Lesson video

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

Today we'll be adding two digit numbers with regrouping.

So let's have a look at our lesson agenda.

First, we'll be adding by partitioning the second number only followed by our top task.

Then we'll be adding by partitioning both numbers, followed by your independent task.

For this 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 partitioning the second number only.

As you can see, I'm trying to add 27 plus 14.

How can I add this? So I'm only partitioning the second number, the 14.

Well, in order to help me do this, I'm going to use a number line.

Great, so how can we solve this equation by partition the second number, the 14? Well, I'm going to use this number line to help me.

I will add the 10s first.

So I know that my first number is 27, so that's where I'm going to start and I'm going to add my 10s.

I can see that 27 plus 14, 14 has one 10.

So I know 20 plus 10 is equal to 30.

Then I know 27 plus 10 is equal to 37.

So I jump to 37.

And that's plus 10, excellent.

Now I need to add my ones.

So I will use the make 10 strategy.

I know that seven plus three is equal to 10.

So that means I can partition the four into three and one.

So first you need to add three.

Well, if I know seven plus three is equal to 10, then I know 37 plus three is equal to 40.

And again, that's plus three.

If I was to count up, I should get the same answer, one, two, three, good.

And let's not forget to add the second part of the partition, the one.

So I jump 40 plus one is equal to 41.

So that must mean 27 plus 10 plus three plus one is equal to 27 plus 14.

These equations are equal because the parts equal the same whole.

10 plus three is equal to 13 plus one, 13, and 13 plus one is equal to 14.

All I did was partition 14.

So now I have another equation, 57 plus 34.

How can we solve this equation by partitioning the second number, 34? Well, I know that I'm going to start at 57, because that's the first number I'm adding.

And I will add the 10s first.

So if I know that 34 has three 10s, because there's a three in the 10s place, I need to add 30 or three 10s.

Now if I know that 50 plus 30 is equal to 80, then I know 57 plus 30 is equal to 87.

So I need to jump all the way to 87.

That's a big jump, remember, because I added 30.

Okay, now I'm going to add the ones, but I'm going to use my make 10 strategy.

So, I have seven ones and I need to add four, how can I make a 10 if I already have seven ones? Well, I know seven plus three is equal to 10.

So that means I need to partition this four into three, and one, three plus one is four.

So first if I know that seven plus three is equal to 10, then I know that 87 plus three is equal to 90.

So I jump to 90, I added three, one, two, three.

And let's not forget to add the other part of the partition, which is one, and 90 plus one is equal to 91.

So I started with 57 plus 34, and this is how I partitioned 34.

Really, what I did was 57 plus 30, which was equal to 87 plus three plus one.

And both sides of the equation are equal because the parts equal the same whole, which was 91.

It's already time for your top task, how exciting.

So for this top task, I'd like you to use the number lines that I've put on the screen and the make 10 strategy to solve the following equations.

So as usual, I'll do one before you go off on your own.

I think I'll choose 48 plus 26.

So I have the equation 48 plus 26, and I will partition 26 into two 10s, and six ones.

Let's add the 10s first.

I know I'm starting at 48 because that's the first number I'm adding.

Now I know that 40 plus 20 is equal to 60, so 48 plus 20 must be equal to 68.

Good, so I've added my 10s, now let's add the ones.

If I know that eight plus two is equal to 10, then I know that 68 plus two must be equal to 70.

So I will partition the six into two, and four.

So 68 plus two is equal to 70.

And 70 plus four is equal to 74.

And there is my answer, your turn.

Pause the video and resume when you're ready so we can go over the answers together.

Good luck.

Well done, everyone, let's go over the answers.

As you can see, 39 plus 14 was equal to 53, 39 plus 15 was equal to 54.

And 39 plus 16 was equal to 55, 39 plus 17 was equal to 56.

And as we said, 48 plus 26 is equal to 74, 40 plus 25 was equal to 73, 40 plus 24 is equal to 72.

48 plus 23 is equal to 71.

Do you notice a pattern here? Because I noticed that we had a nine in the ones each time for our first number.

So that meant when we partitioned our second number, our ones always had to be nine plus one each time.

And then in this column over here, I noticed there was an eight in the ones each time of our first number.

So whenever we partitioned the ones in the second number, we always had to partition so that we had a two because eight plus two is equal to 10.

Strange how that happens.

Let's move on.

So now I'm going to show you how we can add by partitioning both numbers and we will use the number line for this one as well.

Great, so when we first saw this equation, we solved it by partitioning one number.

But this time, let's partition both numbers.

Of course, will partition into 10s and ones because that's what we have here.

So I know that 27 has two 10s and 14 has one 10.

If I know that two plus one is equal to three, then I know that 20 plus 10 is equal to 30.

Now let's add the ones.

How many ones are there all together? Well, let's use the make 10 strategy to see if we can make a 10.

I know that I have seven ones and four ones.

Well, if I already have seven ones, how can I make a 10? Oh, I know seven plus three is equal to 10.

And if I know that seven plus three is equal to 10, then I know that seven plus four is equal to 11 because it's only one more.

So let's see.

If I know that seven plus three is equal to 10, so I know I'm going to add 10.

30 plus 10 is equal to 40.

And 40 plus one more is equal to 41.

So when we solve this equation, we partitioned both numbers, we'd said 20 plus 10 was equal to 30.

Then we partition the four into three and one.

So we had another 10, and then another one.

So both sides of this equation are correct.

27 plus 14 is equal to 41.

And 20 plus 10 plus 10 plus one is also equal to 41.

Let's try the next equation, 28 plus 14 and of course, we'll use our number line to help us.

So remember, I want to partition both numbers.

First, we'll add the 10s.

I have two 10s in 28, and one 10 in 14.

So first we'll add two 10s and one 10.

Well, I know that two plus one is equal to three so 20 plus 10 must be equal to 30.

Great.

So now we need to add our ones.

Let's use the make 10 strategy to see if we can make a 10 with our ones.

Well, I know that I had eight ones in 28 and four ones in 14.

If I have eight, how much more do I need to make a 10? Oh, I know, eight plus two is equal to 10.

So I can partition four into two and two.

Well, if I know that eight plus two is equal to 10, then I know 10 plus two is equal to 12 because it's only two more.

So really, we're going to jump 12.

First we'll jump at 10, 30 plus 10 is equal to 40.

And then 40 plus two is equal to 42.

So our answer is 42.

So 28 plus 14 was really 20 plus 10 plus 10 plus two.

And both sides of this equation are correct, because the answer is the same.

They are both equal to 42.

Let's try one more together.

Here I have 29 plus 14.

Again, I'm going to partition both numbers.

So stay on with me make sure that we're following along.

I know it's a lot.

So what we're going to do here now is add our 10s first, so let's partition In 29, I have two 10s, and in 14, I have one 10.

If I know two plus one is equal to three, then 20 plus 10 must be equal to 30.

So I've partitioned my 10s and added them.

Let's move on to the ones.

I have nine ones in 29, and four ones in 14.

So if I have nine ones can I use the make 10 strategy? Oh, yes, I know that nine plus one is equal to 10.

So I can partition four into one and three, one plus three is equal to four.

So that means I have nine plus one is equal to 10.

And then 10 plus three is equal to 13, because it's only three more.

So that means I should jump 10 first.

So 30 plus 10 is equal to 40.

And then let's not forget our three, 40 plus three is equal to 43.

So 29 plus 14 was equal to 20 plus 10 plus another 10 plus three.

And I know this is correct, both sides are equal because both sides are equal to 43.

Great, it's time to show off what you've learned by completing your independent task.

But this independent task, I'd like you to do two things.

Step one, solve the equation by partitioning one number.

So for example, in 49 plus 15, I will partition the 15.

I have one 10 and 15.

So that means 49 plus 10 is equal to 59.

Now, I still have five ones, 59.

Well I know that I can use my make 10 strategy.

Nine plus one is equal to 10.

So 59 plus one must be equal to 60.

And then I can partition the five into one and four.

So 59 plus one is equal to 60.

And 60 plus four is equal to 64.

Great.

Step two is to solve the equation by partitioning both numbers.

And hopefully you get the same answer in step one and step two.

So again, in 49, plus 15, I will partition both 49 and 15.

I have four 10s and one 10.

I know four plus one is equal to five.

So 40 plus 10, must be equal to 50.

And now I'm going to add my ones, I have a nine and a five in the ones again, nine plus one is equal to 10.

So I will partition five into one and four 50 plus 10 is equal to 60.

And 60 plus four is equal to 64.

So I got the same answer both times I must be correct.

Your turn.

Pause the video when you're done resume so we can go over the answers.

Good luck.

Well done everyone.

So let's go over the answers, for the first one 35 plus 16 is equal to 51, 35 plus 17 is equal to 52,36 plus 15 is equal to 51 and 36 plus 16 is equal to 52.

We have completed 49 plus 15 together, and 49 plus 25 is equal to 74, 49 plus 35 is equal to 84 and 49 plus 45 is equal to 94.

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Don't forget to complete your final quiz.

Good job everyone, that was really hard work today.

I really hope to see you next time.

Bye.