(magical music) - [Children] Math Mights - Welcome back third graders, for another exciting episode of Math Mights.

My name is Mrs. Ignagni, and I'm so excited to be here with you today.

Let's take a look at our plan.

First, we're gonna start off with a number talk, and then we're gonna solve area problems.

For those of you that don't remember how to do our math talk, it's three simple steps.

First, I'm going to pose a problem.

Then, you're going to try to solve that problem mentally without pencil and paper.

Our final step is you're gonna share out how you solved that problem, explaining your strategy.

I wonder, boys and girls, do you think there's anyone from Mathville that wants to help us out with our number talk?

You bet!

It's our good friend, Springling!

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

If you remember, Springling loves to do subtraction problems on an open number line, and she loves it when we use friendly numbers, so she can take the biggest hops that she can.

She doesn't like when we move number by number, because then those little hops flatten her fur.

She also likes to make sure that after we hop, we always add in our distance so that we can calculate the distance between those two numbers.

Let's see what subtraction problems Springling has for us today.

86 minus 48.

Hm, boys and girls, do you think you're able to do Springling's strategy on that subtraction problem?

Let's see what the boys did.

Ethan said, I used an open number line and counted up.

I started at 48 and went to 50, and then I went 60, 70, 80, then went six more to get 86.

I know I want a total of 38, so 86 minus 48, equals 38.

Nice work using Springling's strategy, Ethan.

Let's see if you and I can do the same thing using that strategy as well.

So trying this out, I'm gonna go ahead and draw my open number line.

And I know that 48 is less than 86, so that would make sense that that's gonna go towards the beginning of my open line.

So I'm gonna go ahead and plot my 48, and then my 86 towards the end.

Now, Ethan told us that his first friendly number from 48 was 50.

So he actually hopped two to get to 50.

So if here is 50 on my number line, I know that hop is two spaces.

Next, counting by tens, Ethan was able to get close to that 86 by counting those tens.

So from 50, the next 10 is 60.

That hop is 10, and then from 60 is 70.

And then from 70, our next hop would then be.. 80.

Which is another 10.

From then, Ethan knew that he just needed six more ones to get to 86, which would be then a hop of six.

Now, we can't forget that last part of Springling's strategy, we have to count up those hops.

And so looking quickly, I see that I have three tens, which would be 30, plus two, plus six equals 38.

So now I know 86 minus 48, equals 38.

Nice work, Ethan, using Springling's strategy.

I wonder though, did Han solve it the same way as you?

Let's take a look.

Han said, I used the same strategy, but solved differently.

I started at 48 and went to 78.

Then I went from 78 to 80.

Then went six more to get to 86.

I know I want a total of 38, so 86 minus 48 equals 38.

Nice work, Han.

I think Springling would actually be even prouder of you because you were able to use an even bigger hop than we did when we were working on Ethan's model.

Let's take a closer look at that big hop that Han did.

If I have my number line, again, I'm setting it up, so I have my 48, at the beginning, because it is a smaller number than my 86.

I started out with 48 like Han.

And what he did actually, is he was able to take a big jump, because he knew that counting by tens, three more tens equals 78, which is right there on our number line.

So he did a big hop of 30.

From there, Han's friendly number then, was a little bit of a jump, because the next friendly number from 78 was 80.

So on our number line his little hop went here to 80, which was only two.

From there, Han knew one more hop, just added six more ones, and that got us to 86.

Again, we can't forget that last step for Springling's strategy.

We have to add up all that distance we went.

So 30 plus two, plus six, equals 38.

Great work boys, and great work to all of you.

Springling would be so proud of us using her strategy so well.

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

I can solve area problems.

Look at these pictures.

What do you notice?

What do you wonder?

I noticed that these pictures look like beautiful buildings.

These are examples of painted tile work called azulejos from Portugal.

In Portugal, they have been used for a very long time, both to decorate walls, floors, and even ceilings, and many also show events in Portuguese history.

Looking at these buildings, boys and girls, it takes me to what we're actually gonna be focusing on in today's show.

Looking at real life examples of how to use area.

So with that in mind, boys and girls, take a look at this partially tiled rectangle.

How many tiles do you think it would take to tile that whole rectangle, if it was our job to finish it?

Looking at this, I see that I could just go ahead and start counting, one, two, three, four, five, six.

Wait a minute, we're better than that third graders.

We don't need to count each tile individually anymore.

We have a strategy.

So looking at this, I see that I have one, two, three, four, five, six, seven, eight, nine, 10.

So there are 10 tiles in that top row, but I wonder how many rows would fill up that entire figure.

So we have one, two, three, four, five, six, seven, eight, nine.

So I have nine rows total.

So now I can use my multiplication strategy because I know that there is nine rows with 10 tiles in each row.

So that means that my multiplication is nine times 10, equals 90.

But, we can't forget that, oh, so important is the units, especially when we're dealing with area.

So that's 90 squared inches.

So great work in that example, boys and girls, but I want you to keep in mind that depending upon the size and the surface area of the tiles you're using, really does depend upon how much area that you're gonna be covering, and what that end result number is going to be.

So in this example, we were using squared inches, but if we were using tiles that were square feet, those are a lot bigger than inches.

And so therefore the area is actually going to be a different number, based on that unit that we're measuring in.

Let's take a look at another example.

The title of this is No More Squares.

This rectangle is marked off in meters.

What is the area of the rectangle in square meters?

So in this case, boys and girls, we've actually taken away that partially tiled area, and now we just have those notch marks to figure out our area.

You'll see here, boys and girls, that we have these notches now instead of our square tiles.

And so when you're thinking about those notches though, I want you to remember that they actually represent squared meters.

We're actually dealing with a larger form of measurement now.

Almost think of like a meter stick you might've seen, or if you're familiar with baseball, like a baseball bat.

That's the size of a meter.

So when we're measuring with meters, it's gonna be a larger object, a larger shape that we're actually measuring with.

So looking at our diagram here, thinking about A, we need to find that area, and two, thinking about what would we measure in meters?

So first step, let's find the area.

Now, again, we don't have those tiles, but if you can picture those tiles almost sitting there in those notches, I'm actually gonna calculate the area pretty much the same way.

So I can see that I have one, two, three, four, five, six, seven, eight spaces there.

So I'm gonna go ahead and label my eight.

Now, I just want to point out boys and girls, that this can sometimes be a situation where third graders actually count incorrectly.

Because when we're talking about area, remember it's the spaces, not exactly those notches.

So for example, I want the space in between the notches.

I don't want to start off by just counting those notches.

So again, counting that space, one, two, three, four, five, six, seven, eight.

I have spaces, eight spaces there.

Now I need to figure out how many rows I would have in this object as well.

And again, counting those spaces.

So I have one, two, three, and four.

So I know that I have four groups of eight.

So we have four and eight, but of what?

Did you say meters?

You're right.

We need to make sure we label it.

So we have eight meters, and then we have four meters.

Now to find my area.

I know that I can simply multiply four times eight to get the area of that entire space.

So I have, four times eight equals 32 squared meters.

32 squared meters.

Were you able to do that in your head?

I sure hope so.

And so thinking about that, if we have 32 squared meters, boy, that's enough to build a garden.

See, we need area in real life.

That was so much fun, boys and girls.

Let's try another challenge.

This activity is called No More Squares as well.

This rectangle you'll see is marked off in meters.

And we wanna know what is the area of the rectangle in square meters.

Well, looking closely at that image, it seems like our information is a little bit different than before.

So I see here that I have my rectangle, but instead of having my notch marks on my side, to show my rows, it actually gave me the measurement, three meters.

So I know that that actual side is equal to three meters.

So now I just have to find out how long it is.

So looking, I see, I have, again, my notch marks are there, so I could count them, one, two, three, four.

Did you catch what I was doing?

I was trying to c- to trick you.

We don't count those notches, because with area it's the space in between that's important for us to count.

So looking, I see I actually have one, two, three, four, five, six.

So that side is six meters long.

The last thing we need to do now to find our area is to multiply those two numbers together.

I know that three times six equals?

18.

So three times six equals, 18 squared meters.

For our next example, boys and girls, I actually posed this real life problem to my students, and I want to see if you come up with the same thoughts that they had.

Elena is designing a rectangular garden.

She needs a garden that is at least 20 square feet to fit her plants.

She has enough soil for a garden that is 30 square feet.

The space that she has available is three feet on one side.

So thinking about all that information, my class actually came up with four different choices for a garden that Elena could build.

So looking at the examples they came up with, for my first example, they have the three feet by seven feet.

And so it was 21 squared feet.

I know that we have enough soil for 30 square feet, so that one works out.

Check.

Our second example, we built a garden that was three by eight, which is actually 24 square feet.

Again, with that example, it fits the amount of soil that we have to use.

So, check.

That one works as well.

For our third example, they made a three foot by nine foot garden, which equaled 27 squared feet.

Again, that stuck into our requirements of being able to use up to 30 square feet of soil.

Check.

And now, our final example, three feet by 10 feet.

We now made a garden that is 30 square feet.

Again, meeting those requirements.

Looks like all four of those choices worked.

That was an excellent example, boys and girls, of why we need to make sure that we read those story problems carefully.

Because so many times third graders get one answer and they think it's correct, but they don't necessarily look for what that question was really looking for.

And in this case, we actually had four answers that would have worked.

Now, it's your turn to find the area.

Remember, keep in mind everything that we learned in this show, so that you can get this activity completed.

Excellent work, boys and girls.

I had so much fun learning how to solve area problems with you today.

I can't wait for next time.

But until then, bye.

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- [Girl] Changing the way you think about math.

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