Lesson video

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

In today's lesson we're going to be looking at using the most efficient addition strategy, and we're going to be looking at a different range of strategies that we could use to solve addition equations.

How are you today? I hope you're having a good day.

In a moment I'll run through all of the equipment that we'll need for today's lesson, so don't worry about getting that just yet.

If you can, please turn off any notifications on your mobile phone or tablet or whatever device that you're using to access today's lesson on.

Then, if you can, try and find somewhere nice and quiet in your home where we're not going to be disturbed today.

When you're ready, let's begin.

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

We're going to start off by looking at the different strategies and what they are.

Then we're going to be doing Let's Explore, which is, which strategy is the most efficient? Then we're going to move on to looking at near doubles, and the strategy of round and adjust.

Then we're going to be looking at today's independent task, can you choose the most efficient strategy? 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 then, welcome back, let's begin.

So, we're going to start off by looking at an addition and looking at what the different strategies are that we can use to solve this addition.

My numbers are, well my addition, sorry, my equation is, 2,172 + 4,625 = and we don't know our answer.

So, what different strategies can you think of, different methods, that's another word for strategy that you might know, can you think of that we could use to solve this equation? How would you do it? What would you do? Okay, let's start off by looking at how we could solve it using the number line.

Now, to use a number line we are going to use partitioning within our number line.

Now, I'm starting off, firstly, by using our first number in our equation at the beginning of my number line.

And then I'm going to jump up in steps, using my second number, so let's see.

The first step that I've done is a step of 4,000.

So I've partitioned this number into the thousands, hundreds, tens, and ones that are part of this number.

So my first step takes me to the number 6,172.

Then, what's the next number I'm going to jump up with on my number line do you think? Fantastic, it will be 600.

Jumped up 600, my answer is 6,772.

I can't forget that I have to add on the 20, add on the five.

Add on my 20, takes me to 6,792.

Add on my five takes me to 6,797.

This is one method you could use to solve this equation.

There are other methods that we could use, we're going to go into those now.

So, again, I can put in my answer, 6,797.

Now, the same equation here, I could think about it using the known facts that I know.

So I can do 2 + 5 = 7, 'cause I know 2 + 5.

Then I could use my number facts, my known number facts, to tell me that 7 + 2 = 9.

I know that seven and that two actually represent tens, but I could use them and imagine that they didn't, to derive my new facts.

For example, 70 + 20 = 90.

I could then carry on doing that for the rest of the number to help me work out my whole equation.

I could partition either one of the numbers, like we did, but we did it on our number line, we partitioned this number here and added it along on our number line, or we could partition both numbers.

So I could partition 2,172 into 2,000, 100, 70, and 2, and continue with partitioning 4,625 into 4,000, 600, 20, and 5, and then add them up separately, like that.

So adding the thousands together, then adding the hundreds together, tens together, ones together, and then recombining them.

Or I could do something slightly different, I could start with the greatest addend, so the two numbers here, they're both called addends, I could start with the greatest addend and then add this number onto that number.

Sometimes a bit quicker, if we're looking at our number line, to do that with.

So there's lots of different options that we could use, which one is the most efficient? What does the word efficient actually mean? The word efficient means it's going to save us the most time.

That's what we're looking for, we're looking for an efficient way that's going to save us the most time and get to our answer the quickest way possible.

Now, let's have a look, then, at a different equation.

My new equation is 3,652 and I'm going to add 1,235 to it.

Going to use my number line, I'm going to use that partitioning again with this number here.

So, I'm adding on 1,000 to get me to 4,652.

I'm adding on 200, to get me to 4,852.

I'm adding on my 30, to get me to 4,882.

And then I'm adding on my five, to get me to 4,887.

There we go, we've got our answer here.

If you can think of another method you could use to solve this equation pause the video now to have a go at using a different strategy, different method.

What we're going to do now is, I'm going to turn over onto the next page, and we're going to go through a couple of examples, the same example, sorry, with a couple of different methods that we could use.

If you're feeling confident, I'm more than happy for you to have a go at doing your own method.

Okay, like we were talking about before, we're going to partition both of the numbers.

So I've partitioned them into 3,000 and 1,000 and added them together to give me 4,000.

600 and 200, so if we check here, gives me 800.

50 and 30, here, gives me 80.

Two and five, here, gives me seven.

Then I have to recombine them, have to add up all of my answers together.

So, 4,000 + 800 + 80 + 7 = 4,887.

Was that quicker than doing it on the number line? I think it probably was quicker than doing it on the number line.

Now the number line, you can use it, if you find it helpful.

It definitely gives us a method and a strategy.

But we could also use the same idea as the number line, so partition just the one number, but without doing it on a number line.

So we could partition the one number by keeping our first addend, here, and then partitioning our number, 1,235 into 1,000, 200, and 30, 5 here, and adding them up each time.

So, the thing we've got to remember this time is, once we've added 1,000 for that answer, our sum, we then have to use that to add the next number on.

If we don't, and we keep adding them just to our starter addend, our original number in our equation, we're going to get the wrong answer when it gets down to here, okay? So, let's do 3,652 + 1,000, that gives us 4,652.

Put that number here, now we add 200.

That gives us 4,852.

Put that number over here, we add 30, that gives us 4,882.

Put that number over here, 4,882 + our 5 gives us 4,887.

I would say partitioning just one number without using my number line is probably the most efficient way of solving this equation, because it was the quickest way, and I worked it out without having to write down lots and lots of things, without having to do lots and lots of jumps and getting myself a bit confused and muddled.

This was the quickest way.

However, for you, you might find using that number line really helpful.

It's up to you today, if you would like to use a number line.

But what we're thinking about is the most efficient strategy.

So you might be pushed a little bit out of your comfort zone if you'd normally partition both numbers, but today it's all about giving a different method a try if you think it's the most efficient, okay? That's why we're going through examples of how to do each method.

So if you need to pause and re-look at an example that's absolutely fine today.

So, now it's going to be time for your Let's Explore, which is, which strategy is the most efficient? Okay, your equation today, 3,442 + 2,341 =.

I'd like you to have a think about which strategy you're going to use.

Then on your paper, I would like you to have a go at using that strategy to work out the answer to this equation.

Remember, like I said, if you've not been particularly confident with using one of those methods before, that's absolutely fine, you can give it a go today if you'd like to.

Then what we'll do in a moment is go through the different strategies we could use to solve it and what they look like.

So, please pause the video now to have a go at today's Let's Explore.

Okay, welcome back.

As I said, we're going to go through how we could solve this now.

So, I'm going to use the number line first.

I'm going to take a jump of 2,000, because I've partitioned my number here into thousands, hundreds, tens, and ones, to take me to 5,442.

Then I'm going to add another jump on of, absolutely, 300, to take me to 5,742.

What's my next jump going to be? Absolutely, it's going to be a jump of 40.

5,782.

And my last jump is a jump of one, 5,783.

So I've got my answer.

Did you solve it in a different way? Let's have a look at what other ways we could've used.

So, we could partition both of the numbers.

So let's have a look at how that works.

3,000 + 2,000 = 5,000.

40 + 30 = 700.

I just said 40 + 30, I take that back.

400 + 300 = 700.

40 + 40 = 80, I was skipping ahead.

2 + 1 = 3.

Then I must recombine all of those answers to give me my final number, which is 5,783.

Or, like we did on the number line, but this time without the number line, I could just partition one number.

Now, I think this is probably the most efficient method to solve this equation.

If you needed the number line to help you that's absolutely fine, and if you decided to partition both numbers today, that's absolutely fine too, but we're thinking about the most efficient method.

And the most efficient method would probably be this method.

Even if you tried this method, that's absolutely fine, it will still get you the same answer, it's just not necessarily the most efficient.

So, let's look, we start off with the same addend, 3,442.

We're adding 2,000, to give us 5,442.

Then we take that answer, and we add.

I keep saying 30 today, we add 300 to it, to give us 5,742.

Then we add 40 to it, to give us 5,782.

Then we add one to it, to give us 5,783.

Fantastic work at looking at the different strategies today.

There's quite a lot of different methods and strategies to answer one equation.

Okay then, now what we're going to do is have a look at more strategies that we could use.

So, looking at this number here, I can see 2,603 + 2,621, what do you notice about those two numbers? Well, actually using the bar model here really helps me, because I can see that those two numbers are quite close to each other.

They're not really that different.

And if I look here at my thousands and my hundred, they're very similar.

Even my tens, I've only got two tens here and I've got no tens here.

So they're not that dissimilar in numbers.

So I'm going to use a strategy now which is called near doubles.

They're not exact doubles, because neither of the numbers are the same, but they are near doubles.

So I'm going to use 2,600 + 2,600 which gives me 5,200 here.

So I partitioned 2,603 into 2,600 and 3.

And I've partitioned 2,621 into 2,600 and 21.

So then what I can do is, once I've added the 2,600s together, like we've just done, then I can add on my 3, which takes me to two thousand, five.

Which takes me, sorry, to 5,203.

Then I can add on 21, which gives me 5,224.

So this is a different strategy, and we can only use this strategy if our numbers are close to being double, so if they're close together.

Again, I can put in my answer here, 5,224.

This time, I want you to have a go at doing the near doubles on this example here.

So if you're feeling confident what I want you to do is have a go at near doubles on this, and pause the screen.

If you're not feeling so confident, that's okay, we're going to talk through it now.

So, what we're going to do is we're going to start off with 3,400, and we're going to add 3,400.

You can see 3,405, 3,421 here, I partitioned them into 3,400 and five, and 3,400 and 21.

So, I'm going to add them together, so 3,400 + 3,400 gives me 6,800.

Then I can add my five to give me 6,805 and I can add my 21 to give me 6,826.

And I can put my answer in.

New strategy there.

Next one, and the last strategy we're going to look at today, is called round and adjust.

Ooh, what do you think I have to do with this strategy? How do you think it relates to these numbers? Well, I know that the number 2,498 is very close to a multiple of 100.

It's very close to the number 2,500.

So what I could do is do the jumps on my number line, it doesn't have to be on a number line it could just be written, but I'm going to use a number line to show you what exactly I mean.

So I could do a jump of 2,000 to take me from my addend, 1,325 to 3,325.

Then I'm going to go a jump of 500.

I know that's not this number here but I've rounded it up to 2,500, by adding on an extra 2.

That gives me 3,825.

Can I put that number straight in here? I can't.

I must do this second part of my method, which is the adjust part.

Because I've added two on here, here, sorry, you can see, added two extra here, I must then take two away.

So I'm going to take two away, mark that on, that I've taken two away, which takes me back to 3,823, which will be my answer.

Round and adjust is really good for examples where the number is near to a multiple of 100, sometimes 10, and 1,000.

If it's not near to those numbers it's not really going to be that helpful or beneficial for me.

But if it is, then it's really beneficial, we just must remember to adjust our answer, we can't just round and not adjust.

So, if you're feeling confident at the round and adjust method, I want you to have a look at these two numbers here, decide which number you're going to round, add it on, remember to adjust, and write in your answer.

If you're not feeling so confident, don't worry, we're going to go through it together now.

So, starting with that addend I'm going to round this number here, 2,397 to 2,400, it's three away from it, so when I adjust, I know I need to take three back off.

So, we're going to add on our 2,000 to take us to 3,476.

Now I'm going to add on my 400, because 3 thousand, nine hundred.

300 nine, 397, sorry, is close to four.

I'll start again.

2,000, we've added on, 397 is close to 400, so we've rounded it up by adding on three.

So that takes us to our new total, 3,876.

We then have to adjust it, 'cause we've added on three too many so I have to take away that three, which takes me to 3,873.

I can put in my answer here.

Okay, now it's time for your independent task today.

Can you choose the most efficient strategy? Okay then, so you have got six questions.

Each question you can use whichever strategy you think is going to be the most efficient.

Then my challenge to you today is can you explain why you chose your chosen method? So it might be helpful if you write down what your method was before you have a go at your jottings.

Please pause the video now to complete your task.

Don't forget to resume it once you're finished and we'll go through the different strategies we could use and the answer.

Okay, welcome back, let's have a look then at the first three questions.

As I said, we're going to go through the strategy we use and then the answer underneath.

So, I would use either a number line or partitioning to solve this equation here.

I can't use near doubles because they're nowhere near each other, and I can't use round and adjust because they're not near multiples of 100 or 1,000, so it's not really going to help me.

So my answer would be 5,877.

Ooh, as soon as I see this example I can see those numbers are quite close together.

So my strategy will be near doubles.

I can use it here because they're not too far away from each other.

And my answer, 3,989.

Okay, let's have a look at this one.

Ooh, again, I'm noticing something, I'm noticing they're not that dissimilar to each other, so I'm going to use the near doubles strategy to give me the answer 5,217.

Last three then, let's have a look at which strategy I'm going to use for this question here.

I'd probably use a number line or partitioning either one or both of the numbers, depending on which I felt most confident with to get the answer 7,499.

Again here, I can notice those numbers are quite close together, so I'm going to use my near doubles strategy to give me the answer 7,608.

Last but not least this question here I can see, ooh, this number here is close to a multiple of 100.

So I would probably use round and adjust to make this number 2,500 and then adjust by subtracting nine when I'd completed that to give me the answer 5,708.

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

I've been really, really impressed with all of your work today on the different strategies.

It's quite hard sometimes to think about different ways we can solve the same equation, so well done if you've tried something new that you didn't think you could do before the lesson, I've been really, really impressed and proud.

Hopefully I'll see you again soon.

Do not forget to use all of your hard work by completing today's quiz.

Thank you, and see you again soon.

Bye.