Lesson video

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

I hope you have lots of fun.

And here is our lesson outcome.

So our lesson outcome is I can use doubles and near doubles to add three numbers.

For today's lesson, it would be helpful to have some paper, a pencil, and a tens frame encounters.

And if you don't have a tens frame encounters, you can draw your own and use anything instead, like buttons or shells or even coins.

And here are our keywords.

So three keywords today.

You might know what some of these mean already.

The first word is double.

Second word is equation.

And the third word is sum.

And here are their definitions.

So double means to become twice as many.

Double two is equal to four.

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

And the sum means the total when numbers are added together.

In the first part of the lesson, we're going to be adding three numbers together using doubles.

And in the second part of the lesson, we're going to be adding three numbers together using near doubles.

Okay, let's get started.

So in the lesson today, you will meet Izzy and Alex and they're going to help you today and ask you lots of questions too.

Izzy rolls three dice and finds the sum.

So you might remember the word sum from our keyword slide.

And sum means the total when you add numbers together.

So here's the three dice and this is what she rolls.

So she rolls a three, a three and a two.

And she's gotta find the sum, she's gotta add them together.

Now Izzy is saying, "I know double three, so I'm going to do three and three first." Here's our tens frame, so here's three and three and three and three, six.

So three and three equals six.

Now Izzy needs to add two.

So she's got to add two more.

So she's put the two counts in the tens frame.

What would the answer be? Let's have a look.

So three and three make six.

Six add two equals eight.

So the total of three, add three, add two is eight.

The sum of three and three and two is eight.

Alex rolls three dice and finds the sum.

Here are the three dice he rolled.

So he voted two, a three and a two.

Alex is asking, can you see a double? Now it doesn't matter what order the dice are rolled in, doesn't matter if the double's next to each other or not, but you can see there quite clearly, there is a two and a two and two and two of course makes four.

So add the doubles together first and you get four.

And then Alex has to add the three.

So four, add three, make seven.

So two, add two, add three equals seven.

Izzy rolls three dice and finds the sum.

So Izzy has rolled a one, a four, and a four.

Here's Izzy again, "I'm going to add four and four first." So she's going to use the doubles first of all.

So we've got double four, so let's add those together first.

So four and four.

Here are the four and four in tens frame.

Four and four makes eight.

So four and four equals eight.

And then all she's got to do is to add the one.

Eight and one makes nine.

So four, add four, add one makes nine.

So you can see Izzy and Alex are adding the doubles first.

They're looking for the doubles first.

Adding those together first.

Alex rolls three dice and finds the sum.

So he's rolled a five, a five and a three.

"I'm going to do five and five first" says Alex very sensibly.

So here's our tens frame.

And of course a five.

And a five fills the tens frame so you can see quite clearly what the answer is.

So five and five makes 10.

What we've then got to do is to add another tens frame of course, 'cause you've gotta add a three onto it and you should be able to work out the answer.

So 10, add three equals 13.

So five, add five and three equals 13.

There are four sets of dice, so four sets of dice and each set of dice has got three dice in it.

Can you find the sum of each of the sets of dice? So look for the doubles first.

Add them together.

So pause the video, see if you can work out the answers.

Welcome back.

Let's see how you got on.

So let's look at that first set of dice.

So we've got a two, a three and a two.

You're gonna add those doubles first.

So we're looking for double two, two, add two makes four.

All we've got to then do is to add the three.

So four, add three equals seven.

Very well done.

Let's try the next one.

So four, add four, add two.

So four, add four makes eight.

We've got double four makes eight.

And then all we've got to do is to add the two.

So eight, two makes 10.

Fantastic.

So the total of four and four and two is 10.

Lovely.

Alright, next one.

So we've got three and four and three.

Okay, got double three first of all.

So we've got two threes.

Two threes makes six.

Double three is six.

All we've got to then do is to add the four.

So six of four makes 10.

And that last one not too tricky.

Okay, so let's have a look.

So we've got five and five, we've got double five, makes 10, 10 add one makes 11.

Fantastic if you've got all or at least some of those right.

So next we get on to slightly large numbers, so we're not using dice this time.

We're going to be using number cards.

So Izzy chooses three number cards and finds a sum.

Now spot straight away hopefully the two of the numbers are the same.

So we're still using doubles.

So Izzy says I'm going to double seven first.

And there we are.

So we've got our tens frames there.

A seven, add another seven, seven add seven equals 14, add one more 14, add one equals 15.

So seven add seven and one equals 15.

Okay, so Alex chooses three number cards and finds the sum.

So he's chosen three number cards.

You've got three, six, and six.

So this one you're gonna have a go at trying to do on your own.

So again, pause the video, think about you are going to add together first, think about those doubles and see if you can work out the sum of Alex's three number cards.

Right, let's see if you got it right.

Okay, so Alex is asking you what should I add first? Well hopefully you added the six and the six first.

We're looking for our doubles of course, aren't we? So six add six makes 12, six doubled equals 12.

And then what has Alex got to add next? Well he's still got to add three of course.

So 12, add three makes 15.

So six and six and three equals 15.

So doubles are a really good way of working out an answer quite quickly and quite efficiently.

So next, Izzy chooses three number cards and finds the sum.

So she's chosen eight.

Eight and a mystery number.

Ah, okay, so this time Izzy's going to give us the sum.

She's found the sum already.

She knows what the total of the three numbers are.

We've got to use that to work out the missing number.

So she's telling us the sum is 19, what is the missing number? How would you go about finding out the missing number so we know the sum of the three cards.

How would we work out what the missing number is? Here are our tens frames.

Izzy's pert an eight and an eight in the tens frames already.

And she's worked out what double eight is.

So eight at eight is 16.

What would she do next? What would she do next? How would she work out the answer? About 16 and our mystery number makes 19.

We know the sum of the three numbers is 19 and eight to eight makes 16.

So this mystery number added onto 16 makes it 19.

So what is the number? So let's fill out tens frame up to 19.

Okay, all we added, how many green counters have we got? Three, so our mystery number, our missing number is three.

Eight add eight add three equals 19.

And here is another check.

See how you get on with this one.

So Alex chooses three number cards and finds the sum.

He's got seven, a seven and a missing number, a mystery number and he says the sum is 16.

What is the missing number? So think about how you're gonna work that one out.

Pause the video again, see if you can come up with the answer.

Let's see how you got on.

So Alex is also going to use tens frames.

He started off by doubling seven.

So seven add to seven equals 14 and he knows that 14 add this mystery number makes 16 'cause of course he knows the sum already, he's told us the sum.

So what is this mystery number going to be? Add on one, add on two and we get to 16.

The mystery number, our missing number is two.

Seven add seven add two equals 16.

Very well done if you manage to work out the missing number.

Next, Izzy chooses three number cards and finds the sum.

You may have spotted already that two of the cards, she's not revealing what they're worth.

So there's two cards, we dunno what they're worth and a two, but she tells us the sum of the numbers is 12.

So when you add the three numbers together, you get 12.

The two missing numbers have the same value.

Now that's really important.

What are those numbers? How would you work out the answer? Well she's telling us that we add one of the numbers to the other number and add two, we get 12.

Let's put two in the tens frame where they would equal 12, where if we're counting up to 12, the 12 will go.

Okay, that leaves a whole tens frame over here, which is empty at the moment.

And the two numbers, when we add two to them it makes 12.

So the two numbers must add up to make 10.

So our two mystery numbers in total make 10.

So what number doubles to equal 10? We've got one mystery number, add the other mystery number, makes 10.

They're both the same value, they must be five and five.

So our mystery numbers are five and five.

So five add five, add two makes 12.

Izzy chooses three number cards and finds the sum.

So she's chosen three and two mystery numbers.

She's not revealing what those numbers are worth, what the value of those numbers are, but she is going to give you some information to help you work out the answer.

So she says the sum of the three numbers is nine.

The two missing numbers have the same value.

What are they? Pause the video, see if you can work out the answer.

Good luck.

Did you manage to solve it? Did you get an answer? Let's find at if you are right.

So Izzy is telling us that the sum of the three numbers is nine.

So let's put our three in our tens frame so it makes nine, we know the sum is nine.

So we don't want to fill up the tens frame completely 'cause we're not going all the way to 10.

So I'm gonna leave one space there 'cause we're not filling up 10 but we are going up to nine and we know that one of the numbers, add the other number.

Add three makes nine.

What do the two numbers add up to make in total? What's left? What is missing in our tens frame? It's a six.

So six and three makes nine.

We now know that the numbers added together make six and we know the numbers have the same value.

So what number doubled makes six? Well it must be three and three.

Three and three makes six.

Three and three and three makes nine.

Very well done if you manage to get the right answer.

Let's move on to our practise tasks.

So the first practise task, you're going to use doubles to help you complete the equations.

So for some of them you are just going to be adding the numbers together to find a sum.

Don't forget to use doubles to help you work out the answer.

For some of them you're looking for a missing number within the equation, not the sum but one of the numbers that adds up to make the sum.

And for our second task, you're going to complete each equation using numbers of the same value.

So the two numbers you put into each equation must be worth the same.

Okay, good luck with those.

So pause the video, have a go at the practise tasks and I'll see you a bit later.

Let's see how you got on.

So here are the answers for the first part of task A, sort of careful with those missing numbers.

I'm gonna check to see whether you've got them right and here are the answers for the second part, okay, which is quite tricky in places particularly balancing some of those equations.

Let's move on to part two of the lesson.

So part two of the lesson is going to be adding three numbers together using near doubles.

So we're still using doubles to some extent, but we're now changing them into near doubles.

So doubles can be used to work out near doubles.

So Izzy rolls two dice and finds the sum.

She's rolled a four and a five.

Izzy says I can use four add four to help me.

Izzy knows what double four is so she can use that to help her work out what four add five is.

Four add five is equal to four add four add one says Alex, we've got four and the five is made out of a four and a one.

So to work out the answer to four add five, we can do four, add four, add one.

Here we go, there is four and four add one.

And if we merge them together, you can see there, the four add one makes the five, and here is a tens frame showing four add five.

You quite clearly see that the five is one more than the four.

So four add four is eight, four add five is nine.

Just one more, four add five says Alex is equal to four add four add one.

Alex rolls a three dice this time, three dice and finds the sum.

So Alex has rolled a four, a five, and a one.

Alex is telling us I can use four add four.

Four add four makes eight, four add five makes nine, add one more, so nine add one makes 10.

So Izzy rolls three dice and finds the sum.

So Izzy rolled a four, a two and a three.

Izzy says "I can use three add three." So she knows what double three is, you can use that to help her work out the sum.

Now if you look really carefully, actually there are two sets of near doubles.

We've got two and a three.

We can add those together or we could do the four and three.

But Izzy says it's probably most sensible to start with the bigger numbers because then you've only got to add the smaller number at the end.

So Izzy starts off by doing three, add three, three add three makes six.

And if we put four and three into the tens frames, we can see that four and three is like three add three, add one, three add four makes seven.

If we add two on seven, which is three and four, add two equals nine.

Alex rolls three dice and finds the sum.

So Alex has rolled a five, a three, and a six.

So look carefully.

Can you spot the two numbers that are nearly, nearly a double? Alex is going to tell us I can use five add five.

So five and six are a near double.

They're only one away from each other.

So Alex can use five add five to help him work out five add six, five add five of course equals 10.

Five add six is the same as five add five add one.

So five add six makes 11.

What do you still have to add? Still got to add the three.

There's our three, 11 add three equals 14.

So five add six, add three equals 14.

And here is a task for you to try on your own.

So work out the sum of each group of dice.

Don't forget to use near doubles to help you work out the answers.

And here's Izzy to give you a bit of advice.

Start with five, add five.

So use five add five to help you work out the answers.

So pause the video, see if you can work out the answers.

Let's see how you got on.

So our first set of dice, we've got five and six add two.

So don't forget what Izzy said, Izzy said use a five add five first of all.

So five add five is 10, five add six must be 11, another two would be 13.

So five add six add two makes 13.

It doesn't matter what order the dice come in.

So five, add one, add six.

We can still change, change the dice around, change the order the dice are in and we can still do five, add six, add one.

So five add five makes ten, five add six makes 11 and one more must be 12.

The last one is a little bit trickier.

We've got a four add five and a six.

And again we've got two sets of near doubles there.

You could do four add five first of all, or you could do five add six first of all.

So you could do five add six, add four makes 15.

So five doubled is 10, five add six makes 11, add four makes a 15.

Or you could have done four doubled.

Four doubled makes eight, add one more would be nine.

So four add five makes nine and then add the six makes 15, one may might be slightly easier than the other.

Izzy is saying there are two ways to use near doubles here.

So there might be more than one way sometimes, but sometimes it's looking for the best way of working out the answer.

So Izzy chooses three number cards and finds a sum.

She's got a six, a seven, and a two.

So six and six makes 12.

Here's tens frames to help us work out the answer.

So six add six makes 12.

Six add seven must be 13.

It's the same as six add six add one, add two more, lemme get to our answer.

So 13, which is six or seven, add two makes 15.

Alex chooses three number cards and finds the sum.

Okay, so slightly trickier numbers, slightly bigger numbers eight add four, add seven.

Alex is saying I'll use seven add seven to help me work out the answer.

So seven add seven makes 14.

So seven add eight is the same as seven add seven add one.

Here's tens frames to show us as well to help us see the answer.

Seven add eight makes 15 and then you've got to add the four, say 15, add four would be 19.

And here's an activity which you can do on your own.

Here's is Izzy and Izzy saying start with six, add six.

So you may want to use tens frames to help you work out the answer.

You may want to jot down some numbers, some workings out to try and help you work out the answer.

Don't just try and do it all in your head, but how would you work out the answers to those? So pause the video and see if you can work out the answers.

Good luck.

Welcome back.

Let's see whether you got them right.

So the first one is seven add six add five.

So probably you start off with six add six.

So six and six makes 12.

So you can use that to help you work out six add seven.

So if six add six is 12, six add seven must be 13.

All you've then got to do is to add the five.

So six add seven, add five makes 18 altogether.

Ah, and Izzy said could you start with five add five? So instead of doing six add seven, first of all, you could've started with five add six.

Interesting.

So there's more than one way of doing it.

So our number sentence would look like this.

So five add six add seven.

So we're just adding numbers in a different order.

So five add five makes 10, five add six must be 11, add the seven would be 18.

And our second set number cards, we've got a seven, a three and a six, and two of the numbers are actually the same, aren't they? We've still got a seven and a six, this time we're adding a three instead of adding a five.

So six, add seven, add three makes 16.

Very well done if you managed to get those ones right.

Oh look at that.

Izzy is asking us another question as well.

What do you know about seven add three? Well seven, add three you might know of course is a number pair that totals 10.

That's a different strategy you could use instead.

And here is another task for you to try on your own.

So it says which equations could have been answered using doubles or near doubles.

So there's four equations, which ones could have been answered using doubles or near doubles? They all add up to the same sum.

They've all got the same answer 17 or which ones could you have used doubles for or near doubles for and which ones couldn't you? So pause the video, see if you can mark it out.

Welcome back.

Let's see how you got on.

So the first question is seven, add three add seven makes 17.

We can quite clearly see there is a double there.

Seven add seven.

So we could have used a double to work out the answer.

The next one says six add nine add two.

Is there a double there? There is not.

Is there a near double there? Are there two numbers? Just one away from each other.

There aren't either.

So we couldn't have used doubles or near doubles to work out the answer.

Next calculation is five add three add nine.

So are the two numbers the same? No they're not.

They can't use doubles to work out the answer.

Are there two numbers that are just one away from each other? No, there are not.

So we couldn't have used near doubles either.

And the last one is seven, add four, add six.

Is there a set of doubles? There is not.

Is there a set of near doubles? Yes, there is, seven and six are only one away from each other.

So we've got there a set of near doubles.

Fantastic if you've got those ones right and we're on to our final tasks.

So task one, you're going to be using near doubles to find the missing number.

So look carefully.

Sometimes it's the sum missing.

Sometimes it's one of the numbers that are making the sum that is missing.

So see if you can work out the answers.

So use near doubles to find the missing answer.

And the second task, you're going to be using these number cards.

You've got the number cards one all the way up to nine.

You've got as many of those cards as you want.

So there's not just one one and not just one two.

You've got as many as you want.

So there are several fives, several sixes, several sevens.

You can use as many as you want.

How many different ways can you make 13 using three cards? You must use doubles or near doubles to make each sum.

So when you come to make 13 in your calculation, you must either have two numbers, the same or two numbers that are only one away from each other.

Good luck with those two tasks.

And here are the answers.

So this is the answer to task one.

Use near doubles to find the missing number.

So have a good look, see if you've got the missing numbers right.

And here are some possible answers to task two.

So it's not all the answers, but it's some of them.

You might have got some of these.

So you may have used doubles, so you may have got two add two add nine makes 13.

You may have used near doubles.

So two, add three, add eight makes 13.

So well done if you got some of those answers too.

Well done on today's lesson, you should now be experts on using doubles and near doubles to help you add three numbers together.

And here's our summary.

So the sum is the total when numbers are added together and you can use doubles and near doubles to help you work out a sum.

Thank you for working so hard today, and I hope to see you again soon.