Lesson video

Hello everybody and welcome back to another math lesson with me, Mrs. Pochciol.

As always, I'm hoping that we're gonna learn lots of new things and have lots of fun.

So let's get started.

This lesson is called, "Use near-doubles within 10" And it's from the unit, "Secure fluency of addition and subtraction facts within 10." By the end of this lesson, you should be able to use near-doubles within 10.

Let's have a look at this lesson's keywords.

Double, doubling, near-double.

Let's practise them.

My turn, double, your turn.

My turn, doubling, your turn.

My turn, near-double, your turn.

Fantastic.

Now we know how to say them, let's learn how to use them.

Here is this lesson's outline.

The first part of our lesson, we're going to represent near-doubles within 10.

And in the second part of our lesson, we're going to use those near-doubles to solve problems within 10.

Let's get started.

Represent near-doubles within 10.

In this lesson, you're going to meet Izzy and Alex.

They're gonna help us with our learning today.

Izzy and Alex are playing another addition game to help with their quick recall of facts.

Izzy pulls out 3 cubes from her bowl.

Alex pulls out 3 cubes from his bowl and they add their numbers together.

Alex represents this using an equation.

3 + 3 is equal to something.

He works out that 3 + 3 is equal to 6.

Izzy has remembered that 3 + 3 is double 3, and they know that double 3 is 6.

Well done guys.

This time Izzy now pulls out 3 cubes and Alex pulls out 4 cubes.

Again, they represent this using an equation.

3 + 4 is equal to something.

Alex remembers that double 3 was 6.

So now 3 + 4 is just one more.

They lay their cubes out to see if they're correct.

Izzy places her 3 cubes.

Alex then places his 3 cubes, and he was right, there's one more that needs to be added.

So we know that 3+4 must be equal to 7.

Well done Alex and Izzy using what you already know to help you to solve a new fact.

So let's have a look at this one.

What are Izzy and Alex adding together here? They've laid their cubes out for you to see.

Hmm, what would the equation be? Once you've written the equation, what doubling fact can you see to help you to solve this? So pause this video, write the equation, and then work out which doubling fact you could use to help you to find out what it is equal to.

Come on back once you've had a go to see how you've got on.

Welcome back.

Let's see how we've got on then.

So let's have a look at our cubes.

We can see that we have 4 cubes and underneath we have 5 cubes.

That tells me that this must be 4 + 5 is equal to something.

Hmm, so what double can we see? Well done Izzy.

Izzy has spotted double 4, or 4 + 4.

We've circled them there so we can use this to help us.

4 + 4, or double 4 is equal to 8.

So if we are doing 4 + 5, what do we need to do? What change will we need to make? We know that 4 + 5 is one more.

4 + 4 is equal to 8, but we're adding one more.

Look, the addend in the double is 4, but the addend in our problem is 5 so we need to add one more.

One more than 8 is 9.

So 4 + 5 must be equal to 9.

Well done if you've got that correct and managed to spot and use that double.

So let's have a look at this a little bit further.

So if the addends in an expression have a difference of one, we can say that this is a near-double.

So we can see that 5 is one more than 4, so 4 + 5 is a near-double.

We can use a double fact to make changes in order to solve it.

The first way we can solve this is we can double the smaller addend and add one to find the sum.

So in this one we could double 4.

Double 4 is 8.

Let's use our representation to see this.

Double 4 is 8, but we're now adding 5 to that addend of 4, not 4.

So we need to add one more, which would give us the sum of 9.

Another way we can do this is we could double the larger addend and subtract one to find the sum.

So our larger addend in 4 + 5 is 5.

So let's double 5.

5 + 5 is equal to 10.

Let's represent this with our cubes.

This time we have doubled a larger number, so instead of doing 4 + 5, our double is 5 + 5, so we know that we have one additional cube, so we're going to have to subtract one.

So let's subtract one from that double and that would give us the sum of 9.

So we can see that 4 + 5 must be equal to 9.

Two different ways that you could approach this near-double problem.

So let's have a look at this one then, 2 + 3.

I know that two and 3 have a difference of one so this must be a near-double problem.

Which double facts could we use to help to solve this problem? What changes would we need to make to find the sum? Pause this video and have a go see if you can find both ways that you could solve this near-double problem.

Which doubling facts would you use and what changes would you have to make? Come on back once you've had a go.

Welcome back.

So let's have a look at the two different ways you may have solved this.

The first way you may have solved this is by doubling the smaller addend.

In this near-double problem, the smaller addend is 2.

So let's double 2.

We know that double two is 4, but our addends aren't both 2.

In this problem, it's 2 and 3, so we need to add one more.

That's the change we need to make to find the sum.

So we're adding one more, which would give me 5.

Hmm, let's use the other way to see if we get the same sum.

Then we will know if we're correct.

The other way that you could have solved this is by using the larger addend.

So let's double the larger addend, which is 3.

We know that double 3 is 6, but what change are we going to have to make this time? My double is 3 + 3 or double 3, but the equation we're trying to solve is 2 + 3.

So that must mean we need to subtract one from the double to give us our final sum.

Let's subtract one and that leaves us with 5.

Both of our ways have given us the sum of 5.

So 2 + 3 must be equal to 5.

Well done if you got that correct, and well done if you managed to solve this using both strategies.

Alex and Izzy now represent a near-double calculation using counters.

What can we see? Hmm, what can we see? I can see red counters and blue counters.

Izzy can see double 3 is 6.

So she's looking at the red counters.

We can see 3 and 3, which we know double 3 is 6.

Alex can also see one more which is equal to 7.

So we can say double 3 is 6, add one is 7.

So what calculation have we shown here? Hmm, what calculation have they solved using this strategy? Izzy moves the blue counter to the left hand side so she can see 4 + 3 is equal to 7.

Could that blue counter go anywhere else? Alex moves the counter this side so he can now see 3 + 4 is equal to 7.

We have used the same method to solve two different calculations.

Why can Izzy and Alex see two different calculations but still have the same sum? Hmm, that's because the addends have just been swapped around and we know that addition is commutative.

So 4 + 3 and 3 + 4 both equal to 7.

Well done if you spotted that.

Izzy now represents 4 + 3 is equal to 7, but by doubling the larger addend, because remember we can double the smaller addend, which we've just done, or we can double the larger addend.

So here you can see that she has got double 4.

So double 4 can also help her to solve 3 + 4 or 4 + 3.

Double 4 is 8.

So what change will they have to make to find the sum to 4 + 3? We know that doubling the larger addend means that we have to subtract one to find the sum.

So double 4 is 8, subtract one is 7.

So we can see that 4 + 3 or 3 + 4 is equal to 7.

Right then, over to you then.

Here are two more representations that Alex and Izzy have shown using their counters.

Can you use the representation to complete the sentence to explain what is happening? Once you've completed those explanations, could you then write the equation that has been solved underneath? So pause this video.

First of all, complete the explanation sentence, and then try and work out what equation is being solved.

Pause this video and come on back once you've had a go to see how you've got on.

Welcome back.

Let's see how you've got on.

So in this first representation I can see that we have one red counter on the left and one red counter on the right so I know that we have doubled one.

Double one is two, and I've added one more counter, the blue counter, so that means the sum is 3.

Double one is two, add one is 3.

Well done if you've got that one.

So let's have a look at this other representation.

I can see that I'm subtracting one here so I know that this is my larger addend that's been doubled.

So I can see two red counters on the left and two red counters on the right.

So double two is 4, subtract one because we've doubled the larger addend, and that has given me 3.

Well done if you completed those explanations.

Now, let's have a look what equation has been solved.

Both of these representations show the same sum, they both equal to 3, but in the first one we can see that the smaller addend has been doubled, which we know is one.

So my equation must be 1 + 2 is equal to 3 because they've doubled one and added one more.

So what other equation may have been solved using these representations? Remember addition is commutative, and I know in the second representation they have doubled the larger addend.

So we know that the larger addend is 2, so they may have also solved 2 + 1 is equal to 3.

All they've done is swapped the addends around.

Well done if you got those correct.

Okay then, over to you with task A.

So, can you complete these sentences to explain these near-double representations? So just like we've been practising , you can see that there are some that have doubled the smaller addend, so we are adding one extra, and there are some where we have doubled the larger addend and have subtracted one.

Pause this video, complete the explanations underneath and then come on back to see how you get on.

Welcome back.

Let's see how you've got on.

So, in the first one we can see that we have 3 red counters on the left and 3 red counters on the right.

So we know that this is double 3, and we know that double 3 is 6.

We then added one more, which means the sum is 7.

Well done if you got that correct.

Let's have a look at the next one.

Double 2 is 4.

We've got our two red cans on the left and two red counters on the right.

We've added one more, so the sum must be 5.

Let's have a look at our first subtraction one.

So what have we doubled here? I can see that I've got 5 on the left and 5 on the right.

So we must have doubled 5.

Double 5 is 10.

We subtract one which leaves us with 9.

Well done if you've got that one.

And finally I can see 3 red counters on the left and 3 red counters on the right.

So we must have doubled 3.

We know that double 3 is 6 and we have subtracted one, which has left us with 5.

Well done for completing that task.

We've done lots of representing of near-doubles now within 10 so let's start to use this to solve some problems. Let's look at the second part of our lesson, using near-doubles to solve problems within 10.

Let's get started.

So, Alex and Izzy are using what they've learned about near-doubles to help them to work out what the missing number is from this bar model.

We can see that 9 is the whole and 5 is the part.

So we are looking for that missing part.

Alex has remembered that double 5 is 10, but the whole is one less so we know that that part can't be 5.

So let's take that double, 5 + 5 is equal to 10, but our problem is 5 + something is equal to 9, and we know that that is one less.

So what change can we make to that double to help us to solve what the missing part would be? Hmm, if 5 + 5 is equal to 10, we know that 5 + something is one less.

So what must be that missing addend? The missing part must be one less than 5.

So the missing part must be 4.

Well done Izzy, a really good spot there, and well done to you if you spotted that 4 would be the missing part.

Let's see if you can use Alex and Izzy's method to help you to solve this one.

What is the missing number from this bar model? What information do we know that can help us? Pause this video and have a go at calculating what the missing part would be.

Come on back once you've had a go to see how you get on.

Welcome back.

Let's see if your strategy was the same as Alex and Izzy's.

Izzy knows that double 2 is 4, but we know that the whole is one more than 4 so the addend must be more than 2.

She writes down the equation for the double to help her.

2 + 2 is equal to 4.

This problem is 2 + something is equal to 5.

We can see that the whole is one more.

So what does that mean for the missing addend? Alex has noticed that the missing addend must be one more than 2, which is 3, so 3 must be our missing part.

2 + 3 is equal to 5.

Well done if you managed to find that 3 was the missing part.

Alex and Izzy now continue with their recalling of key facts using their addition game.

Izzy now pulls out 5 cubes and Alex pulls out 6 cubes.

How many cubes do they pull out all together? Hmm.

Izzy notices that the sum will be more than 10.

Izzy thinks that she can still use the near-doubles within 10 to help her to solve this problem.

Is she correct? Hmm, let's see what she's thinking.

Izzy knows that 6 is a part and 5 is a part, so she's finding the whole.

She knows that double 5 is 10 because she's done lots of practise with her doubles.

So what would 5 + 6 be? She knows that that would be one more because 6 is one more than 5.

She's going to use this knowledge to help her to solve it.

One more than 10 is 11.

So 5 + 6 must be equal to 11.

Well done Izzy, I love how you use that method even though your sum was going to be larger than 10.

Let's recap some of the near-doubles that Alex and Izzy have solved so far.

1 + 2, can we remember? We know that double one is two, so one more will give me 3.

Well done if you've got that one.

2 + 3, I'm gonna use the larger double this time.

Double 3 is 6 but I need to subtract one 'cause I'm only adding two, would give me 5.

And finally 3 + 4.

I'm gonna double 3, which I know is 6, and this is 4 so it's one more which is 7.

Well done if you solved those quickfire equations.

Ooh, Alex has noticed something.

Alex has noticed that all the near-double problems are odd.

Hmm, why is that? 3, 5 and 7.

Yes, they're all odd.

Why do we think that is? Izzy is explaining, we know that all doubles are even so one more or one less will always be odd.

Well done Izzy, a lovely explanation.

Could you show us a little bit more? Izzy's going to show us using her counters.

Double one is 2, plus one more is 3.

2 is the even number because it's a double.

One more makes it odd.

Double 2 is 4, an even number, but I'm adding one more because my addend is 3.

One more makes it 5 and an odd number.

That extra one on the top that's on its own, it hasn't got its pair.

And finally double 3 is 6, an even number.

We add one more because we are adding 4 not 3, and that makes it an odd number.

Well done Izzy, thank you so much for explaining that.

A really good thing that you've noticed there, Alex.

Well done.

Right then, over to you.

The children are describing a number using double facts.

Can you use the children's description to say what their whole is? Alex, Andeep and Jacob have all described a number for you to work out.

Izzy has given you her sum.

Could you help Izzy by describing using your doubling facts, the sum of 7.

Pause this video, see if you can work out what the boys' wholes are and then see if you can help Izzy by writing your own description.

Come on back once you've had a go to see how you've got on.

Welcome back.

I hope you had lots of fun working out what those missing wholes were.

Let's start with Alex.

"My sum is one more than double 4." Hmm, so we know that double 4 is 8, so double 4 is 8, one more is 9.

Is your number 9, Alex? Let's have a look.

Well done if you got 9.

Let's look at Andeep's.

"My sum is one less than double 3." We know that double 3 is 6 and one less than 6 is 5.

Andeep, is your number 5? Yes, well done if you've got that one.

And finally, Jacob.

"My sum is one more than double 1." Hmm, double 1 is 2.

One more than 2 is 3.

Jacob, is your number 3? It is, well done Jacob.

Now, let's have a look at Izzy.

Let's see how Izzy described the sum of 7.

Two different ways you may have got.

One more than double 3, because double 3 is 6 and we know that one more is 7.

Or you might have described it as one less than double 4 because double 4 is 8 and one less is 7.

Well done if you got either or if you got both of those descriptions.

Okay then, over to you for task B.

So task B has got two parts.

The first part is using your knowledge of doubles to solve some near-doubles problems. So you can see here that we've given you the double factor at the top.

Can you then use that knowledge to help you solve the problems below? Once you've done that, question two is to use your knowledge of near-doubles to describe these numbers to your partner.

So just like the children were doing earlier in our check, can you describe these numbers using double facts? Describe one to your partner and see if they can guess which number you are describing.

Pause this video and have a go at question one and question two, and come on back once you've had a go.

Welcome back.

Let's have a look at question one then.

Using our knowledge of doubles to solve some near-double problems. So we know that 2 + 2 is equal to 4.

So 2 + 3, I can see that that's one more than the double, so that must be 5.

3 + 2, I can see that they are the same addends, they have just been swapped around and we know that if we swap the addends around, the sum remains the same.

So that must also be equal to 5.

1 + 2.

I can see that this is one less than my double because one of my addends has changed from 2 to 1, which is one less.

So that must be equal to 3.

And again, my addends have swapped over, but my sum remains the same.

So I know that 2 + 1 must also be equal, so 3.

Well done if you got those.

Let's have a look what near-double problems we can solve using double 4.

So we know that 4 + 4 is equal to 8.

So 4 + 5 must be one more because my addend is not 4 anymore, it's 5.

One more than 8 is 9.

4 + 5 is equal to 9.

And again, we can see that they are the same addends, they have just been swapped over, so the sum will remain the same.

So if 4 + 5 is equal to 9, 5 + 4 must also be equal to 9.

And 3 + 4, I can see that one of my addends is one less.

So I need to find one less than 8, which is 7.

3 + 4 is equal to 7.

And again, 4 + 3, it's the same addends, they've just been swapped over.

So if 3 + 4 is equal to 7, 4 + 3 must also be equal to 7.

Well done if you got that correct.

Let's have a look at question two.

Question two.

You were describing using your double facts, one of these numbers to your partner.

So let's see how Izzy and Alex did this.

Izzy says that her sum is one less than double 5.

Alex knows that double 5 is 10, so one less is 9.

Izzy is describing the sum of 9.

Well done Alex, you've got that correct.

Well done for all of your hard work today and using those doubling facts to solve some near doubling problems. Let's have a look at what we've learned today.

We can use double facts to solve near-double calculations.

We can double the smaller addend and add one.

So if we know that 4 + 4 is equal to 8, then we know that 4 + 5 is one more than 8, which is 9.

Or we can double the larger addend and subtract one.

So an example here is if we know that 5 + 5 or double 5 is 10, we know that 4 + 5 is one less than 10, which is 9.

Thank you again for all of your hard work and I can't wait to see you again soon for some more maths learning.

Goodbye.