(upbeat music) - Welcome 3rd graders.

My name is Mrs. Ignagni, and are you ready for some fun with math today?

We have a great show planned for you.

Let's take a look at that plan.

Our plan for today is we are gonna warm up our brains with a mystery math mistake.

Then we are going to solve problems with addition and subtraction.

Oh no, 3rd graders, what has happened to our Mathville characters, their strategies are all mixed up?

DC is carrying Abracus's wand, what is going on?

Well, I'll tell you boys and girls, we have a math mystery mistake and here is how it works.

What is gonna happen is one of our math characters is going to give us a problem that they have been struggling with.

It is our job as detectives to take a close look at that problem, and see where they went wrong so that we can hopefully help correct it.

What do you think boys and girls are you up for a challenge?

Let's see which Mathville character needs our help today.

It looks like DC needs our help.

DC is trying to figure out what 99 plus 97 equals.

And he has decomposed 97 into two and 95.

Let's see what DC has done.

DC showed me that he decomposed 97 into two and 95 so that he could make a friendly number.

And the friendly number he made was 100 plus 95 to get 195.

What do you think boys and girls, did you see perhaps a mystery math mistake?

What do you think the boys are gonna say?

Let's find out.

Jameson said, I think DC decomposed 97 correctly, because two plus 95 equals 97, but something doesn't seem right.

So we decompose 97 into two and 95 that does equal 97, so it is decomposed correctly.

But what do you think boys and girls is Jameson, correct?

Something doesn't still seem right.

Let's see what Josiah thinks.

Josiah said, DC has the answer incorrect.

He should have decomposed 97 into one and 96.

So if I have 97, I could decompose into two and 95, but Josiah is saying you should actually decompose it into one and 96, because way 99 plus our one equals our 100.

And then we have our 96 for a total of 196.

Nice work boys and girls and great job Josiah, it looks like we were actually able to solve that mystery math mistake.

Let's take a look at our I can statement of the day.

I can solve real world problems with addition and subtraction.

Take a look at this picture.

Iguazu Falls in South America marks the border between Paraguay, Brazil and Argentina.

It is the largest waterfall in the world.

The waterfall falls into two parts.

The water falls 115 feet in the first part and 131 feet in the second part.

How far does the water fall altogether?

What do you think boys and girls?

Listening closely to that story problem, what type of operation do you think we need to use to figure that out?

Let's see what thoughts those boys have.

Jameson said, I know we must add since it is asking for the total of the two parts.

Well, if I have my first part and my second part, then yes, it would make sense to add these together so that I can get my total.

So I have drawn out a visual model here showing that I'm talking about the waterfall, and using that information that I got from the story problem.

So in the story problem, it gave me how many feet for the first part and as well as the second part.

So I've written out that in the first section I have 115 feet, and then in my second section, I have 131 feet.

And if Jameson is correct we would in fact add these two distances together to get our total.

I wonder though what Josiah has to say about it.

Josiah said to solve 115 plus 131, I think we should use Value Pak.

That's a great idea.

Hey, Value Pak, we have our friend Value Pak here and he lives in Mathville, and as you can tell by his name, he loves to work with place values.

Together as a family, they represent the value of 27, but when our family members separate, they show their individual value.

So our red character here would have a 20 on his belly, while our white character would have a seven to represent those ones.

Let's see together how Value Pak would solve this problem.

So let's go ahead and write that addition problem.

If I have a 115 plus 131, and I want to use Value Pak strategy, I'm going to look at those place values.

So let's now try solving this problem using Value Pak strategy of partial sums.

If I have a 115, I know that that actually breaks up into 100 plus 10 plus five.

We have 100, one 10, and five ones.

I now know that 131 breaks apart using that strategy into 100, three tens for 30, and one one.

So 131 breaks apart showing that value.

Now what I need to do is solve for that.

Knowing that we're solving for partial sums, I don't have to start in the ones column, I can start with my hundreds and I know that 100 plus 100 equals 200.

And then if I look at my tens, 10 plus three tens of 30 equals 40 or four tens.

Finally adding my ones columns, five plus one equal six.

So I have my number of 246.

Now we can see boys and girls that that water falls 246 feet altogether.

So let's answer our equation, 115 plus 131 equals 246 feet.

The Eiffel Tower in Paris, France has 674 steps that go from the ground to the second floor.

There are 328 steps from the ground to the first floor.

How many steps are there from the first floor to the second floor?

Looking at this story problem let's create a visual model.

If we have the Eiffel Tower and we are showing the distance of the ground floor to second floor, we see that we have 674 steps.

Now for the ground floor to the first floor, there are 328 steps.

The problem is asking us how many steps are there from the first floor to the second floor?

What do you think boys and girls?

looking at that visual model, can you tell if we need to add or subtract to figure this out?

Let's see what the boys think.

Jameson said, I think we should subtract so we can find the number of steps between the first and second floors.

What Jameson is trying to say I believe that if we know the total of the second floor of 674, he thinks that if we take away 328, that would give us the total amount that we need to find that's left.

I wonder if Josiah thinks the same thing.

Josiah said, I agree, I think we could use the strategy counting up with Springling.

That's a great idea, Josiah.

It's our great friend Sprinkling.

You know Springling, she lives in Mathville and she was born with these beautiful eyelashes, this fluffy fur and this coily tail.

Springling loves to solve subtraction problems by using an open number line.

She loves it though when her friends count by friendly numbers like fives or tens, so she can use that tail to hop real far.

She doesn't like though in her friends count by ones because it flattens her fur.

Let's see how Springling would solve this problem.

So with my equation already written out, I'm gonna go ahead and set up my open number line.

I'm gonna put my 328 towards the beginning, because I know that 328 comes before 674.

Springling strategy loves to use friendly numbers.

So when I have 328, I'm gonna start with a little hop of two to get to my 330.

But then because I'm using my 3rd grade skills, I know that I can actually count by hundreds to get closer to that total of 674.

So using my 3rd grain math brain, I know that I can do a big hop to get me over here to 630, which is closer to 674.

I know using Springling strategy, I can do that big hop and I can count by hundreds if I have 330, 430, 530, 630, I have a distance of 300, what a hop?

Now being at 630, I can go ahead and get close to my 674 by hopping to a friendly number of 670.

And I know again that I've actually hopped a distance of 40, and my final hop then would just be four.

Now remember with Springling strategy, that second step is to make sure that we add all those distances together so we can actually figure out what our total is.

So if I put my plus signs in, I know that I have 300 plus 40, plus my ones, which equals six, I have 346.

So now I know the distance of that first floor to that second floor is 346 steps.

Boys and girls that you are doing such an excellent job with this, let's take a look at one more story problem.

In Washington, DC, there are many monuments to famous people in American history.

The Lincoln Memorial is 99 feet tall.

The Washington monument is 456 feet taller than the Lincoln Memorial, how tall is the Washington Monument?

Let's take a look and put this into a visual model.

So if we are talking about the monuments, and we know that the Lincoln Memorial is 99 feet tall.

And the other information that we got was that the Washington Monument was 456 feet taller than the Lincoln Memorial.

What do you think we need to do to solve this problem?

Which operation would you use?

Let's see what operation the boys used.

Jameson said, I think we should add so we can put the two parts together to figure out how tall the Washington Monument is .

Looking at what Jameson was talking about, he believes that we need to actually add these two together, taking that feat of the Lincoln Memorial to get the total of the Washington Monument.

I wonder if Josiah thinks the same thing.

Josiah said, I agree, I think we could use this strategy compensation with Abracus to solve.

Well, that's a great idea Josiah.

Abracus is our most magical Mathville character.

He works with the strategy called compensation, and what Abracus likes to do is he likes to use his magic wand to zap unfriendly numbers, to make them more friendly to work with.

But what's important is that if he's zaps a number, Abracus has to remember to zap it back so that it makes sense and that it's equal.

Let's see how Abracus would solve this problem.

Looking at this problem to solve it the way Abracus would, I'm gonna go ahead and make my 99 into a friendly number by zapping that 99 into 100.

So I'm gonna add one to that 99.

Next, I can see that if I have 100 plus 456, that would equal 556.

But I'm not done yet boys and girls, because I have to remember that that one is still hiding there in Abracus's wand, and we still have to deal with that.

So if I zapped one to get 100, I now have to take my number 556 and take away that one to get my true answer, 555 feet.

Now I know that the Washington Monument is a total of 555 feet tall.

Is that the answer you got?

Excellent work.

Now it's your turn to add and subtract with our Math Might Friends.

Remember you are going to have to use all three of those strategies.

You're going get a question posed to you and you have to show how each one of our Math Might Friends would solve it using their technique.

Nice work today, 3rd graders, we were such a big help with our friend DC to start off our show, when we were able look at a mistake that he had made, and be able to find out how to correct that mistake, that's tough work.

We then introduced and worked with so many of our different Math Might characters and showed how we could use so many different strategies, to solve real life world problems.

This is exactly what math is all about, showing why we use it.

I had so much fun working with you today.

I can't wait for our next episode, but until then, bye.

(upbeat music) - [Narrator] Sis4teachers.org.

Changing the way you think about math.

- [Narrator] The Michigan Learning Channel is made possible with funding from the Michigan Department of Education, the State of Michigan, and by viewers like you.

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