(upbeat music playing) - [Child Narrators] Math Mights!

- Welcome third graders, My name is Mrs. Ignagni, and I'm here for another episode of Math Mights.

Let's take a look at what we have stored for you today.

Our plan for today is first, we're going to start off with a Number Talk, and then we are going to find the Area of Figures.

For those of you that may not remember, there's three easy steps when we're dealing with the Number Talk.

First, I'm going to pose a problem to you.

You're going to try to solve that problem mentally, without using any paper or pencil.

Last, you're going to share out how you solved, making sure that you explain your strategy.

I wonder if there's any friends with us from Mathville that want to help us out with our Math Talk today.

It's our good friend Springling from Mathville!

If you remember Springling, she was born with these beautiful eyelashes, this fluffy fur, and this coily tail.

Springling loves to do subtraction open number line, and she likes to use that coily tail to hop onto friendly numbers.

She doesn't like when we hop one-to-one, because then that flattens her fur.

At the end, she likes to make sure that she adds up all of that distance, so that she gets the correct answer with her subtraction problem.

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

Springling has the problem 101 - 76 = ?

I wonder boys and girls, can you use only your brains, no paper or pencil, to solve this problem?

Let's see what our friend Maeve did.

Maeve said that she used an open number line and counted up.

She started at 76 and went to 80.

Then she went from 80 to a hundred.

She went up one more to get 101.

She knew that she went a total of 25.

So 101 - 76 = 25 That was an excellent explanation, Maeve!

Let's see if we can do it as well.

I have my problem written out 101 - 76 = ?, and I've already set up my open number line.

And I know that I'm starting at 76.

And so with what Maeve was talking about, the next friendly number that she went to, actually, was 80.

And so she hopped four hops to get to 80.

From then, she was able to actually make a big hop, which really made Springling happy, to get to the friendly number of 100.

So over here on my number line, I know 100 is going to be right over here, and Maeve was able to hop 20 spots to get to a hundred.

She then just had one hop left to get to 101.

Now we have to add up that distance, we have 20 + 4 + 1, which is 25.

Nice work Maeve!

You did an excellent job showing Springling strategy, but you know what, boys and girls?

I wonder if there's another Mathville character that would solve this problem, a different way.

(playful music plays) It's our good friends, Minni and Subbi!

Minni and Subbi are twins from Mathville, who have an adjoining tail.

And just like siblings, these sisters don't always get along, so their parents like them to keep that tail's length apart.

Minni and Subbi actually stand for their nicknames, "Minni" for minuend and "Subbi" for subtrahend, because they actually deal with subtraction and they use the strategy of compensation, or shifting the number line, for solving their subtraction problems.

What the girls like to do though, is if one girl's goes one way, the other has to follow, because they don't like getting their tail dirty.

Let's see how Keisha used their strategy of compensation.

Keisha said, "I shifted the number line.

I took away 2 from 101, to make it 99.

Then I took two away from 76, to make it 74.

So now it's easy to subtract 99 - 74 = 25".

Excellent job using their strategy!

Boys and girls, let's see if we can do the same thing.

I have my number lines set up, but if I'm following Keisha, what she did is she actually shifted that number line to make it 99.

And then she shifted over here to make this 74.

So she actually took away 2 from each one of those numbers.

She shifted her number line, just like Minni and Subbi would like her to do.

So, using our original equation, we have 101 to 76, but since Keisha shifted her number line, we are now actually looking at 99 - 74.

Let's see if Minni and Subbi are shifting and we did it accurately.

If we started here, we shifted two spots on each and got our new equation that we're dealing with, that is actually easier to subtract with.

So, if I was to stack up my original equation, 101 - 76, I wonder, is that as easy as using compensation for the new problem that I was able to create with subtracting 99 - 74.

I can look right at both of those problems, boys and girls, and see that using that compensation strategy, is much more easier to subtract, than using that original one.

So, looking at our new problem with compensation, you can see that we actually don't have to do any regrouping, which is a good thing, because Minni and Subbi don't like to regroup.

So I can see that from this problem, I can go ahead and take my four ones out of nine to get five.

And then I can easily take my seven tens from my nine tens, to get two tens, which equals 25.

So 101 - 76, again, our answer, is 25.

Nice work team!

You know you're getting good at third grade math, when you're able to use two different strategies to solve your problems.

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

Our "I Can" statement of the day is: "I can find the area for figures".

Let's take a look at this image.

What do you notice, boys and girls?

What do you wonder?

I'm noticing that this image, isn't really like the rectangles that we've been figuring out the area for, before.

I wonder if the girls noticed the same thing.

Maeve wonders, "it looks like two rectangles.

What is this shape called?".

Keisha says, "well, it looks like a big rectangle with a chunk missing.

Can we find the area of that shape?".

I wonder boys and girls, can we?

Are these girls noticing the same that you have, and those same wonders?

Can we find the area of a shape when a piece is missing?

Are you up for this challenge?

Let's see if we can!

To answer Maeve's question, she was right.

This isn't a shape that we have a name for, like a square or a triangle.

So we're just going to refer to it as "the figure".

And to take a closer look at Keisha, let's go ahead and see if we can find out that area of this figure.

So, looking at this figure, I do see that I'm missing this piece here.

So it's going to make it a little bit trickier to calculate this area.

But I do see right here, that I have an actual nice section that I am used to dealing with, when focusing on area.

So I've highlighted that and outlined it in orange, and now I can use that section to calculate area like I'm used to doing.

So, I see that I have 1, 2, 3, 4, 5, a five by 1, 2, 3, 4.

So I know that I have a 5 x 4, which equals 20 squared inches.

Next, thinking about the rest of this shape, I now need to calculate the area for the remaining portion, which again, is a nice rectangle.

I've outlined it as you can see, in green.

And so, now using my same strategy, I'm going to count up those rows.

I have 1, 2, 3, 4, 5, and in each one of those rows, I can count that I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

I have 10.

Doing that multiplication problem, I know that 5 x 10, is going to be 50 squared inches.

Because, again, I'm working with area, so, those units are so important.

Now that I know the area of those two individual pieces, it's time now to combine those totals, so that I can actually find the area of the total figure.

So, taking the totals of my sections, I have my 20 plus my 50, and I know that 20 + 50 = 70 squared inches.

And now another way that we could solve this is if we actually envisioned, if that missing piece was actually there.

So, for example, I'm going to draw it in with a dotted line, 'cause it's not really there, but I'm going to imagine that it is.

So, if I think that this piece is actually a whole rectangle, I can actually use this bottom row to figure out what this top row would actually be.

So I know that I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and then looking at here, I have 1, 2, 3, 4, 5, 6, 7, 8, 9.

So now I know, if I was going to find the area of that total figure, imagining that piece is there, my area would be 9 inches x 10 inches = 90 squared inches.

Now, in real life, boys and girls, that figure is not actually a perfect rectangle like that.

So we have to make sure that we take away that part that's not really there.

So, if the whole figure is actually 90, but this portion right here is missing, and I can tell that this portion is equal to this portion, then I can use those dimensions, of this portion, to take this away.

So for example, I'm going to count 1, 2, 3, 4, 5, and I have 1, 2, 3, 4 rows.

So I know that I need to take 20 inches away from that 90 to get my 70 inches squared.

Let's take this one step further.

Taking a look at this figure, I want you to imagine that this is flooring that's going to be put in and we need to tile it.

How do you think we can find the area to this floor?

So, looking closer at my figure, I have to use the same strategy as I did last time.

And when I'm dealing with a shape, that's not a perfect square or rectangle, I need to see where I can actually make those in out of the irregular shape.

So, looking down here, I see that I have a three by three, and so, that quite quickly, by outlining that, that makes my square 3 x 3 = 9.

So I have the 9, but remember, we have to remember those labels and it's "squared feet", because now that we're dealing with flooring, we're going to want to use a larger unit of measure.

So I have 9 squared feet in this section.

Next then, I have to decide what numbers am I going to use for the measurements and for that problem, for the other shape that I'm using, to find the area.

And now, I need to find the area of this larger section.

So I have a lot of numbers that they're giving me for measurements, and this is where it can get sort of tricky.

So, looking I see that I have a length of 7, a length of 5, and then a length of 8 feet, but, we have to remember, we've already used some of this 8 feet.

So we're actually looking at our rectangle here, that is only using this area.

So it wouldn't make sense to use 8 feet, because it's actually a shorter amount of length that we're using.

So I'm actually going to use my length of 7, and my length of 5, and I know that 7 x 5 = 35 square feet.

So I have 35 squared feet.

So now that I have those two measurements, that we're going to eventually add together, I want to take a little bit of time to explain again, why we didn't necessarily use the 8 or the 4, even though we could have.

Looking at my figure, this whole length is eight, but remember I actually used 3 feet of it already.

And so if I wanted to have used this 8, I would have had to subtract that 3 feet that I took from that first measurement that I did.

And so, then it makes sense now, when you have one side is 5 feet and the other side would equal that 5 feet too, because we've already used 3 out of the 8.

So I would have 5 feet, and then 5 feet of length that I'm using.

The same thing goes for that 4.

We have a measurement of 4, right here is our length of 4.

But again, we decided to use 7 because we actually were taking that whole length across.

Now, if we were going to use the 4, we just would have had to remember to add in that 3 feet, that would've made it 7, because then that rectangle would have had the same length, on both sides.

Now, we need to find the total area of our figure.

35 + 9 = 44 squared feet.

Now it's your turn to play "Find the Area".

Remember, use all of that great knowledge that we learned from today's show to help you with that activity.

What a show, third graders.

You did such a great job today.

If you remember, we started off with two different Mathville characters for our Number Talk, Springling and Minni and Subbi.

Then, we learned how we could actually solve area for shapes that aren't perfect, and we could actually solve the area for those figures!

I had so much fun with you today, I can't wait for next time.

But until then- (playful music plays) (upbeat outro music playing) - [Child Narrator] sis4teachers.org Changing the way you think about math.

- [Adult Female 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.