Lesson video

Welcome to your maths lesson.

I'm Mrs Harris, and together we're going to be looking at strategies for addition.

Here's what we're going to do.

We're going to look at mental strategies for addition and efficient strategies, we'll move on to column addition and we'll finish off with an independent task and you'll show me everything you've learned.

You'll need a few things.

pencil, maybe rubber, a ruler is always handy and something to write on, a paper, piece of paper sorry or a book.

If you haven't got those things, pause the video, go find them and then come back to me.

Hey, got everything? Let's get on with our learning then.

Okay, the first thing we're going to look at is mental strategies for addition.

That means that we're not really going to write any of our addition down.

We might write the answer, sums, but we wont write any of the strategies we've used as it will all be in our heads.

So to get our brains working, I thought we would have a little go at magic squares.

Here's your first magic square.

And you need to fill in the blank correctly to complete the squares.

I'm giving you some numbers to get you started, I hope it helps.

And digits one to nine are only used once and the sum of each row and column is 15.

Now the sum is the total of all your addends in that row or column.

So pause the video, have a go and then come back to me.

Welcome back.

I wonder if you found that rubber useful.

I certainly did.

Now, I've got my answers and I wonder if you found a different way.

I certainly did a lot of checking and it looks if knowing my number bonds.

So here's my answers.

I checked at each column and each row, I added up everything.

Hey, let's try.

A little one that's a little bit trickier.

So, this one, you can use any of the numbers as long as they're less than 15 and you can't use any number twice.

The sum of each row and each column is 19 this time.

So, pause the video and have a go at this one.

Welcome back.

I certainly found this one a lot more challenging and I did need the rubber.

Now, here's what I got.

I used a lot number bonds when I was working this out.

And I had to think about the value of each number quite a lot.

I knew I couldn't use too many really big numbers.

If I took the top row seven, four and eight, I very quickly know that seven plus four is 11, and if I added 8 onto that, I'd get 19.

And that's how I did it all, all in my head.

I hope you got some of them right and I wonder if you could find any other answers to the magic squares.

Now sometimes we know facts and we know a lot of facts, numbers under 10.

And if I knew the fact, six plus three equals nine, I wonder what other facts I can derive from that.

Lets have a think.

There's quite a lot of ways you could go with this.

This is how I've taken this problem.

We know all these facts.

I've been thinking about the powers of ten and making my numbers greater.

So if I know six plus three equals nine, I know 60 plus 30 equals 90.

If I know six plus three equals nine, I know 6,000 plus 3000 equals 9,000.

And if I know that six plus three equals nine, I know that 6,000,000 plus 3,000,000 equals 9,000,000.

They are derived facts.

But there's more that I could tell from knowing six plus three equals nine.

I also know 63 plus 33 equals 99 or 666 plus 333 equals 999.

So remembering them facts that we feel really secure with, helps us when we start dealing with bigger, greater numbers.

Now lets have a quick look at some efficient strategies for addition.

Let's solve this problem.

This word problem efficiently.

Lets read it first thing.

On Monday, 634 people visited the zoo.

The zoo had 374 visitors on Tuesday.

How many people visited the zoo altogether? What known facts may help you solve this problem and how do you know? Now before we jump right into solving it, I want you to think about it.

So you spend a few seconds and you pause the video, and think what known facts you can see in these numbers.

Okay.

Shall we go through it together? We've got a problem again.

I can tell you the answer is 1008 people.

Let me show you two ways of getting there then you can decide which one was more efficient.

Let's look at strategy A.

So, in strategy A, I thought well, I know that six plus three equals nine, so I know that 600 plus 300 equals 900, I know that three plus seven equals 10, so I know that 30 plus 70 equals 100.

And I know that four plus four equals eight.

And all I had to do was add up my 900, 100 and eight and I got 1008.

I kind of like breaking it down to known facts.

Then I had strategy B.

And I know that 63 plus 37, is a number born to 100.

So, if I knew 63 plus 37 equals 100, I'll know that 630 plus 370 equals 1,000.

And I know that four plus four equals eight, so a thousand plus eight, 1008.

Which do you think was more efficient? I'm going with strategy B, but we got the same answer.

Now, something else we can do is some rounding and adjusting for addition.

Sometimes you might hear it, maybe people say that they're making the numbers a bit more friendly.

Let's take a look at this problem.

We've got 23,417 plus 10,986.

Well, 10,986 rounded to the nearest 100 is 11,000.

And using number bonds, well, I know that it's 14 less.

That was quite close, placed around it too.

And I know it's 14 less than 11,000.

So I'm going to use my number line.

I started on 23,417.

I made my jump forward to show that I'm adding 11,000.

And I landed on 24,517.

But, that was not my answer.

I needed to remember take away the 14 that I'd added on to round it up at the beginning.

So the answer to this problem, 23,417 plus 10,996 is actually 24,503.

And quite like that way in rounding and adjusting.

The only thing you need to remember that's super important is to remember to take off the bit you added on at the end.

I'd like you to use the bonding technique that we just talked about to solve this problem.

It's about Dan.

And Dan is preparing for a costume party.

He spends 36.

85 on costume space suit and 23.

18 on some gloves.

How much does Dan spend? Now I think there's one of the numbers there that you should be able to round and use the number line to work out the total.

Pause the video now and have a go.

Hey, welcome back.

So, this is how I've worked out the problem.

I started with my number line.

I popped on my 23.

18.

And then rather than make a jump of 36.

75, I decided to rank 36.

85 up by 15 pence, 37 pound.

So I make a jump of plus 37 pounds.

And that took me all the way to 60 pounds and 18 pence.

But that isn't Dan's total.

Dan's total is 15p less than that.

Remember, because we added it here to make 36.

85 to 37 pounds.

So now we need to take off 15.

8 giving us Dan's total of 60 pound and three pence.

That is how much Dan spent.

It's time for us now to look at some column addition.

The first step towards column addition, make sure that we're secure in partitioning numbers.

Now I've got to use a problem here that we can use to begin to partition.

A space shuttle has two tanks of fuel.

When full, there's 65,091 litres of liquid oxygen and 1,741,154 litres of liquid hydrogen.

And we want to know what is the total volume of fuel carried by the shuttle.

Now, we're going to choose one of them numbers, partition into powers of 10.

Now, I know that the 65,091 comes first in our problem, but I also know, that it doesn't matter which order we do addition in.

So, I'm going to keep the 1,741,154 as it is.

The number I'm going to ask you to partition sorry is 65,091.

I want you to break it down into its powers of 10.

Can you do that for me? Now.

How did you get along? We were taking 65,091 and breaking it down into its powers of 10 and this is what I got.

My powers of 10 were 60,000, 5,000, 90 and one.

I've written it as an equation.

I've written 1,741,154 plus 65,091 is the same as 1,741,154 plus, and these are all powers of 10, 60,000, 5,000, 90 and one.

So now what I'm going to do is take my 1,741,154 and add 60,000, 5,000, 90 and one.

And I'm going to use the number line to do that.

I decided, I add my 5,000 first, then my 60,000 and my 90 and then my one.

Telling me that the total volume of fuel carried by the shuttle was 1,806,245 litres.

Well done.

I like the partitioning and I think it's going to help us in a minute.

We just partitioned one number, what if we partitioned both numbers.

You can see these numbers are on screen.

We could partition both of them.

Which ones represented in the top half of the place value chart? How'd you know? Right.

It the 73,000 number.

We can tell that because there's seven planters in the 10,000 column and there's only one in the one below it.

So our first number is in the top row and our second number is in the bottom row.

And we can add all of them up to find your answer of 92,382.

Just remember, we may have had to some exchanging.

Now, Tom has had to get some column addition to answer an equation.

He's got three numbers, three addends in his equation.

I just want you to take a second and explain what has happened at each stage of his working.

Remember, I'm not asking you to solve the problem, I've already done that, Tom has.

So, what did Tom do best? Well, Tom wrote every number didn't he? And he wrote them so their place value wasn't above each other.

So everything that had the value of the ones was in the ones column, everything that had a tens value was in the tens column and so on.

But Tom also did something rather interesting.

He changed the order of the addends and he put the greatest number first.

Then Tom began adding up his ones, one plus five plus two is eight and he wrote that at the bottom.

Then he added up his tens, look, in the first number he's got zero tens, so he just needed to add seven and four.

The seven and four makes 11.

So you'll notice that the red one is the 10 that has moved over to be 100 and then he's got his 110 in that column.

So now what's for me to do is add four hundreds, zero hundreds, four hundreds and the 100 and he gets 900.

We mustn't just think of that as a nine all the time, we need to remember its place value.

I need to is representing nine hundreds.

After that, he added up his thousands, two, nine and seven and that made 18.

So it means he's got a tens of thousands there as well.

So he puts his eight in his thousands column and he put his one which represents one lots of 10,000 in the 10,000 column, which means he needs to add up one and one, a knowing fact two, we know it represents 10,000 at 10,000 making the answer to this equation, 28,918.

Well done if you can explain every stage of Tom's working.

That shows me that you understand column addition and maybe you're starting to realise, hey, you can fall back on known facts.

So now it's time, do you need to apply some of your addition strategies, your independent learning.

I've prepared for you lots of different equations I need you to find the answer to.

I'd like you to try and find two different strategies each equation and find the answers.

the answer right actually.

And then explain which of your chosen methods you find more efficient and why? So we'll speed here now and navigate your independent tasks.

Welcome back.

How did you get on? How about we have a leak of the answers together.

So, here's a reminder of some of the methods you might have used to solve these equations.

You might've used derived facts, you might have used rounding and adjusting, maybe you partitioned one number, maybe you partitioned all the numbers or maybe you found it was most efficient in that situation to do column addition.

I'd love to hear which one you chose and why.

And here are the answers.

So, we've got the first one, 67,843.

I thought that one was the good opportunity to do some rounding and adjusting.

After that, we have numbers in the millions and our answer is 7,799,819.

What did you find was most efficient facts? I'm thinking nine facts.

Then you had a three addend addition equation.

The answer was 67,203.

What did do for that? Column addition like the example we saw with Tom maybe? How about the next one? The answer is 5,780,001.

I wonder what tactic you chose, which strategy.

And our final answer is 5,011,000.

Well done if you go all of them right.

If you didn't, now you know the answer.

You can go back and try one of the strategies, maybe different strategy and see if you can find the right answer because how we get there is just as important as getting the right answer.

Well done everyone.

Great work in this lesson.

If you'd like to share any of your work with me or everybody at Oak National, you could ask your parents or carer to upload your work to Twitter or other social media tagging @OakNational.

I'll be looking out for it.

Your final job is to go and complete the quiz.

Bye.