(upbeat music) - Math Mights - Welcome back third graders.

My name is Mrs. Ignagni and I'm here for another exciting episode of Math Mights Let's take a look at our plan for today.

First we gonna get started with a mystery math mistake.

Then we gonna spend some time working with the traditional algorithm to subtract within 1000.

Let's go ahead and warm up our brains with our mystery math mistake.

Oh no.

What happened to our friends in Mathville?

It looks like they got stuck in a cyclone and all of their strategies are all mixed up.

Is that T-Pops holding Abracus's wand?

Hmm.

Let's find out what we're going to do about this.

Here's how it works.

One of our characters is going to share with us a problem that they have been having a difficult time solving.

You and I have to work like little detectives and look closely at that problem, to see if we can figure out where they went wrong.

And then help them correct it.

Let's see who's gonna bring the mystery math problem to us today.

It looks like T-Pops is upside down and needs our help.

T-Pops is trying to solve 548 plus 253 and he got 791.

T-Pops told me how to solve this.

And we're gonna to go ahead and solve it, just like he did T-Pops has and started with his ones and he added eight plus three to get 11.

Then he went to his 10s column and he knew that 40 plus 50 equals 90 or nine 10s.

Lastly, he added his 100s 500 plus 200 to get 700 for a total of 791.

What do you think boys and girls, did you see a problem with T-Pops' strategy?

Let's see what the boys think.

Landon said.

I don't think T-Pops has the correct answer.

I know because when I add eight plus three, it doesn't equal one, it is 11.

Well, let's take a look at what T-Pops did.

So when we'd add eight plus three up Landon's right it is 11, but we only put one, one.

We didn't show where that 10 went.

Nice work, Landon.

Let's see what Ryan says.

Ryan said, I think when T-Pops was adding, he forgot to regroup his 10s and 100s.

The answer should be 801.

So starting off with our problem and fixing now, we gonna go ahead and erase 791.

Cause we know that that is not correct.

And we gonna start off with Landon and we gonna start in our ones, just like he said.

And he told us that eight plus three is 11.

So we're actually going to have one, one, and then one 10.

I know that one 10 and one equals 11.

Next looking at my 10s, I have four 10s plus five 10s plus one 10, which actually equals 100.

So I'm not actually going to write anything but a zero in the 10s because I now have a renaming.

So I'm gonna go ahead and put zero because I don't have any 10s.

And I actually have 100.

So now adding up my hundreds, I have 500 plus 200 plus 100 equals 800 for a total of 801 just like the boy said.

Did you get that too?

Did you find that math mystery mistake?

Excellent work.

We have to remember when we're using T-Pops strategy, that we are regrouping and we are looking at all of those columns to make sure that we're adding correctly.

Let's take a look at our "I can" statement of today.

Our "I can" statement of the day is "I can use the traditional algorithm in more than one way to subtract within 1000".

Let's take a look at some of the classwork from my students to see how they were subtracting within 1000, Tyler was subtracting 391 minus 215, and he used DC strategy.

Do you remember our friend DC?

DC is our friend who lives in Mathville, and he wears this hard hat and carries this mallet and he loves to decompose numbers.

And so you'll see that he used that mallet to decompose numbers.

And that's the strategy that Tyler used.

Setting up our equation into the traditional method.

Tyler actually put his into expanded form.

So we have our 391, we have 300 plus 90 plus one.

And then our 215 is 200 plus 10 plus five.

Now that we have it written like Tyler, let's go ahead and walk through how we are going to subtract this.

So if I'm going to start with my subtraction, I'm gonna start with my ones.

But wait a second.

Can I take five away from one?

I can't.

And so this is where DC strategies come into play.

We're gonna have to do some renaming and regrouping.

So with my ones column, I already know that I cannot take five from one one.

So I'm gonna go ahead and I'm going to rename my 90 into 80 so that I now have 11 ones.

Wait a minute though, does it still equal 391?

Let's check, if I have 300 plus 80 that's 380 plus 11.

Yup.

it's still 391.

We just renamed it.

So now that I have 11 ones, I can take my five ones from there to get six ones.

Now let's go to our 10s column.

If I have 80 take away 10, that leaves me 70.

And then when I have 300 takeaway 200, I have a 100 left.

Adding those up, I have 176.

And so now I know that 391 take away 215 equals 176.

That was a really great way and I think I can understand a little bit better now how Tyler solved it.

Let's see how another one of my students Kiran has solved the problem.

Kiran had the same problem, 391 minus 215.

But he still did a little bit differently.

He seemed to have used T-Pops strategy.

Hey, T-Pops.

Here's T-Pops , his our most senior citizen of Mathville.

You'll see that he wears these glasses, he carries a cane, he's even balding, but he does get around with these cute little bunny slippers.

T-Pops believes that the traditional method is the best way.

But after he spent some time with some of his Mathville friends, he's learned that the other strategies are equally important and should probably be learned first.

Let's see how T-Pops would have used his traditional method to solve.

Here I have T-Pops place value mat with our equation already set up.

But before we get started, let me give you a tour of his mat.

First and foremost, you'll see that we have the mat set up in 10 frames.

Now, sometimes our friends want to go ahead and label our 10 frames with the correct titles at the top ones and 10s.

However, T-Pops doesn't necessarily like us to keep doing that.

It's okay if we start that way, but as we're moving on through his strategy, we wanna actually get rid of those labels because as you'll see, when we pop in our disks here that are labeled.

So for example, I have two 10s that actually would say 20 10s, and we know that that doesn't make sense.

So we're gonna go ahead and remove those labels because we don't need them.

So the first thing that we gonna do now is go ahead and build our minuend.

I know that my minuend is 391.

So I'm gonna go ahead and put my 100s.

One, two and three.

I know I need nine 10s.

So I'm gonna go ahead and build that.

I have 10 20 30 40 50 60 70 80 and 90.

And then I have one, one.

391.

Now that I've built my minuend, it's time to build my subtrahend.

So using my place value cards, I have 215 is my subtrahend.

And I'm gonna go ahead and expand that out to show the place value.

Two 100s, one 10 and one five.

Now that I've gone ahead and built both my minuend and my subtrahend, it's time to go ahead and solve this problem.

So the first thing that I'm going to do is go ahead and try to take my five ones from my, oh one ones.

But that doesn't necessarily work, I don't have enough ones.

So I need to go ahead and regroup.

So now I'm gonna take my 10 and I'm actually going to rename it into 10 ones.

And I'm gonna go ahead and show that on my board.

So I have my 10 is now going to be renamed 10 ones.

Now that I actually have 10 and my one, so 11 ones, I now can go back and if I need five of those, I have one two three four five I can go ahead and I can take away those five ones.

Now that we've made a move on T-Pops board, we have to make sure that we show it in our algorithm.

So I couldn't take five ones from one ones, I had to go ahead and rename.

And now I have eight 10s and 11 ones.

So from there I can see that I was able to take my five ones from my 11 ones, and I was left with six ones.

Now it's time to go and work into our 10s column.

So I see that I need to take one 10 away from my 10s column.

So I'm gonna go ahead and take that, and I'm gonna take one 10 away and I don't need that 10 anymore.

But remember if I make a move on the mat, I've got to show that in my algorithm.

So if I have eight tons and I'm taking away one 10, that leaves me with seven 10s.

Now it's time to finish this problem working in our 100s column.

I know that I need to take away two 100s from the 300 that I have.

So I'm gonna go ahead and scoop up those 100s, take those away.

And I am left with 100.

So I know that 391 minus 215 equals 176.

I really like using T-Pops method to show that traditional algorithm.

Let's go ahead and see if we can do another one using his strategy.

If T-Pops has 428 minus 156, how would he solve that using his mat?

Let's check it out.

I have my algorithm written out 428 minus 156.

I'm gonna go ahead and set up my minuend.

And I know that I have four 100s, one two three and four.

I have two 10s.

And then finally to make 428, I have eight ones.

I really like how these are set up in 10 frames so I can easily see that I have eight ones.

Now that I have my minuend, already built.

It's time to build my subtrahend.

So with 156 being my subtrahend, I can go ahead and show that 156.

I'm gonna spread that out into my place value.

So I have 100 50 and six.

And now that I have both my minuend and my subtrahend it's time to go ahead and solve this problem.

If I have eight ones and I need to take six away, I'm gonna go ahead and scoop up those ones two four five and six.

I'm gonna take those six ones away and I no longer need those.

So when I have eight ones and I take six away, I am left with two ones.

Now let's go ahead and look at our 10s column.

So when I have now my two 10s, but I need to take away five 10s.

I'm gonna go ahead and grab 10, 20.

Oh, wait.

I don't have enough 10s to take away five of them.

So I'm gonna go ahead and have to rename.

So I'm gonna put those down and I'm gonna go ahead and rename one of my 100s into 10 10s.

So I have my 100 and I'm gonna go ahead, and I have one 10 20 30 40 50 60 70 80 90 100.

I have 10 10s, which equals my 100.

Now, remember, whenever we make a change to T-Pops mat, we have to make sure that we show it in our algorithm.

So I have 428, but now looking at my 100s, I don't have four 100s anymore, I've renamed them.

I have three 100s and instead of two 10s, I now have 10 plus my two, I have 12 10s.

So now that we have shown it in our algorithm, let's go ahead and finish this problem.

Remember I was working with my 10s, so I needed to take five 10s.

I have two, so finishing that up 30 40 50 or five 10s I'm taking away.

Which then that actually leaves me with seven 10s.

So I know 12 10s take away five 10s are seven to 10s.

So now finishing up, I just have to go to my 100s.

When I have 300 and I need to take away 100.

I'm gonna go ahead and take that away.

And now I'm left with two 100s so that I know that 300 minus 100 is 200.

So my total answer is 272.

Excellent work boys and girls.

Showing that traditional method in more than one way, which is pretty complicated work that you're doing as third graders.

You're gonna be able to try all of this on your own because now it's your turn to solve subtraction problems, with T-Pops using all of that great information that we learned on today's show.

Nice work today, boys and girls, I had so much fun using that traditional algorithm to solve subtraction problems within 1000.

I can't wait for next time.

But until then see you later.

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