Lesson video

Hi there.

My name is Ms. Cone.

I am really excited to be learning with you today as we continue to think about addition and subtraction within 10.

If you're ready, let's get going.

Welcome to this lesson within the unit addition and subtraction facts within 10.

In this lesson, the outcome is that you'll be able to use knowledge of doubles to calculate near doubles.

Let's look at our key words.

I'm going to say them and I'd like you to say them back to me.

My turn, double, your turn.

My turn, near double, your turn.

My turn, addends, your turn.

I wonder if you can listen really carefully to hear these words used throughout our lesson today.

Our lesson today is about using knowledge of doubles to calculate near doubles, and we have two parts to our lesson.

In the first part, we're going to be calculating using near doubles, and in the second part, we're going to be finding out whether it's a near double or not a near double.

If you are ready, let's get started with our first lesson cycle.

In our lesson today, we're going to be working with Sam and Jacob and they're going to be helping us with our learning.

Let's start by remembering the doubling facts we know and we're going to show these on a 10 frame.

One plus m is equal to m.

Hopefully you know that one plus one is equal to two.

Can you say that with me? One plus one is equal to two.

Well done, what comes next? Two plus something is equal to something.

Can you tell me? Great job, we know that two plus two is equal to four.

I wonder what double's going to come next.

Three, what is double three? Well, we know that three plus three is equal to six.

Great job if you said that, I think I can see a pattern now.

The next number we're going to look at the double of is four.

Four plus m is equal to m.

Can you tell me, that's right.

Four plus four is equal to eight.

And finally, what's our last factor going to be? Five plus m is equal to m.

That's right, five plus five is equal to 10.

These are the doubling facts that we know When we add two equal addends, we are doubling.

So double five is the same as saying five plus five.

Sam is solving this addition problem using her 10 frame.

Can you see the addition problem? That's right, it's three plus four is equal to something.

Sam's going to use her counters to solve the problem.

She's going to start with having three counters and then she's going to add on four more there.

We can see she's started with three and she added four more.

If she looks at these counters that we've highlighted, she can see three and three.

Can you see three and three? There we go, we have three and three more.

So the addends at the start of both our problems are the same.

We can see three plus four is equal to something and we know our double fact.

We know that three plus three is equal to six.

Now if we think about the addend four, well it's one more than three, so that must mean that we can use three plus three or double three to help us solve three plus four.

The sum the answer is going to be one more because one of the addends is one more.

What is one more than six? Well, three plus three is equal to six.

One more than six is seven says some.

So three plus four is equal to seven.

We can talk about three plus four as a near double.

Sam's going to use that idea to find the missing sum in a different equation.

So this time we have four plus five is equal to something.

I wonder what double Sam might use.

We representing the first addend, which is four and then we've represented the second addend, which is five.

Can you see a double factor now? We can see double four or four plus four in the 10 frame that Sam's made.

So if we look at those counters, we can see four and four.

Sam can see that double fact and she says that she can use four plus four or double four to help because the sum is going to be one more.

Four plus four is equal to eight, those addends.

The first addends are the same.

Four and four are the same.

But our second addends, the five is one more than four.

So if we know that four plus four is equal eight, we know the sum of four plus five is going to be one more because five is one more.

So because one more than eight is nine.

Four plus five is going to be equal to nine.

Jacob used a different method to Sam to find the sum.

So we've still got the same equation.

Four plus five is equal to something.

I wonder what Jacob's going to do, let's have a look.

Jacob uses a different double fact to the one Sam used.

Remember, Sam used four plus four to find out four plus five, but Jacob is going to use five plus five or double five to help him solve four plus five.

Let's see how he does that.

Jacob knows that five plus five is equal to 10.

He knows that double five is 10.

Now this time the sum is going to be one less, says Jacob.

Let's see why, in these examples, the first addend is one less.

So five plus five is equal to 10 with four plus five, the first addend is one less.

The second addends are both five, so they are both the same because one of the addends is one less, we need to find one less for the sum.

So we know the sum of five and five is 10.

So one less than 10 is nine.

So four plus five is equal to nine.

That's a really nice method Jacob, I wonder which one you preferred.

Time to check your understanding, using your 10 frame and some counters find the sum, explain to a friend how you could use a near double.

So the equation this time is three plus two is equal to m.

Think about what near double you could use, pause the video here and have a go.

Welcome back, how did you get on? There are two different ways that we could have answered this.

We could have used double two or two plus two.

I know that two plus two is equal to four.

Three plus two is a near double because three is one more than two.

If two plus two is equal to four, then three plus two must be equal to five because one of the addends is one more or we could have looked at it the other way.

You might have said that I know that double three or three plus three is equal to six, but this time we've got three plus two.

One of the addends is one less, so sum must be one less as well.

The sum was six for three plus three is equal to six.

So the sum has to be one less, one less than six is five.

Well done if you explained in either of those ways.

So this time sum and Jacob are looking at a problem and talking about which known double fact they could use to find the sum.

The equation, the problem is four plus three is equal to m.

We dunno what the sum is.

I wonder what strategies Sam and Jacob are going to use.

Jacob says, I will use double three or three plus three is equal to six.

One of the addends is one less so the sum will be one more.

We can see that for three plus three is equal to six.

One of the addends in that example is one less than four plus three.

So therefore the sum, the answer to four plus three will be one more, good thinking Jacob.

This addend is one less.

So the sum will be one more.

One more than six is seven.

So we think the sum will be seven.

Let's see what Sam has to say.

Sam is going to use double four or four plus four is equal to eight.

One of the addends in Sam's example is one more.

So the sum will be one the less.

In Sam's example we can see that the second adend in four plus four is equal to eight is one more.

So that means because that ad end is one more, the answer will be one less.

One less than eight is seven, so both of them agree.

Jacob says that four plus three is equal to seven and he says that they both found the sum, which they did, but they used different double facts and it's okay to use different double facts.

Sam said you used the double fact before and I used the double after.

So you can use the doubles either side, it doesn't matter.

Time to check your understanding.

Which of these double facts would help to solve this near double problem? What would we have to do to find the sum? So the equation is two plus three is equal to m.

Option A for the double fact that would help you find the near double is five plus five is equal to 10.

B is two plus two is equal to four and C is three plus three is equal to six.

Which of those do you think would help you answering two plus three is equal to m? And what do you have to do to find the sum? Pause the video here and have a go.

And welcome back.

What did you think, did you agree with your friend? Sam says that two plus two is equal to four would be a good double factor use to find two plus three is equal to m.

And Sam says that she would have to add one to the sum.

She could also use three plus three is equal to six.

She would then have to subtract one from the sum.

So we know that two plus three is equal to five.

Well done if you used either of those doubles to answer that problem.

Jacob however, is reminding us that actually we don't always need to use our double facts.

He remembered his number pairs to five.

He knew that five can be partitioned into two and three, so two plus three is equal to five.

So sometimes you don't even need to use your double facts.

Well done Jacob.

Time for your first task, I would like you to use the double facts that you know to find the missing sum.

So A, I would like you to use four plus four is equal to m to find five plus four.

You have B and C as well.

Remember you can use a 10 frame and counters to help you if you need to, but really think about which double fact you're using to find the near double pause the video here and have a go at that task.

Welcome back, how did you get on? Did you carefully think about which double fact you needed to work out the missing sum? Let's have a look at some answers.

We know that double four is equal to eight, four plus four is equal to eight and we can use that to find five plus four.

One of the addends is one more.

So therefore the sum had to be one more.

One more than eight is nine.

Five plus four is equal to nine.

For the second one, double two is equal to four and in the second one, two plus three, one of the addends is one more.

So the sum had to be one more.

One more than four is five, and finally five plus five or double five is equal to 10.

This time one of the addends in four plus five was one less.

So the sum had to be one less, one less than 10 is nine.

So four plus five is equal to nine.

Well done if you spotted those near doubles and found the sums. Let's move on to our second learning cycle, near double or not a near double.

Sam and Jacob are using their knowledge of near doubles to solve this problem.

I'm going to read it to you.

Listen carefully for the numbers that you can hear.

Seven children are in the dinner hall.

Four children have school dinners and the rest have sandwiches.

How many children have sandwiches? I wonder what the equation will be for this problem.

There are seven children in total, says Sam, so seven is the whole and we can show that on a bar model.

So in this case the whole is shown at the long bar at the top.

Sam goes on to say that we know that four children have hot dinners and so this is one of the parts.

So we can show that in our bar model as filling in one of the parts as four.

We don't know the other part, but we can write an equation of four plus m is equal to seven.

Four plus something is equal to seven.

I wonder how we can use our doubles to solve this problem.

Sam says that she knows that double four or four plus four is equal to eight.

Now the sum in our case is not eight, so it's not quite right, but I think it's going to help us.

We know that four plus four is equal to eight, but eight is one too many.

Remember there are seven children in the dinner hall.

So we know that the missing part must be one less than four.

Seven is one less than eight.

So our missing parts must be one less than four.

One less than four is three.

So the missing part must be three.

Four plus three is equal to seven.

That must mean that three children have sandwiches for their lunch.

Four children have dinners and three children have sandwiches.

Now the following day the numbers are different.

Let's listen to the problem.

Six children are in the dinner hall.

Three children have school dinners and the rest have sandwiches.

How many children have sandwiches? I wonder what the wholes and parts are this time.

Jacob says there are six children in total.

Six is the whole.

Now remember in our bar model, the six is going to go at the top.

We know that three children have hot dinners, so this is one of our parts.

I wonder what the missing part is.

We can also write this as an equation.

Three plus something is equal to six.

I wonder what that missing number is.

Jacob says, well I know that double three or three plus three is equal to six, so sometimes our double fats can be super helpful to find an answer.

So three plus something isn't actually a near double at all.

It's just a double, well spotted if you spotted that, three plus three is equal to six, we can fill in our bar model and we know that three children have hot dinners and three children have sandwiches.

Jacob has solved a different problem and draws this bar model.

As you can see, he's been a little bit cheeky because he has covered up one of the numbers in his bar model.

Can you see the counter that he's used and he's going to ask Sam to work out which number is missing? Well, Sam says, I can see that five is the whole and two is a part, so you can write that as two plus is equal to five.

Can you see the five and the two in the bar model? I wonder what the missing part is.

Sam says that she knows that double two will not be enough.

Two plus two is equal to four.

Now what's our whole? Ah yes, the whole is five, which isn't enough if we're using two plus two, but she says she can use this to help her.

How might she do that? If we know that the whole that we need is one more, it's five.

The missing addend must be one more as well.

One more than two is three.

So if two plus two is equal to four, the near double, two plus three, must be equal to five.

So which number has Jacob covered up? That's right, three is the missing part.

Three plus two is equal to five.

Sam now gets her own back and creates her own missing number problem.

Which number has she covered up? Can you see where it's covered on the bar model? Jacob says that he can see that six is the whole and five is a part and he's written an equation to show that.

Five plus m is equal to six.

I wonder how he's going to work this out? Now here you can see that this is not a near double.

I wonder why he says that.

Well he knows that five is one less than six, so he just knows that one will be the missing part.

Five plus one is equal to six.

So it can't be a near double because five and one aren't close to each other.

They're not one apart.

They're quite a few apart and he reminds us that we've learned lots of strategies to help us add and subtract so far.

Sometimes we need to choose the best strategy for each problem that we face.

So when you see a word problem or when you see an equation, have a think.

Which strategy do you know that will be the best one to use? Time to check your understanding.

What is the missing number here? Can you tell a friend how you worked it out? Have a good look at that bar model.

What is the whole? Pause the video here and have a go.

How did you get on, did you find the missing part? Well we know that nine is the whole and four is one of the addends or one of the parts and we can think about this as something plus four is equal to nine.

I wonder if I know something that can help me with that.

I know that double four or four plus four is equal to eight, now eight is not nine, but we can think about this, well we know eight is one less than nine.

So I know that the missing number must be one more than four.

One more than four is five.

So the missing number must be five.

Five plus four is equal to nine.

Well done if you said the missing parts was five.

Time for another check of your understanding.

What's the missing number in this bar model? Can you tell a friend how you worked it out? Pause the video here and have a go.

Welcome back, how did you get on? So this time I can think of this as two plus m is equal to eight.

Double two is only four and double six is too many.

So I can't use a near double in this case.

This one is not a good one for using a near double, but I know that two less than an even number is the even number before, so I can count back two from eight.

Six is the even number before eight.

So six must be the missing number, two plus six is equal to eight.

Well done if that's what you said.

Time for another task.

Tick the problems where a near double can be used to help find the missing number, then find the missing number.

So your first job is to decide which of these are good to use for a near double.

So for example, A, we have a part of four and a part of three and we don't know what the whole is.

I can think of as four plus three is equal to mm.

Would a near double be good for that one? Once you've decided which of these are good to use a near double for, find the missing numbers.

Good luck with your task, pause the video here.

Welcome back, how did you get on? So for A, four and three are very close to one another.

So you could use a near double here.

Four plus three is equal to seven.

I knew that three plus three was equal to six and I knew that four is one more than three.

So my sum had to be one more.

B could also be found using a near double, five is equal to three plus something, three plus two is equal to five.

In this case I knew that double three was six and five is one less than six.

So my missing part on my missing addend had to be one less.

D could also be found using a near double, nine is equal to something plus four, five plus four is equal to nine.

I knew that double four was eight, so therefore my addend had to be one more than four.

C would not be a useful one to look at your doubles.

But we know that three is one less than four, so the missing part had to be one.

And for E, I used my pairs to 10 here, I know that 10 can be partitioned into eight and two, so the missing parts had to be eight.

Well done if you found all of those missing parts and wholes.

We've come to the end of our lesson and I really hope you've enjoyed it as much as I have.

Let's summarise our learning.

We know that we can use our double facts to help us calculate near doubles.

So if two plus two is equal to four, then two plus three is equal to one more than four because one of the addends is one more.

Remember, this is just one of many strategies we can use for addition and subtraction.

Thanks so much for learning with me today and I look forward to seeing you again soon, bye.