Lesson video

Hello, my name is Mr. Goldie and welcome to today's maths lesson.

I'm sure you're going to have lots of fun.

And here is our lesson outcome.

So I can choose the best strategy to add three small numbers together.

And here are our keywords for today's lesson.

So the keywords are addend, commutative, equation, sum.

An addend is a number added to another.

Commutative means the same answer is reached even if the order of addends is changed.

An equation is a number sentence that uses =, the equals sign.

The sum is the total when numbers are added together.

And here's our lesson outlined.

So two parts of our lesson today.

The first part is using known facts to add three addends, and the second part is using known facts to find missing addends.

In this lesson you'll meet Izzy and Alex and they'll be helping you today and asking you some tricky questions too.

So Izzy and Alex are keen to practise their addition.

They know lots of number facts.

Izzy says, "I like using doubles." Alex says, "I know all the number pairs that total 10." And today's lesson, we'll be using doubles and number pairs that total 10.

But the really key thing is, is knowing when to use the right strategy.

So addition is commutative.

That means it can be done in any order.

Here's number cards.

So we've got two, and four, and five.

Izzy says, "I could find the sum "by doing 2 + 4 + 5." Alex says, "5 + 4 + 2 would also give the same answer." Find the sum of the three addends.

How would you add together the three dice? What would you do? Izzy says, "Use doubles.

"4 + 4 is equal to 8 "and 8 + 3 is equal to 11." So the sum of the three dice, she's saying, is 11.

Remember, addition is commutative.

You can add in any order.

So we could do the 4 + 4 first.

That makes eight.

Then 8 + 3 = 11.

How would you add together 2 + 5 + 5? How do you find the sum? If we know that double five is 10, we can quickly work out 5 + 5.

5 + 5 = 10.

And all we have to do is to add two.

10 + 2 = 12.

Let's look at three different dice.

So this time we've got a six, a one, and a six.

How would we add together those three dice? Again, Izzy's saying, "Use doubles." What could you do? So we could do 6 + 6.

Double six is 12.

6 + 6 = 12.

And then add the one.

So 12 + 1 = 13.

How would you find the sum of seven, four and seven? "Doubles are really useful," says Izzy.

Remember, Izzy likes doubles.

7 + 7 is equal to 14.

Then 14 + 4 is equal to 18.

So we could add 7 + 7 first.

Double seven equals 14.

And then add four.

14 + 4 = 18.

How would you add together three, and eight, and eight.

Let's start off with 8 + 8.

Double eight equals 16.

Then add three.

16 + 3 = 19.

What about 9 + 1 + 9? 9 + 9 = 18.

So we could use doubles.

18 + 1 = 19.

There is another way of finding the sum as well.

What else could you spot about those three numbers? 9 + 1 = 10.

And 10 + 9 = 19.

It's the same sum of course, we still get the same answer.

We just had a different way of working it out.

How would you find the sum? How would you add together 5 + 2 + 6? Here's Izzy.

Izzy says, "You can also use near doubles." You might remember that near doubles are when two numbers are only one away from each other.

There's only a difference of one between two numbers.

So five and six are only one away from each other.

There's a difference of one.

So Izzy says, "I know that 5 + 5 = 10 "and I can use that to calculate 5 + 6.

So if 5 + 5 = 10, if double five equals 10, then 5 + 6 must make 11.

5 + 6 = 11.

Then 11 + 2 = 13.

How would you add together two, and seven, and six? Again we can use near doubles.

Seven and six are near doubles.

6 + 6, double six equals 12.

6 + 7 is just one more.

6 + 7 = 13.

And then 13 + 2 = 15.

How would you add together 7 + 1 + 8? Well, 7 + 8 are a near double.

7 + 7 makes 14.

7 + 8 = 15.

And then all we have to do is to add the one.

15 + 1 = 16.

How would you find the sum of seven, four, and six? Well you could use near doubles again.

Seven and six are near doubles.

Is there an easier way of working out the answer? Here's Alex.

Alex says, "I can see a number pair to 10." Two of those numbers add together to make 10.

Can you see what they are? They are 6 + 4.

6 + 4 = 10.

And then all we have to do is add the seven.

10 + 7 = 17.

Look at the next one.

3 + 7 + 8.

Again, there's a near double there isn't there? 7 + 8 is a near double.

But is there an easier way to add up the three numbers? Yes there is.

You've got a number pair to 10.

So 7 + 3 = 10, and then 10 + 8 = 18.

What about our last one? So we've got four, two, and eight.

Can you spot a number pair to 10? Well, we have got eight and two, 8 + 2 = 10, and then add four equals 14.

10 + 4 = 14.

How would you find the sum? Sometimes you can add two addends, then you have a number pair to 10.

Let's have a look at that one there.

So we've got one, five, and four.

So Alex is saying you could actually add 4 + 1 together first.

4 + 1 = 5, and then you can add the five.

5 + 5 = 10.

So sometimes two of the numbers add together and they help you make a number pair to 10.

Let's look at that one.

Can you spot two numbers that add together to give you a number pair to 10? Well, we've got 3 + 2.

3 + 2 = 5.

Three and two is also a near double of course.

So 3 + 2 = 5, and then we add the five.

5 + 5 = 10.

How would you find the sum of six and four and six? Well Izzy says "I would double six then add four." Remember Izzy likes doubles.

But Alex, who likes number pairs to 10, says, "I would do 6 + 4 first "because they total 10." Which method is easier? What do you think? So 6 + 4 + 6.

So we could do number pairs to 10.

We could do 6 + 4 = 10 and then 10 + 6 = 16.

That seems quite straightforward, doesn't it? It doesn't seem too tricky.

The other way we could try is, we could do 6 + 6 first of all.

So 6 + 6 = 12, double six equals 12 and then 12 + 4 = 16.

Both of those are actually good strategies.

It depends on what you find easier.

Now Izzy's already said she prefers doubles so she might use the double strategy.

Alex says he prefers the number pairs that total 10 strategy.

So he might have used that one instead.

It doesn't actually matter for those particular numbers.

They're both pretty good methods.

How would you work out the sum? So you've got two sets of number cards there, how would you add them together? "Can you use doubles or near doubles?", says Izzy No, I don't think you can.

There's no doubles in those two sets of number cards.

Alex says, "Can you see any number pairs that total 10?" Are there any number pairs that total 10? I don't think there are, Alex.

Sometimes it is easier to start with the biggest number.

So sometimes that is the best strategy to use.

Just find the biggest number, start with that first.

Because it's easier to start with bigger number and add on the smaller numbers.

How would you work out the sum? So 2 + 4 + 9.

We start with the nine and then we probably add the next biggest number, which is four.

So 9 + 4 = 13.

13 + 2 = 15.

It's not a particularly easy calculation but it's probably the best way to do that one.

And then how would you add together 3 + 8 + 1? Again, no doubles, no number pairs to 10, so we start with the biggest number.

The biggest number is eight.

We have the next biggest number, which is three.

So 8 + 3 is 11.

Not a particularly easy calculation but then all we have to do is to add the one.

11 + 1 = 12.

Now have a look at these sets of number cards.

How would you find the sum? What is the easiest way of finding the sum of those three number cards? So pause the video, have a good think about it.

You may want to jot down some answers, and then we'll check to see whether you were right.

So the first set of number cards is six and two and eight.

How would you add together 6 + 2 + 8? Probably easiest to start with 8 + 2.

8 + 2 is a number pair that totals 10.

8 + 2 = 10.

10 + 6 = 16.

What about our second set of number cards? We've got a six, a seven and a six.

Probably the easiest way to do it is Izzy's favourite method, use doubles.

So 6 + 6 = 12.

12 + 7 = 19.

And what about the last set of number cards? We've got an eight, a seven and a five.

How would you add together the three numbers? Well, you could use near doubles.

Eight and seven are a near double.

And eight's also the biggest number, isn't it? So let's start with eight and seven, or seven and eight because it doesn't matter which order we add them in.

7 + 7 = 14.

Double seven equals 14.

7 + 8 = 15.

And then 15 + 5 = 20.

So well done if you've got those ones correct.

And let's have a go trying to find the sum of these bar models.

So here's Alex.

Alex is saying, "Which method would you use to find the sum?" And here's Izzy.

Izzy's saying, "Will you use number pairs to 10, doubles, or will you use another method?" How will you work out the answers? So our first bar model, we've got the numbers one, seven and nine.

So how would you add them together? Probably do 9 + 1, which is a number pair to 10.

9 + 1 = 10 and 10 + 7 = 17.

Our next bar model, we've got a double, so we've got 6 + 6.

6 + 6 = 12.

And then add the five.

12 + 5 = 17.

And our last bar model, how would you add together the three numbers? Well, we haven't got a number pair that makes 10.

We haven't got a double, but we have got a near double.

So we've got 4 + 5.

It's probably easiest to start with those first.

So 4 + 4 = 8.

Double four equals eight.

4 + 5 = 9.

So we could do 5 + 4 = 9, and then 9 + 2 = 11.

Izzy says there are other ways to use doubles too.

She says, "Sometimes two addends "add together to make a double." So a bit like Alex said earlier, sometimes two addends add together to make a number pair to 10.

Izzy's saying, "Sometimes two addends "add together to make a double." Let's look at our first bar model.

So we've got the numbers eight, three and five.

Can you spot anything? Well you might have spotted, that actually, 5 + 3 = 8.

5 + 3 = 8, and then all we'd have to do is double eight.

So eight add the other eight equals 16.

What about our next bar model? So we got the numbers four, eight and four.

Well, 4 + 4 = 8.

8 + 8 = 16.

And what about our last bar model? Do you spot anything about that one? Well you've got a double actually there.

But if you add those doubles together, 3 + 3 = 6, and then 6 + 6 = 12.

Now here's one for you to try on your own.

Find the sum of this bar model.

So pause the video, have a think about how you'd find the sum of the three numbers.

What did you spot about the three numbers? What we've got there, is seven and a seven, haven't we? Double seven is 14.

So 7 + 7 = 14 and then 14 + 5 = 19.

Let's try another one.

So find the sum of this bar model.

So pause the video and see if you can work out the sum of the three addends.

How did you get on? Did you find the answer? Well, you might have spotted a near double, but there's an easier way of working out the answer.

So we've actually got there, a number pair that totals 10.

7 + 3 = 10.

And then all we have to do is to add the eight.

10 + 8 = 18.

That's probably an easier way than doing the near doubles.

And here's your task.

You've got to sort the equations.

How would you find the answer? So you may actually want to find the answers as well, and actually write down what the answers are, but how would you work out the answers? So we've got here in our first one, pairs to 10.

We've got an example of an equation where there's a pair to 10.

So 6 + 4 + 3.

6 + 4 makes 10.

6 + 4 = 10.

And then + 3 would be 13.

And then under double we've got an example of a double.

We've got 4 + 4 + 3.

So we've got an example of a double there.

4 + 4.

In our last column we've got near double or other method.

So if you work out the answer in a way that isn't a double or a number pair that totals 10, then it would go in this column here.

And here are the equations which you are going to be sorting.

So you can cut them up and then put them in the right columns.

So good luck with that task.

Think really carefully and see if you can find some of those sums as well.

So pause the video and have a go at that task.

How did you get on? Did you manage to sort all of the equations? Did you manage to find some of the sums as well? Very well done if you did.

And here are our answers.

So we've got there, examples of number pairs that total 10.

So 3 + 6 + 4 is a number pair that totals 10 'cause there's a 6 + 4 in there.

And in our middle column there we've got interesting one.

At the top we've got 5 + 9 + 4 = 18.

Is there a double there? Well actually there is, if you look really carefully, 5 + 4 = 9, and then 9 + 9 = 18.

So sometimes it isn't obvious straight away.

And then in our near double or other methods, we've got 16 = 7 + 8 + 1.

We've got that example of a near double.

7 + 8 is a near double.

So only one away from each other.

The two numbers only have a difference of one.

Now you may have answered questions using a different strategy.

You may have a favourite strategy you might rely on a bit more than others, and that's okay as long as you are finding the answer efficiently and you are looking really carefully at the numbers and thinking about the best method.

And let's move on to our second part of the lesson.

So the second part of the lesson is using known facts to find missing addends.

You can use known facts to find a missing addend.

So here in our bar model we've got a missing addend.

So one of the numbers that adds together that makes the sum is missing.

Alex is saying, "How could you work out the missing number?" So we've got a two and an eight and a 17 as the sum.

The three numbers add to make 17.

What do you know about eight and two? 8 + 2 = 10.

What do you need to add to 10 to make 17? 10 add what makes 17? The answer is seven, so the missing addend is seven.

So 2 + 8 = 10.

And add seven would equal 17.

Use number facts to work out the missing addend.

So this time we've got a five and a five and our sum is 16, and we're trying to work out the missing addend.

What method could you use to solve this? 5 + 5 = 10.

10 add what number equals 16? What do you have to add to 10 to get to 16? We'd have to add six.

So our missing addend is six.

5 + 5 + 6 = 16.

You can use doubles to find a missing addend.

Add the doubles, then work out the missing number.

So our first bar model, we've got 6 + something + 6 = 14.

Our sum is 14.

6 + 6 = 12.

12 add what number equals 14? You'd have to add a two.

So our missing addend is two.

What about the other bar model? We've got a four and a four as two of the addends and 10 as the sum.

Again we could use doubles, 4 + 4 = 8.

What would you have to add to eight to get to 10, to get to our sum? What's the missing addend? It must be two.

4 + 2 + 4 = 10.

Find the missing addend.

Can you use doubles? Can you use number pairs to 10? So pause the video and see if you can work out the answer.

What is the missing addend? Let's see how you got on.

Did you manage to find the answer? Well you might have used doubles.

Hopefully you did.

The double eight, 8 + 8 = 16.

Then what do you have to add to 16 to get 17? 16 add what number equals 17? We only have to add one.

So our missing addend is one.

Well done if you managed to find the missing addend.

Let's try another one.

Again, Izzy's saying, "Can you use doubles?" Alex is saying, "Can you use number pairs to 10?" Again, pause the video.

Can you work out the missing addend? Did you manage to find the answer this time? Let's have a look.

So you might have spotted there's a number pair that totals 10.

9 + 1 = 10.

And all you have to do is to work out what do you have to add to 10 to get 18, to get our sum? 10 add what number equals 18? The missing number is eight.

Very well done if you got that one right.

And here's another bar model.

Can you work out the missing addend? Can you use doubles this time? Can you use number pairs to 10? Again, pause the video.

Can you work out the missing addend? Did you work out the answer? Let's have a look.

We've got a number pair to 10.

6 + 4 = 10.

Then all you have to do is work out what you have to add to 10 to get to 17.

10 add what number equals 17? The answer is seven.

And again, very well done if you solved that one.

Sometimes one of the pair to 10 could be missing.

So Alex is saying, "I know that 10 + 8 = 18." So one of the addends is eight and the sum is 18.

10 + 8 = 18.

That means the other two addends must add up to make 10.

Five add the missing number is equal to 10.

So what do you have to add to five to get 10? And here are some tens frames to help you.

So eight has already been put into the tens frame and we are left with 10.

And we know one of the numbers is five.

So we've got there all the way up to 18.

We've added all the way up to 18 in our bar model.

One of the numbers is five, one of the numbers is eight.

What is the other missing number? Must be five.

5 + 5 = 10.

Our missing number is five.

5 + 5 = 10.

10 + 8 = 18.

And again, one of the pair to 10 is missing in this calculation.

And here's Alex, and Alex is saying, "I know that 10 + 9 = 19." So we've got a nine as one of our addends and our sum is 19.

That means the other two addends must add up to make 10.

And again we can use tens frames to help us understand the answer.

So we've got there, the tens frames with the nine in the second tens frame, filling it up all the way to 19.

And we're left with an empty tens frame at the start to represent our 10.

We know one of the numbers already is six.

So what number added to six equals 10? Here's our six.

What's the missing number? Six add what makes 10? Must be four.

Four and six are a number pair that totals 10.

So our missing number is four.

Find the missing addend.

Here's Alex.

Alex is saying, "Use number pairs to 10 "to help you work out the missing number." So have a good look at that bar model.

Can you work out the missing addend? Pause the video.

Can you work out what it is? Let's have a look, see whether you were right.

So our sum is 12, and we've got two of the addends, nine and two and we've got a missing addend.

Those three numbers add together to make 12.

You might have spotted one of the addends is two, and you should know that 10 + 2 = 12.

That means the other two addends must add up to total 10.

One of them is nine, so the other one must be one.

9 + 1 = 10.

9 + 1 + 2 = 12.

Fantastic work if you got that one right.

Sometimes it could be the doubles that are missing.

So Izzy's saying, "The two missing numbers "have the same value.

"Can you work out what they are?" It's a bit of a tricky one, this one.

So let's use tens frames to help us.

Let's think about filling up up the tens frame to 17.

Where would we put our three? Well if we arrange them like that, we haven't quite filled the tens frames.

We've still got three at the end.

So we should have filled up to the point where 17 should end, and that leaves us with 14 empty spaces on our tens frames.

14 + 3 = 17.

That means our two numbers must add up to make 14.

Now Izzy's told us the two missing numbers have the same value.

So what number when you double it equals 14? Here's seven and another seven.

7 + 7 = 14.

So our two missing addends are seven and seven.

Let's look at this bar model here.

So we've got 10 as the sum and four is one of the addends, and two of the addends are missing.

But again, Izzy is telling us that two missing numbers have the same value.

Can you work out what they are? So you may want to use a tens frame.

You may want to draw the bar model out.

You may want to have just a think about it.

Can you try and work out what the two missing addends are? And remember they have the same value, they've gotta be worth the same.

And when they add together to four they make 10.

So pause the video.

Can you work out the missing addends? And welcome back.

Let's see whether you got it right.

So again, we could use a tens frame.

Now luckily the sum here is 10.

So the three numbers add up to make 10.

So let's put four in our tens frame already and we can see straight away what number is left.

So the two numbers must add up to make it six.

So 6 + 4 = 10.

That means our two missing numbers add up to make six.

One of the missing numbers, add the other missing number, equals six.

The two missing numbers have the same value.

So we're thinking about a number that we double to get to six.

What number doubled makes six? Let's use our tens frames.

We've got three and three.

So our missing numbers are three and three.

3 + 3 + 4 = 10.

Well done if you've got the solution.

Well done if you've got the right answer.

To find different ways to complete the bar model, use different numbers each time.

This is another one for you to try on your own.

You can try any numbers at all, but they've got to add together to make 16.

So three addends that add together to make 16.

So there are lots and lots of different ways you could find the answer.

Izzy's saying, "What doubles could you use?" Alex is saying, "What about pairs that total 10?" So pause the video, give yourself a little bit of time to think about how many different ways you could make 16.

Let's see how you got on.

So Izzy's saying, to make 16, you could do 6 + 6 + 4.

Double six equals 12, add four equals 16.

Alex, because he likes number pairs to 10, says, "You could do 7 + 3 = 10, and then add the six to get to 16.

So lots and lots of different solutions.

Very well done if you managed to find one way.

If you managed to find more than one way, absolutely brilliant.

Very well done.

And here's task B.

You're going to find different ways to complete the bar models.

So one of the bar models has a sum of 13.

One has a sum of 15, one has a sum of 18.

Can you find ways that use number pairs that total 10? Can you find a way that uses doubles? Can you find a way that uses near doubles? Can you use the same addend three times? So the same three numbers add up to make the sum.

So when you're making the sum of 13, could you use a number pair the totals 10 and another number to make 13.

Could you use a pair of doubles and another number to make 13? Could you use some near doubles and another number to get to 13? Could you use the same addend three times? So pause the video and have a go at your task.

Let's see how you got on.

So there are lots and lots of different answers.

So here are just some of them.

You may have come up with different answers of your own.

So we've got for 13, we've got a way you could use number pairs to 10.

So you could have done 6 + 4 + 3.

To make 13 a different way, you could have used doubles.

So you could have used 6 + 6, which makes 12, and then add one more, which would equal 13.

You could have used near doubles.

So you could have used 6 + 5, they're a near double.

5 + 5 makes 10, 5 + 6 must be 11, add two more would equal 13.

Now you can't use the same addend three times to make 13, but you could do it for 15.

So 5 + 5 + 5 = 15.

You could also do it for 18.

So 6 + 6 + 6 = 18.

So very well done if you found lots and lots of different ways of making those different sums. And here is our summary.

Now there are several different strategies you can use when you are adding together three addends efficiently.

So when you're thinking about different ways you can add them together.

You could be looking for number pairs that total 10.

You could be looking for doubles, you could be looking for near doubles, you could be looking for the largest number.

Now the strategy you use depends on the addends that you are adding.

So you've gotta look really carefully at the numbers and think about which strategy it would be best to use, and don't just use the same strategy every single time.

Well done in today's lesson.

Excellent work.