Lesson video

Hello, everyone, I'm Mrs. Crane, and welcome to today's lesson.

In today's lesson, we're going to be choosing the most efficient subtraction strategy.

So we're going to be finding out about different strategies that we could use to solve some subtractions, and then working out which is going to be the most efficient, which is going to get us to our answer the quickest, without having to do lots and lots of working out and calculations.

In a moment, I'll explain any of the equipment that we will need for today's lesson.

So for the moment, if you can, can you please turn off any notifications that are on your phone, tablet, or whatever device you're using to access today's lesson? And then can you please, if you can, try and find somewhere nice and quiet in your home, so that you're not going to get distracted whilst we're doing today's lesson together.

When you're ready, let's begin.

Okay, then, let's run through today's lesson agenda.

So to begin with we're going to be finding out what are the different strategies.

Then we're going to be exploring which strategy is most efficient and why.

Then we're going to be looking at a new strategy called round and adjust.

Then for your independent task today, it's going to be can you choose the most efficient strategy, and then we'll go through the answers together.

So for today's lesson, you will need a pencil and some paper.

Please pause the video now to go and get those things if you haven't got them already.

Okay, welcome back.

Let's get started then.

So let's have a look at our first equation today.

My equation is 7,498 and I'm subtracting 3,152.

What is my answer going to be? How would you solve this equation? What would you do? Okay, we can use the bar model here to help us because we know our whole is 7,498.

We know one of our parts is 3,152.

We just don't know that other part.

So you can also see I've got a number line drawn out here.

This number line is going to help me, because I could use this as one method.

I could count on on my number line from my part until I get to my whole.

So I've put my part here, 3,152.

And now I'm going to count on until I get to this number here.

Going to count on firstly like by trying to get up to a multiple of 10.

So I'm going to add eight to get me to 3,160.

Now, I want to get to the nearest multiple, the next multiple, sorry, not the nearest, the next multiple of 100, which is going to add 40 to get me to 3,200.

Now, I want to get up to the next multiple of 1,000, which is 4,000.

So I'm going to add on 800 to get me to 4,000.

Now, I'm ready to do a bigger jump.

I'm trying to get to 7,498.

So I'm going to jump 3,000 to get one to 7,000.

Then I'm going to jump 400 from here, to get me to 7,400, then jump 90 to get me to 4,000, to 7,490.

Then I'm going to jump eight to get me to 7,498.

That was a lot of jumps on my number line.

Was that efficient? Was that the best method that I could have used? I'm not sure that was the best method I could have used.

Did you have a different method in your head? Let's have a look then at two other methods that we could use to solve this equation.

So, oh, I haven't even solved it yet.

I'm getting carried away.

I now need to add up all of these numbers here to get me to my answer.

So I would start with my greatest number 3,000, add 800 to give me 3,800.

Now, add my 400 to give me 4,200.

Then I'm going to add my 90 from here to give me 4,290.

Then I'm going to add my 40 to give me 4,330.

Then I'm going to add my 40, or, there it is, sorry.

I think I added that already.

Have you noticed what has happened? I have got confused with which numbers I've added because this is quite confusing.

This probably isn't the most efficient way.

It is one method you could use.

It's just not going to get me there in the quickest, in the quickest way possible, and it's easier to make errors in what you're doing.

Then I need to add my eight and my eight to get me to 4,346.

So I have my answer.

So I still got to the answer.

So it's a method that works, a strategy that works, but it took me quite a long time.

It was quite difficult for me to explain, and I got myself a bit confused, even when I was adding it.

You've got to really careful if you're using this method, for this kind of equation, anyway.

So let's see what other strategies I could use.

Now, I could do some partitioning.

That might be a more efficient strategy here.

So I could partition either both numbers, or one number, and we'll look at what happens when we partition just one number in a moment.

So I've deposited both numbers.

I've partitioned them into thousands, hundreds, tens, and ones, both of them, and then subtracted them.

So 7,000 subtract 3,000 is 4,000.

400 subtract 100 is 300.

90 subtract 50 is four.

Eight subtract two is six, and I've recombined 4,346 to 4,346.

Was that quicker than my last method? Absolutely it was.

Did I get to my right answer without getting confused or mixed up or muddled in any of my steps? Absolutely I did.

So I would say for that equation partitioning is definitely going to be a more efficient method than counting on on my number line.

We'll come back to when counting on on our number line can be really effective later in the lesson.

So don't worry if you think, "Actually, sometimes Mrs. Crane, "I can think of an example where I really like to use it." Now, let's look at when we partition just number.

So we keep the whole here.

We're just taking away the one number, and we're partitioning just the one number.

So our whole stays the same.

This time we partitioned 3,152 into thousands, hundreds, tens, and ones, just like you can see if you're looking at my pointer.

Now, we must remember that we need to subtract from our answer to the previous equation.

Otherwise, we're not going to get the right answer.

So, our number 4,000, 7,498, we're subtracting 3,000.

Takes us to 4,498.

Now, from that same number, our answer, we're subtracting 100 to give us 4,398.

Now from the same number we're subtracting 50 to give us 4,348.

Now we're going to subtract two to give us 4,346.

I would say partitioning one number probably takes me the least amount of time.

So it's probably the most efficient.

If you feel more confident partitioning both numbers, it's not that different to partitioning one of them.

Get our answer again, 4,346 We get the same answer each of the methods that we've used.

It's just today we're thinking about which is the most efficient, which gets us there the quickest without making any errors.

Why was it most efficient? Because I got there most quickly without making any errors.

I only needed to partition one number, which is really straightforward, and I got to my answer without making any errors, and without it taking a very long time, and lots and lots of little jumps on the number line.

Now, if you're feeling confident, what I want you to do is have a look at this next equation, 5,634 subtract 2,122, and think about which strategy you would use because it's the most efficient strategy.

Now, it doesn't have to be on a number line just because there's one here.

It might be that you've chosen to use a different strategy.

If you're feeling really confident, pause the screen now to have a go at using one of your strategies that you think is most efficient to solve this equation.

If you're not feeling that confident, don't worry.

We're going to go through the example together now.

So going to start with my parts that I'm taking away from my whole here, and I'm going to keep going in jumps up until I get to my whole.

Already, those two numbers are quite far away from each other.

Do you think I'm going to have to do a few little jumps, or do you think this number line's going to look quite busy by the end of it? Absolutely, I think my number line is going to look quite busy.

So let's start off by trying to get to my next multiple of 10 by jumping eight.

Now, to get to my next multiple of 100, by jumping 70.

Sent me to 2,200.

Now, I want to jump up to my next multiple of 1,000 by adding 800 to take me to 3,000.

Then I'm trying to get to 5,634.

So I'm going to do a jump of 2,000 to get me to 5,000, a jump of 60 get me to 5,060, not 60, sorry, 600, to get me to 5,600, a jump of 30 to get me to 5,630, and a jump of four to get me to 5,634.

Now, I must add up all of those numbers here.

Otherwise, I don't have the answer.

So I'm going to do 2,000 add 800, 2,800, 2,800 add 600 from here, 3,400.

Now I'm going to add my 70 from here, which gives me 3,470, and my 30 from here, which gives me 3,500.

Then I can add my eight to give me 3,508.

And finally, I'm going to add my four to give me 3,512.

I don't know about you, but I definitely need a sip of water after saying all of those numbers.

Was that strategy efficient? I'm not convinced that it was.

It took me quite a long time and it was quite a lot of work because I had to jump up.

I had to think about the multiples that I was jumping up to.

I had to mark those on, and then once I'd even done that, I had then had to look back and add up all of these numbers here.

So it wasn't the most efficient strategy.

What other ways could I have solved it? What other ways did you use to solve that? Put my answer in.

Don't forget that.

After all that hard work, I can't forget to put my answer in.

So we could partition both of the numbers, just like we talked about in the previous example, 5,000 subtract 2,000 is 3,000.

600 subtract 100 is 500.

30 subtract 20 is 10.

Four subtract two is two.

Recombine them by adding them together, gives me 3,512.

Oh, that was much easier than doing all of those jumps on the number line.

Or I could partition just one number.

I could take 2,000 away from 5,634 to give me 3,634.

Then I'm going to take 100 away to give me five, 3,534.

Then I'm going to take 20 away to give me 3,514, taking two away to give me 3,512.

I would say either of these two methods is much more efficient than jumping and counting on on the number line.

I would say if you can partitioning just one number is going to be the most efficient strategy.

But if you find it more confident today to have a go at it with both, that is absolutely fine.

If today you're thinking, "Oh, I've never tried partitioning "with just one number before," today is a brilliant time to have a go at doing that, and using that strategy to see if you feel more confident with that.

So oh yeah, again, I can't forget, I've done all that hard work, to put in my answer.

We think this is probably the most efficient strategy because it took the least amount of time, and I didn't make any errors or get confused or need to pause for a moment, because I'd done so much hard work and thinking to get to the same answer that I did on the previous slide.

So for your Let's Explore today, it's going to be you thinking about which strategy is the most efficient.

Which one are you going to choose? So in a moment, I'd like you to pause the video to have a go at answering this equation here, by either counting on on our number line, partitioning one number, or partitioning both numbers.

Think carefully about which you think is the most efficient strategy before you give it a go.

Then we're going to go through the strategies to decide which is the most efficient.

Pause the video now to have a go at today's Let's Explore.

Okay, welcome back.

Let's have a look then at which strategy you have used.

So you might have used either of these three, any of these three strategies.

We're going to think now about which is the most efficient.

So we could use counting on on a number line.

Now, be prepared.

We've got a lot of jumps ahead of us.

So we're going to jump to nine to get ourselves to the next multiple of 10, which is 2,440.

Then we're going to jump 60 to get to 2,500.

Then we're going to jump 500 to get to 3,000.

Then we're going to jump 3,000 to get to 6,000, then 70, to get to to 6,700, not 70, 700 to get to 6,700.

Then we're going to jump 50 to get to 6,750.

Then we're going to jump three to get to 7,000, to 6,753.

Finally, we've made it.

Now, what must I do? I must do that second part of really hard work, by adding up all of these numbers to get to my answer.

So 3,000 plus 700, 3,700, plus 50, not 50, 500, 4,200.

Then I'm going to add my 60 from here, 4,260.

Then I'm going to add my 50 from here, 4,310.

Then to that, I'm going to add my nine, 4,319.

Then to that number, I'm going to add my three, 4,322.

Quite a lot of hard work there.

It requires quite a lot of thinking and hard work and accuracy to get to the answer, which is 4,322.

Did you do it a different way? Which method did you use? Was it more efficient than my method? I hope it was.

So let's have a look at the other two methods we said we could use.

We could have used partitioning both numbers.

So 6,000 subtract 2,000 gives me 4,000.

700 subtract 400 gives me 300.

50 subtract 30 gives me 20.

Three subtract one gives me two.

Oh, then I need to recombine them by doing 4,000 plus 300 plus 20 plus two is equal to 4,322.

Same answer.

You could though have just partitioned one number.

So you could keep our whole here, just partition one of our parts.

So from our whole from 6,753, we could subtract 2,000, then 400, then 30, then one.

So each time, let's have a look, 4,753 subtract 400 gives me 4,353, subtract 30 gives me 4,323, subtract one, 4,322.

I would say either of these two methods work for me and subtracting by partitioning one number is going to be the most efficient method, because I didn't make any errors, and I find that more straightforward.

Now, we're going to look at some more strategies we could use and when we could use them.

So let's have a look at these two numbers here, 5,004 subtract 4,998.

We've got our same three methods, but we need to think about which is going to be the most efficient before we try them.

We're also going to add in another strategy now called round and adjust.

That's a strategy we could use in equations where our numbers are close to multiples of 100 or 1,000.

These two numbers are close to multiples of 1,000.

The number 5,004 is close to the , to the number 5,000, sorry, and so is the number 4,998.

Now, because they're both quite close together, in this example, round and adjust isn't going to be the most useful, the most efficient strategy.

This time, finally, our number line is actually going to come in really handy, because they're close together.

I'm not going to have to do lots and lots and lots and lots of jumps here, because they're not far away from each other.

So I need to do a jump of two to get me to my next multiple of 1,000.

And then I only need to do a jump of four to get me to 5,004.

Oh, that was much more straightforward than all of those jumps.

Now, what was the next thing I must do? Recombine them, but I know two and four is equal to six.

That's really straightforward.

So my answer would just be six.

That is a much more efficient method used when the numbers are close together than when those numbers are far apart.

Let's have a look then at this example here.

Which do you think is going to be the most efficient strategy? Do you think you know an efficient strategy? Pause the video now to have a go at using it to solve this equation here.

Now, again, I'm looking at these two numbers, and I'm thinking, ooh, they are quite close together.

So I'm going to use counting on our number line again.

Going to put my part here, and I need to count up to my whole.

I need to jump one to get me to the next multiple of 1,000, and then I need to jump six to get me to the next multiple, to get me to my whole, sorry.

One add six is seven, so my answer is seven.

Again, much more straightforward than when my numbers were really far apart.

Now, we're going to look at one example of when we would use the round and adjust strategy.

Now, here, my numbers aren't close together, but I can see that the number 1,997 is very close to a multiple of 1,000, the number 2,000.

So I'm going to round it to 2,000, and then I need to adjust it.

So I'm going to show you how I would do that.

So I would round 1,996 to 2,000.

It's actually three less than 2,000.

So we're going to 2,000 away to give me 4,863.

Then I have to adjust it by adding three on.

So, because I took three, because I added three on here, I then need, sorry, because I rounded my number to 2,000, I now need to adjust it by adding the three.

So we're going to do 4,863 plus three is equal to 4,866.

So my answer is 4,866.

Can you see how much easier that strategy is than partitioning, or even counting on on a number line? The number line strategy is only really efficient when the numbers are close together.

Round and adjust is only really efficient when one of the numbers is close to a multiple of 1,000 or 100.

Okay, have a look then at this equation here.

If you're feeling confident, pause the video to have a go at using the strategy you think is the most efficient.

If you're not feeling so confident, that's okay.

I've spotted the number 2,998 is very close to a multiple of 1,000, is close to the multiple 3,000 of 1,000.

So I'm going to round 2,998 to 3000.

It's actually two less.

So then I can take away 3,000 for say, which would give me the answer, 4,563.

Then I have to adjust it by adding on two.

So I'm going to add two to that number, which gives me 4,565.

Put in my answer here.

Now, your independent task today is can you choose the most efficient strategy? Okay, I'm just going to hide myself a minute, so you can see really clearly.

You've got six questions here, six equations here.

I'd like you to have a go at solving these equations using the method you find most efficient.

Then your challenge is can you explain why you chose your method? Please pause the video now to complete your task.

Don't forget to resume it when you're finished, and we'll go through the answers together.

Okay, welcome back.

You can see me again now.

So let's have a look at our first question here.

I would probably partition here, because they're not that close together.

So partitioning either one or both numbers, and it'd give me the answer 1,012.

Next, then, I can straight away see that these numbers are close together.

So I'd probably count on, or use my number line to count on to give me the answer 151.

Next, I can see one of my numbers is close to a multiple of 1,000.

So I would probably use the method round and adjust to give me the answer, 1,459.

Then here I can see the numbers aren't that far away from each other, so I'd probably use the number line to count on, and my answer would be 301.

Here, I can see they're close together again.

I would probably use the number line and counting on again this time.

Give me the answer 18, and again, here I can see this time they're close together, so I could use round and adjust.

Sorry, I could use the number line, or I could use round and adjust here to take away 3,000 and then adjust it.

In this instance, those two are both pretty efficient methods of solving this equation.

It would give me the answer 35.

If you'd like to, please ask a parent or a carer to share your work today on Twitter, by tagging @OakNational and using the #LearnwithOak.

Well done today.

There was lots of different strategies there that we looked at, and trying to find the most efficient is quite tricky sometimes to remember all of those different strategies and which one you're going to use.

So I've been really, really impressed with how hard you've worked today.

Don't forget to show off all of that amazing knowledge in today's quiz, and hopefully I will see you again soon for some more fun math.

Thank you, and good bye.