(happy music) ♪ Math mights - Welcome back third graders.

My name is Mrs Ignani and I am excited for another great episode of math mites.

Let's check out our plan for today.

First, we're going to warm up our brains with a number talk.

Then we are going to find area with missing side lengths.

For those of you that may not remember what a number talk is, it is a simple warmup activity that consists of three steps.

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

The next step is you are going to try to solve that problem mentally without using any paper and pencil.

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

I wonder if there's any characters in mathville that would like to help us with our number talk today.

(happy music) It's our good friend Springling!

Springling is a character in mathville who was born with these beautiful eyelashes, this fluffy fur, and this coily tail.

Springling loves to use an open number line, but she really likes when her friends use decade numbers to hop on that number line instead of counting one by one, cause that flattens her fur.

I'm so excited to see what problem Springling has for us today.

The problem Springling has for us today is 202 minus 88.

I wonder boys and girls.

Do you think you can use her strategy?

Let's see what the girls did.

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

I started at 88 and went to 90.

Then I went from 90 to 100 and 100 to 200.

Last, I went from 200 to 202 then added up the distance 202 minus 88 equals 114."

Interesting strategy.

Let's see if we can take a closer look at that.

So looking at my equation, I'm going to go ahead and set up that open number line.

And I have to think to myself, where would I put that first number 202 or 88?

What would make sense?

I hope you're thinking the 88 would go first because that is the lesser number.

So I'm going to go ahead and write 88 towards the beginning of my number line and 202 towards the end.

Now the first friendly number that Maeve was able to come to from 88 was 90.

So she, I'm going to go ahead and put my 90 and then Springling is going to do the distance of one hop, but actually moved two places to get there.

From there Maeve actually used the next friendly number from 90, which was a 100.

So on my number line, I'm going to write my 100 and Springling is going to hop 10 paces and get through the distance of 10.

From there, Maeve was able to use a great third grade concept where she was not only able to count by tens, but by hundreds, she was able to go from 100 to 200 and you can bet that made Springling so happy.

Look at that hop!

She covered the distance of 100.

From there, we only had to go two, to get to 202, which is one small hop to get us to.

Now we have to remember Springling's final step, is that to figure out the distance between those two numbers, we have to add the distance that we actually went.

So looking at our distance, I have one 100, one 10, and then that would make 110, plus two, plus two, which is four equals 114.

So now I know that 202 minus 88 equals 114.

Maeve it a great job showing us how to use Springling's strategy.

I wonder if you're able to explain to someone how to use that strategy too, or maybe a different way that you solved the problem.

Let's take a look at our, "I can" statement of the day, "I can find the area of figures with missing side lengths."

Take a look at this figure, boys and girls.

What do you notice?

Do you have any wonderings?

Looking at this figure, I noticed that it doesn't look like all of the measurements are there.

I wonder what the girls noticed.

Maeve said, "We can break this figure into two rectangles."

Kesha said, "Some of the side lengths are missing.

Some of the side lengths are given in centimeters."

Looking at the figure, I can see what the girls are talking about.

Maeve's right, I could break this rectangle up in a couple of different ways and Kesha's right.

I do see that the measurements are in centimeters, but some of those side lengths, like I thought, were missing.

Those are really great notices.

Let's take a look though at what the girls are wondering.

Maeve wonders, "Can we still find the area of this figure?"

while Kesha wonders, "How can we find the missing side length measurements?"

Those are excellent wonders girls.

And I think we should look further into that.

So, can we still find the area?

Well, as we learned before, when we have this figure, we need to be able to break it up into two different rectangles, like Maeve said before.

So I'm going to go ahead and break up this rectangle so that I can more easily solve it.

Now, there's two different ways I could break it up, but I'm going to go ahead and break it up in two rectangles, just like that.

Next, in order to solve for my missing lengths, I have to figure out the measurements of the sides of those rectangles, keeping in mind that the sides match in length.

So if the top length is one, the bottom length is going to be the same and the same thing with the sides of those rectangle.

If one side is four centimeters, for example, the other side is going to be four centimeters too.

So solving for my first rectangle here.

I know that if this is the shape that I'm looking at, that if I know the length of this one side is two centimeters, then this other side is going to be two centimeters as well.

But now the tricky part comes for the other length of the other side of that rectangle.

So, for the other side of the rectangle, this is where it gets a little bit tricky.

So looking at this, I see that if I'm solving for this part right here it doesn't follow all the way through like my top line.

So I sort of have to be a little bit of a detective and figure out what that length is going to be by using the information that I have.

Now looking, I can see that this line right here of my rectangle would match the same length of this bottom part of that rectangle, would make that portion four.

If the whole thing is 10 centimeters, then I know that I need to subtract those four centimeters to get the length of this side, which would be six centimeters because six centimeters plus those four centimeters would equal that total length of that 10 centimeters.

Now that we have the lengths of the sides of that rectangle, we're going to solve for the area.

So I know that two times six equals 12 centimeters.

And remember boys and girls, it's not just centimeters because when we're dealing with area, it's actually squared centimeters.

So I have to make sure I put that for my unit, which is 12 squared centimeters with my little two up there.

Now though, we're still not done because we need to solve the area of the other rectangles so that we can get the entire area of the entire figure.

So looking at my rectangle that I have left, I see that I have some missing information, but I know that again, using what I know about the rectangle sides having to be equal, I can solve this.

So if I have four centimeters at the bottom of the base of my rectangle, I know that this is going to be four centimeters across with that same length.

Now I have to figure out though, if I have a length of nine centimeters and oh, look at that, we now have a full length of nine centimeters too.

Those are equal.

So I know that this missing length is actually nine centimeters.

Now I need to solve for that area.

So I'm going to go ahead and solve nine times four equals 36 squared centimeters.

Did you get that?

But we're not done yet because now we need to add those two rectangle areas together to get the full area of our figure.

So I'm going to take my 12 centimeters, my 12 squared centimeters, plus my 36 squared centimeters.

And that is going to give me 48 squared centimeters, total.

This is some really tough work, third graders, but I'm really glad that we were able to actually show those wonderings of the girls that even though we might be missing some of those lengths we can still use what we know to find that lengths for those missing areas.

We're going to look into this further as we keep going on, take a look at this image.

Tyler says that the missing side length is five meters because it looks longer than the four meter sides.

Do you agree or disagree?

Can you explain your reasoning?

Maeve says, "I disagree with Tyler.

The side does look longer than four meters, but I think it is six meters long."

Kesha says, "I agree, if we add the side to the six meter side, they need to add to 12 meters to match the other side of the figure."

Think about what those girls said.

Does that make sense to you?

Looking at our figure, if we're trying to figure out the length of this, Maeve says that she thinks it's the length of six meters and that she estimates that, that is the same equal length.

Kesha also agreed because she looked at that length of that full line of that rectangle and she noticed that it is 12 meters.

And so when we're picturing that half, she was able to see that if this is six meters, well, six meters plus six meters would equal 12 meters.

Now that we have figured that out, I'm going to go ahead and put in that missing length that we have decided that this is six meters because six meters plus six meters would equal that 12 meters.

Now let's see if we can find the area of this figure.

So I have to remember that I need to be able to break up this figure into two rectangles so that I can easily solve for that area.

So I'm going to go ahead and break my rectangle up, draw my imaginary line there.

And now I know that if this whole side is 12, I've already figured out that half of that would be that six meters to match the other side.

So I then know if this is six right here, six times four is 24 squared meters.

Now I have to solve for my other rectangle.

I know looking over here that if this is eight meters then this line has to be the length of eight meters as well and I know that six times eight equals 48 squared meters.

For my last step to find the area of the total figure, I just have to add those two rectangle areas together.

So if I have 48 plus 24, when I set the problem up that way, it might be sort of hard to solve for that.

So I'm wondering if there's a strategy that we could use to help us solve this problem.

What do you think?

I think I'm going to try DC.

So if I have 48 plus 24, I'm going to go ahead and decompose 24 into two, and 22, because I know that 48 plus two makes that friendly number of 50.

Then I just have to add 22 and I know 50 plus 22 equals 72, which will be 72 squared meters.

That would be the total area of that figure.

That was so much fun boys and girls.

Let's try another one.

How can we solve for the missing sides of this figure?

Now, looking at this figure, it's going to be a little bit trickier.

So we have to look at this closely.

If I go ahead and make my rectangle, I'm going to go ahead and split this into two separate rectangles, but looking here, I see I have my one length of four, so right away, I know that I can make this side, this length, the same four feet.

However, I don't actually have the lengths of both of those top, the top and the bottom of this rectangle.

So this is where we have to be a little detectives and look at the information that we do have.

If I look over here, I see that I have a length of three feet.

I don't know this length.

And then I have two feet over here, but following my rules of a rectangle, if this side is seven feet, then this side altogether has to be seven feet too.

So if I know I have three feet and two feet, that equals five feet.

And so if I take the five feet away from seven I'm left with two feet.

So my missing length right here is two feet.

So now I know four times two is eight squared feet.

So now that I have the area of that first rectangle, I now need to solve the area of the second rectangle.

I have my lengths already there for me, so I know that two times seven is 14 squared feet.

Now the last step that I need to do is then add those two lengths together so that I can get the area of the total figure.

So I'm going to take 14 plus eight, and I'm going to go ahead and use DC strategy and I'm going to decompose 14 into 12 and two, because I know that eight plus two makes a 10.

And so then I can easily add my 12 into my 10 to get 22 so that I know the total area of this figure is 22 squared feet.

Wow third graders, you did an excellent job helping solve for those sides that were missing.

This is tough work.

Now it's your turn to practice area with missing sides, just like we did on today's show.

Great job third graders.

I had so much fun working with you today, finding the area of those figures, even though we didn't necessarily have all those lengths to start off with, can't wait for next time.

But until then, bye.

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