Lesson video

Hello everyone, and welcome to Maths with Ms. Dobrowolski.

Today, we'll be looking at adding with near doubles.

So, looking at our lesson agenda first we have near doubles-adjusting by adding on.

Then we'll have our talk task.

Then we'll have near doubles-adjusting by subtracting, followed by your independent task.

For today's lesson you will need a pencil and a notebook.

If you don't have these items, pause the video now and go get them.

Super.

So, first let's practise our doubles.

So the way we do this, is we're going to read from left to right.

So, in the green we have the number, and in the pink we have the double.

So I would say double one is two.

Double two is four.

Double three is six.

So we're going to do that, but together okay? So you're going to start from one with me, and we're going to go through our doubles till 20.

Okay, so here we go.

Double one is two.

Double two is four.

Double three is six.

Double four is eight.

Double five is 10.

Double six is 12.

Double seven is 14.

Double eight is 16.

Double nine is 18.

Double 10 is 20.

Good job, everyone.

Okay, so we have the builders really hard at work.

And it looks like they've used 20 plus 21 bricks.

So I want to know how many bricks have they used altogether? Well, I can use my near doubles strategy for this equation.

So let's have a look at how I do that.

So let's use the near double strategy to solve 20 plus 21.

Let's double 20 and add on one, because 21 is only one more than 20.

So we can double 20 and add on one.

Okay, so first I have my first 20.

10, 20, okay.

And now, if I know double two is four, then I know double 20 is 40.

So here's is another.

10, 20, 30, 40, good.

Now, we can just add the one from 21.

You have to adjust that part.

So then, 40 plus one is equal to 41.

So 20 plus 21 is equal to 41.

Now, 20 plus 21 is equal to 20 plus 20 plus one, because we partitioned 21 into 20 and one, when we made our near double.

We could also use the same strategy if perhaps we had this equation.

We could also double 20 and then add on one.

That's because addition is commutative.

That means it doesn't matter what order you add the numbers in, as long as you add them, 'cause you will get the same answer.

So, we could also have 20 plus one plus 20.

And that would be the same.

So let's try the near double strategy again with this equation.

I have 22 plus 20.

Okay, so let's double 20 and then add on two because 22 is only two more than 20.

So we'll double 20 and add on two, okay.

So, here's 20.

Now, if I know double two is four, then I know double 20 is 40, okay.

Now we need to adjust.

We need to add the two from 22.

So 20 plus 22 is equal to 42.

10, 20, 30, 40, one, two, 42.

So that means 20 plus 22 is equal to 20 plus 20 plus two.

Because 20 and two are equal to 22.

Now, we could also use the same strategy if we had 20 plus 22, if these were reversed.

And that's because addition is commutative.

It doesn't matter what order you add the numbers in.

They will always equal the same value.

So let's try this strategy again of adding near doubles with 31 plus 30.

Mm? What near doubles will I use? Well, I know that 31 is only one away from 30, so I'm going to double 30 and then add on one.

So here's 30, and I'm only putting it sideways 'cause otherwise you won't be able to see it if I put it like this.

My camera's too small.

So here we have 30.

So let's see.

Double three is six.

So double 30 must be 60, excellent.

And now we need to add on one from 31.

So let's add on one.

So 60 plus one is equal to 61.

That means 31 plus 30 plus must also be equal to, 30 plus 30 plus one.

And that's because 30 and one were partitioned and are still equal to 31.

It is now time for your talk task.

In this talk task, I'd like you to choose an equation and find a doubles fact that will help you solve the equation.

And the doubles fact that will help you are here on the side.

So, I have the equation 50 plus 51.

I think 50 plus 50 can help us.

I can double 50 and then add on one.

So 50 plus 50, well, I know five plus five is 10.

So 50 plus 50 is equal to 100.

100 plus one is equal to 101.

Your turn.

Pause the video, complete your talk task, and resume when you're ready.

Great job everyone.

So let's review 41 plus 40.

You can double 40 and add on one, which is equal to 81.

20 plus 21, double 20 and add on one, which is equal to 41.

22 plus 20, double 20, add on two, which is equal to 42.

30 plus 31, double 30, add on one, which is equal to 61.

11 plus 10, double 10, add on one, which is equal to 21.

32 plus 30.

You can double 30 and add on two, which is equal to 62 40 plus 42.

You can double 40 and add on two, which is equal to 82.

50 plus 52.

You can double 50 and add on two, which is equal to 102.

43 plus 40.

You can double 40 and add on three, which is equal to 83.

20 plus 22.

You can double 20 and add on two, which is equal to 42.

12 plus 10.

You can double 10 and add on two, which is equal to 22.

Great job.

Great! So let's add on.

So before, when we were looking at our equations, we were always doubling and then adding what we needed to add, whatever we needed to add on.

So 20 plus 22.

We would double 20 and add on two.

But now we're going to take a look at some equations where you have to adjust with subtraction.

So you still need to double your numbers, but you don't add on.

You adjust by subtracting.

So for example, here we have 20 plus 19.

When we double 19.

Oh, sorry, when we doubled 20, okay, we'll have 20 plus 20, and then we'll still have to adjust.

Now, 19 is one less than 20.

So let me show you how I double and adjust when I have to adjust with subtraction.

So, how can we solve this equation? Well, we can still use the near double strategy.

What we can do, is double 20, and then subtract one.

Because if we double 20 we're actually going over by one.

We're adding one more than we're supposed to.

So we'll have to adjust and subtract one.

Okay, so let's double 20.

I know, two doubled is four.

So 20 doubled must be 40, okay.

And now we can adjust by subtracting one back.

So 40 minus one is equal to 39.

So that must mean 20 plus 19 is equal to 20 plus 20 minus one.

So here we have the equation 18 plus 20.

I can also use the near double strategy to solve because I know 18 is a near double to 20.

So I will double 20, and then subtract two back.

So, we start with 20 and now we need to double 20.

If I'm going to double two as four, then I know double 20 is 40.

Now, we can adjust by subtracting one, two, two back.

And now we have 38.

So 18 plus 20 is equal to 38.

18 plus 20 is then equal to 20 plus 20 minus two.

And both sides of this equation are equal because 20 minus two is equal to 18.

Okay, let's try one more.

30 plus 29.

Let's use the near double strategy.

Well, I know that I can double 30 because 29 is only one less than 30.

So I'm going to double 30, and then I'll have to subtract one back because 29 is one less than 30.

So I have to subtract one back.

Okay, let's first start with 30.

Now, I need to double 30.

Well, I know that double three is six, so that must mean double 30 is equal to 60.

And now remember that we can adjust by subtracting one back.

So 60 minus one.

Well, I know 10 minus one is equal to nine.

So 60 minus one must be equal to 59.

Excellent.

So that must mean 30 plus 29 is really equal to 30 plus 30 minus one.

And these equations are equal because 30 minus one is the same as 29.

So these equations are equal.

Great! Ready for your independent task? Here we go.

So for your independent task, I'd like you to solve each equation using the near double strategy.

And remember to use your doubles fact to help you calculate mentally.

Now, don't forget, sometimes you'll have to double and add on, and sometimes you have to double and then adjust through subtraction.

So as usual, I'll do the first one, so you're super clear on what to do.

So, I have the equation 30 plus 29.

I'm going to double 30.

So three doubled is six.

So that means 30 doubled is 60.

Now, I need to adjust by subtracting one, because 29 is one less than 30.

Okay, 60 minus one.

10 minus one is equal to nine.

So 60 minus one must be equal to 59.

Super! Now it's your turn.

Pause the video, resume when you're ready to go over the answers.

Good luck.

Great, so let's go over the answers.

Here we had 32 plus 30.

So I doubled 30 and then added two, equal to 62.

30 plus 28.

Doubled 30, and then subtracted two, which is equal to 58.

50 plus 51.

I doubled 50, added on one, which is equal to 101.

48 plus 50.

I doubled 50 then had to subtract two, which is equal to 98.

50 plus 52.

I doubled 50, and then added on two, which is equal to 102.

40 plus 39.

You should have doubled 40, and then subtracted one, which is equal to 79.

38 plus 40.

You should have doubled 40 and subtracted two, which is equal to 78.

40 plus 42.

You should have doubled 40, added on two, which is equal to 82.

19 plus 20.

You should have doubled 20 and then subtracted one, which is equal to 39.

22 plus 20.

You should have doubled 20 and added on two, which is equal to 42.

21 plus 20.

You should have doubled 20 added on one, which is equal to 41.

And nine plus 10.

You should have doubled 10 and then subtract one, which is equal to 19.

11 plus 10.

Double 10, add on one, which is equal to 21.

10 plus 12.

Double 10, add on two, which is equal to 22.

That was a mouthful.

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As always, don't forget to complete your final quiz.

Good job, everyone.

That was some really good work today.

I really hope to see you next time.

Bye.