(bright music) (magical music) (funny music) - [Children] "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.

As you can see, we are going to start off with a number talk.

Then we're gonna look into using different units to measure area.

For those of you that may not be familiar with a number talk, remember, a number talk is done in three easy steps.

First, I'm going to pose a problem.

Then you are going to try to solve that problem mentally without using any paper or pencil.

Finally, you're gonna share out how you solve that problem, explaining your strategy.

I wonder if there's anyone out there that can help us with our math talk today.

(upbeat music) Yay, it's our good friend Springling.

You remember Springling?

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

Springling loves to do subtraction on an open number line where she gets to use that tail to hop in friendly numbers, but doesn't like to hop one by one because then that flattens her fur.

She also loves to add up all those hops to find the distance between two of those numbers.

Let's see what problem Springling has for us today.

64 - 26.

What do you think boys and girls, can we solve that using Springling's strategy?

Let's see what Ethan did.

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

I started at 26 and went to 30.

Then I went 30, 40, 50, 60, then went 4 more to get 64.

I know I went a total of 38, so 64 - 26 = 38."

That's an excellent example, Ethan, of what Springling would want you to do.

Boys and girls, let's see if we can follow that example as well.

I have my problem written out for us, 64 - 26.

If I'm drawing my open number line, I know that 26 is less than 64.

So that's gonna go at the beginning of my number line.

I'm gonna plot that there.

And then I know that 64 is going to go towards the end being the bigger number.

Ethan said that he started at 26 and he did a hop to 30.

And by taking that hop, he actually went four spaces.

Next, counting by tens, Ethan was able to go to 40, to hop to 50, hop to 60.

And then at the end, he went to 64.

Now Ethan was able to count by tens.

So from 30, he hopped 10 to get to 40, hopped 10 to get to 50, hopped 10 to get to 60, and then hopped 4 to get to 64.

Now, what Springling tells us is that we have to add up all those hops so that we can get that total distance.

Counting by tens, I have 10, 20, 30.

So I have 30 + 4 + 4, and that equals 38.

So 64 - 26 = 38.

Nice work, Ethan.

And nice work you boys and girls for doing that along with us.

I wonder though, did Han solve it a different way?

Let's take a look.

Han said, "I used the same strategy, but solve differently.

I started at 26 and went to 30.

Then I went from 30 to 60, then went 4 more to get 64.

I know I went a total of 38, so 64 - 26 = 38."

That's a little bit different than Ethan's way.

Let's see if we can actually chart out the way Han did it, too.

So on my number line, I'm gonna go ahead and set it up the same way.

And again, I know that 26 is a lower number from 64, but the difference now then is that Han then jumped to 30 to make a nice friendly number of 30 'cause that's the friendly number that's closest to his 26, four hops.

But what I liked about Han is that using his big third grade brain, instead of just hopping by tens, he was actually able to know that 30 + 30 = 60, which actually gets us closer to the end of our open number line.

So he actually went a hop into 60, 30 to 60 of a hop, which probably made Springling so happy 'cause he actually hopped a total of 30 to get to 60.

Next, we just have a small hop to get our total, which is four spaces, four hops to get to that 64.

Now again, just like Springling teaches us, every hop that we make, we need to add those hops up to get that distance between those two numbers.

So now I know that 30 + 4 + 4 = 38.

Great thinking, boys.

Sprinkling strategy is an excellent way to compute math, especially subtraction, mentally.

Let's take a look at our, "I Can" Statement of the Day.

"I can use different units to measure area."

Take a look at these four rectangles.

What do you notice?

What do you wonder?

Looking at these rectangles, I noticed that there seems to be a bunch of smaller rectangles inside of the big rectangle itself.

I wonder if the boys noticed the same thing.

Ethan noticed that the rectangles are tiled with different-sized squares.

Where Han noticed that A takes a lot of small squares to fill the one rectangle, but in D it only takes two squares to fill.

Those are great notices, boys.

I wonder if there's anything else that you wonder.

Ethan wonders, "Why are there different squares?

And are the squares related?"

Han wonders, "Could there be even smaller squares to cover the area?"

Well, those are great wonderings, boys, and I think you're onto something.

Looking at my shapes, I believe you're correct, that there are different squares and that those squares could be related, but they're different sizes.

And I think that this is actually gonna help us for the rest of our show when we start looking very close into area and the fact that you can use different size measurements to use and measure for area.

So let's look at this concept, same rectangle, different units.

Hmm.

That's an interesting title, same rectangle, different units.

I wonder what exactly this is going to be talking about.

It says that we're gonna build the expression with centimeter cubes and 1-inch square tiles, a 2 X 5.

So looking at the tools that we're using, our centimeter cubes and our 1-inch square tiles, both you're able to measure area, but if you'll see there's a big difference in their size.

So you wanna make sure that you're paying attention to that when you're using these tools for area.

So looking back at this, I can see that I can still build my 2 X 5 with my centimeter cubes.

I have my two groups of five and I can do the same thing now with my 1-inch square tiles build my 2 X 5.

So I have my two rows of five.

And as you can see, both technically are a 2 X 5, but when you look closely, you'll actually see that the area that each one is covering actually is different.

Our centimeter cubes cover an area that is much smaller than our 1-inch tile squares cover when it comes to area.

Now that we've mastered looking at the tools for measuring area, let's see now if we can use a pictorial representation for area.

So sometimes when you're using area, you'll have two different grids you can use.

And you'll notice that those grids actually match up with the tools.

So for example, in our first grid, you'll see that it actually matches the 1-inch square tiles where our second grid shows our centimeter cubes.

So looking at that closer, you'll see that my 1-inch square tiles actually fit quite nicely right there in that grid.

And then so do my centimeter cubes fit nicely in that grid.

But what's really important is when we start using these different tools of measurement, third graders, is we have to make sure that our units match what we're using to measure.

So looking at our example here on grid 1, since I have my two 1-inch tiles, I would actually record that as 2 square inches, which looks like this.

2 inches squared.

Next, when I'm looking and using my grid that has my centimeter cubes, my unit is going to change.

So, whereas I still have two, I now have centimeters squared.

So taking a closer look at this concept, boys and girls, let's create a rectangle for the expression 7 X 3.

We're gonna use both our grid 1 and our grid 2.

So if we are creating a 7 X 3 using squared inches, how that is going to look is I'm gonna again, get my 7... 6, 7, and then I'm gonna go over three.

And I'm going to color in that area.

My 7 X 3.

(marker pen scratches) Making sure I get and cover all of that area inside my shape.

Now that I have my rectangle filled in, I know that I can do that multiplication 7 X 3, because I have seven groups of three, which equals 21.

7 X 3 = 21 squared inches.

Have to remember that unit.

Now I wonder what is this image going to look like using my centimeter grid?

So if I have my grid set up in centimeters, again, I'm making a 7 X 3.

And so same thing, I'm gonna count 1, 2, 3, 4, 5, 6, 7.

I'm gonna go over three, color in all that area.

'Cause remember, that is what we are calculating, boys and girls.

And again, looking at those images, both are 7 X 3's, but looking at my centimeter grid, do you notice that the shape is somewhat smaller?

Because I know that 7 X 3 = 21, but now I've used squared centimeters.

And so again, bringing those a little bit closer, you can see, even though I'm calculating area, when I'm using a different unit of measurement, that actually is going to change the size of the area in which I'm calculating.

Now taking everything that we've learned about area, let's see if we can estimate how many centimeters and inches it'll take to tile this square.

What do you think?

Taking a look at that square, how much will it take to tile that entire thing in inches and then using centimeters?

Let's see what the boys guess.

Ethan estimates that he thinks it will take 9 square inches to cover.

Where Han thinks it'll take 40 square centimeters to fill the square.

Well, let's explore this.

Let's take a look at Ethan first and we're using those square inch tiles.

Now having my square here, Ethan things that'll only take nine, but as I'm trying to calculate this out by putting my square tiles in there, remember, when you're calculating area it's inside that counts.

Putting my square tiles in there.

I see, well, I have four that make that first row.

And so now I'm gonna see how many rows I could actually make.

So I have one row.

Now I'm gonna add my second row, third row, and my fourth row.

Using what I know, I can estimate that I have this complete row of four, that I would actually have 1, 2, 3, 4 groups of four, which would get me 4 X 4 = 16.

Ethan, we can't forget that unit though.

It's actually 16 squared inches.

So I feel like we need to take a look now at Han's estimation.

So Han believes that 40 square centimeters, it will take to fill the square.

Looking here, I've already started to plot that out.

And to be honest, Han's estimation is a little bit off.

It actually took 10 squared centimeters in each one of my rows of 10 rows to actually fill that entire square.

So using squared centimeters, we actually have a 10 X 10, which is a 100 squared centimeters.

But the big takeaway here, boys and girls, is that it really depends upon what you are using to measure because you can measure area in a variety of units.

And in our example, when we're talking about inches and centimeters, obviously with centimeters being a smaller unit of measure, you're gonna have to use a lot more of those centimeters to cover up an area than you would have to do with those inches.

Now it's your turn to play Area Compare to apply what you learned in our show.

Great work today, boys and girls.

We started off our show working with our mental math and using Springling's strategy for subtracting on an open number line.

And then we took a close look at how to use different units to measure area.

I had so much fun today.

I can't wait for next time.

But until then, I'll see you.

(bright music) (cheerful music) - [Narrator 1] sis4teacher.org.

- [Narrator 2] Changing the way you think about math.

(cheerful music) - [Narrator 3] 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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