to subtract them that easily.

You can also use a counting on strategy.

So I could have started at 325 added on until I got to 530.

That would have been fine as well.

So for the next one, I want to work out what's in this box here.

I'm going to need to think about what I have to do to 710 and 205 to work that out.

Can you think of a way we could use that same partitioning strategy that I've just shown you, where we don't fully partition the numbers to work out that missing value.

I'm going to give you five seconds.

Five.

Four.

Three.

Two and one.

Let's have a look together.

So I want the 710 minus 205.

So again let's partition this out 700 and 10, and then I've got 200 and I've got five.

And so if I start there with my hundreds, I'm doing 700 minus 200, which is equal to 500.

So five goes in the hundreds column and then I've got 10 minus five, which which is equal to five.

So I don't have any tens.

And I've got five in the ones.

So again, you can see really clearly there that actually partitioning work, even though it looks like this would require regrouping because of the way we've partitioned it.

And because of the way, these numbers are fairly easy to manipulate, we can use partitioning in this case as well.

A counting on strategy would have worked just fine as well.

So I could have started at 205 and then added on incrementally until I got to 710.

So you can use either of those methods in order to find the answers for the addition pyramid.

Now, if you were to try and find out what the number for this particular box would have to be, you would need to add together these two numbers below.

And for this, you can decide, are you going to use the partitioning method? Are you going to decide that you're going to use rounding and adjusting? Does that work particularly well? or is commutativity going to help you here in this particular case? So trying to avoid using the column method if you can.

Try and look at those mental arithmetic strategies to solve these where possible.

So it's time for you to have a little practise.

We've got the ones that I have just done there, 505 and 205 built in.

I would like you to have a go at working out what's in those boxes that are highlighted in pink on your screen.

Pause the video to complete your task and resume it to once you've finished.

Okay.

How did you go on and which of those methods did you use to work out those missing values? Let me show you what the answers are and you can mark your work.

So you've got 1105 there, and we've got 1240 there.

So hopefully some of those strategies that we've been talking about have helped you with solving those particular parts of there.

So it's time for you to have a go at your independent task, which is to solve two addition pyramids by yourself.

So you can see that up here on the screen and I'd like you to use the strategies that we've spoken about today in order to solve these.

Try and avoid using the column method where you can.

For all of the equations and all of the calculations you're going to do, any of the methods we've spoken about today would suffice.

So you don't need to use the column method.

Try and use mental arithmetic where possible.

Pause the video to complete your task now and then resume it once you've finished to have a look at the answers.

Okay.

If you'd like to spend a bit of time pausing your learning right now and pausing the video to mark what you've done and to see how well you go on with the answers that we've gotten the screen.

We've comes to the end of the lesson.

Thank you so much for joining me.