(cheerful music) (energy twinkles) (spring boings) (floor creaks) (glass squeaks) - [Kids] Math Mights!

- Welcome, second grade Math Mights.

I'm so excited that you've joined me today for some math.

My name's Mrs. McCartney, and we have an awesome show planned for you today.

Let's check out our plan for today.

Today, we're going to do a Mystery Math Mistake, and then we're going to be doing some estimating and measuring with centimeters.

Let's warm up our brain with a Mystery Math Mistake.

(mysterious music) Oh no, what's happened to all of my Math Might friends?

They've gotten stuck in a cyclone and have all of their strategies all messed up.

DC, What are you doing?

You're holding Abracus' wand.

And T-Pops is holding DC's mallet.

Oh, my goodness.

Let's check out to see how a Mystery Math Mistake works.

One of my Math Might friends has explained a strategy to me, but they're all mixed up.

It's your job to be a detective to see if you can use your magnifying glass and find that Mystery Math Mistake and be able to help set our Math Might friends straight.

Let's see who is our Math Might today that's having some trouble.

It looks like my friend that's having trouble today is Abracus.

He's all upside down and turned around.

He's trying to solve the problem 25 plus 27, and he got the answer of 50.

He looks like he tried to change a number and add it together for easier computation.

Do you think you found the Mystery Math Mistake that Abracus did or did he solve the problem correctly?

Let's take a closer look at how he solved it so you can really think about this one.

We have the problem 25 plus 27.

Our friend Abracus, I think, was trying to make this 27 friendlier and making it a 25 by subtracting 2.

Then he brought the 25 down to add 25 plus 25.

That kind of reminds me of quarters.

25 plus 25 equals 50.

Do you think that Abracus solved this problem correctly?

Now that we've taken a closer look, you might have found the Mystery Math Mistake.

Let's see what my friend Sunshine is thinking.

Our friend Sunshine says, "I think Abracus was trying to make 27 into a 25 so he could add 25 plus 25 easier."

I don't know about you, but I definitely think that Sunshine has a great point.

25 plus 25 is way easier to add than 25 plus 27.

Let's see what our other friend is thinking.

Our friend Mariah says, "I agree with Sunshine.

I think he forgot though, to add back the 2 he subtracted from the 27.

So the answer should be 25 plus 27 equals 52."

I think she also has a great point.

Let's take a look.

I see what she's saying here.

Originally, Abracus uses that strategy of compensation to zap that number and change it back to, but he can't forget, he has to add it back.

So to continue the problem, we should add back that 2 that we took away to get the answer 52.

Abracus uses that strategy of compensation, which really makes addition a lot easier.

I know that he would be so happy that we've set him straight to make sure he doesn't forget to switch back what he changed in the problem.

Great job, Math Mights on that Mystery Math Mistake.

Let's check out our "I Can" Statement of the Day.

The "I Can" Statement says, "I can estimate and measure with a centimeter ruler."

Speaking of centimeters, I know in second grade we don't wanna always have to carry around our centimeter cubes, so I think it would be a great idea to make our own centimeter ruler.

We would like to be able to take our base 10 blocks that we were using and be able to put it out a number line as you see pictured there.

Here I have the number line that we're working with that's actually gonna turn into a ruler.

One way that you can make a centimeter ruler, boys and girls, is by lining up our centimeter cube and making a line to kind of put where one would land on that centimeter ruler.

I could then use that same width and continue writing until I have my centimeter ruler already created.

So here I have 2.

If I kept going, I could put 3 and then I could keep going and put 4.

We're using the measurement of the centimeter cube to help us measure to make our centimeter ruler.

Now I went ahead and put all the marks on our centimeter ruler for today's show, but I blew it up a little bit bigger for you so it's not quite to the actual size, but we'll be able to use it today to measure.

Let's check it out.

Here I went ahead and blew up our centimeter ruler so you could see it.

Each time I put that one-inch square tile in, I was able to keep adding the centimeters to now have a ruler that is 20 centimeters long.

So even if you don't have a ruler, boys and girls, you can create your own portable ruler.

Now we gave this assignment to some second grade students and they decided to make their rulers.

These might be some of the common mistakes that might happen while you're creating your ruler.

I want you to take a look at these four images.

Here is an example of four different students rulers.

I see A, B, C, and D. What do you notice about these students centimeter rulers and how they measured?

I'm wondering if each of those rulers look like they're perfect, that they're measuring just fine and they're accurate.

When we're doing measuring, we really wanna make sure we're using a standard measurement of unit, just like we are today with centimeters.

We have to be careful though, because if we're not all commonly looking at centimeters correctly, we could be measuring things improperly.

Let's take a look at what I have here.

In our measurement for A, I can see a ruler that starts at 0.

I'm seeing these sections just like our ruler counting and the measurement of this particular triangle goes from endpoint to endpoint to show that it's four centimeters long.

I don't know about you, but I think that ruler looks pretty good.

Let's check out B.

Over here, this person started off with 1, 2, 3, 4, 5, and put their measurement at the very end of the ruler.

What are your thoughts about that?

When we're looking at our ruler, can we just start it at the edge of the ruler?

Let's take a look at mine again.

Here I have my ruler.

Could I just start right here on the endpoint, just like this person did?

What do you notice is missing from B?

I don't know about you, but what I'm seeing is there isn't a 0 on this ruler so we could gauge and this could be measured incorrectly.

It looks like it's four centimeters, but this student forgot to put the 0 in.

So make sure that your centimeter ruler has a 0.

Let's look now down at C. This person looks also like their rectangle is four centimeters long.

But wait a minute.

What are you noticing in between the gaps of where these numbers are written?

I don't think that that is universally done the same size.

Some of them look smaller and some look wider.

Do you think that this measurement is going to be accurate?

I don't think so.

When I'm looking here and here, there's no real way to show that that is actually four centimeters.

You wanna make sure that you're putting the increments in while you're doing the ruler.

Let's check out D. D here shows that the 0 is here and then the 1 is here where they've started measuring, and they go all the way to 5.

Is that okay?

Can you just put the measurement into certain spots?

Well, this one's actually tricky.

One thought might be, we didn't line it up at 0, so indeed this is not 5.

So you could not look at this rectangle and say the length of it is five centimeters.

But I could count the distance in between and see how long it is.

One centimeter, two centimeters, three centimeters, four centimeters.

But to some students, this could be confusing because it's ending at 5.

It is possible to measure that way, but you have to make sure you're looking at the increments in between.

Wow, measurement is so technical in the way that we do it.

We wanna make sure as mathematicians when we're learning how to measure that we're properly measuring things in an accurate way.

Let's see if we can estimate the length and measure line A, B, C, D, and E. What does estimate mean?

Estimate does not mean it's the exact answer.

It's a good educated guess.

A lot of second graders struggle with this because we always wanna be right.

In this case, we're gonna give our best educated guess to figure out how long each of the lines are, and then we're gonna measure to see how close we were.

I wanna start off first with A.

And now to estimate, I want you to think of our enlarged ruler that we have here that we're using to measure these lines.

If I put that out here, kind of giving you a picture in your head of about how long that is, what would be a good guess?

I think if I was looking at this particular line, I would guess that it's about the length of my ruler.

So in blue, I'm gonna go ahead and put in 20 centimeters.

I think that that is about 20 centimeters long.

Now we're gonna go ahead and go to B.

Kind of looking at my ruler, could you make an estimate?

Again, the estimate doesn't have to be perfect.

It's about how long.

I think in blue for this estimate, I'm going to write that this one is about 7 centimeters long.

Let's look at C. Kind of comparing with the estimate, thinking about how long it is, I think that this one is a little bit shorter than A, so I'm gonna put down 15 centimeters.

Now looking at D, thinking of I put the 7 here, I know it's not gonna be as long as 15, hmm, I'm gonna say about 10 centimeters long on my guess here.

Looking at E, I'm gonna make an estimate, thinking of it's going to be a little bit shorter than C, so I'm gonna say about 12 centimeters long.

So in blue, I've written the estimate for how long we think the lines are.

You will use this a lot in everyday life.

Have you ever made bracelets maybe, and tried to estimate the length of the string that you would need for somebody's bracelet?

Maybe the string that you're measuring, you're kind of estimating, oh, you need about eight inches, but when you actually make the bracelet, you might cut it or trim it to figure out the exact length.

That's what we're gonna do next, is we're now gonna take those lines and figure out the exact length.

Let's start off first with A. I'm gonna go ahead and make sure that I'm not lining it up on the edge of my ruler.

I want to make sure it's at 0.

We have this blown up for you so that you can see it and get the idea to see how long it is.

This line here is 17 centimeters long.

So in red, I'm gonna go ahead and write our actual measurement.

Were we close?

I said it was about 20 centimeters.

That was a pretty good estimate, kind of thinking of our ruler.

Remember, the estimate doesn't have to be exactly right.

Let's check out line B.

Line B, I'm gonna go ahead and line it up from endpoint to endpoint.

If you're struggling with endpoint to endpoint, you can always put a line there to help you measure your ruler to make sure you see the distance that you're looking at.

The actual measurement of this line was 4 centimeters.

I guess I was a little bit off on that one, but still, it was a good estimate to guess when I was looking at it but we know the actual measurement.

Now looking at C, I'm gonna line it up endpoint to endpoint, and I can see that this length is 13 centimeters.

Here, I was off by three.

Here, It was off by three.

Maybe I'm getting closer, I'm only off by two there.

Now let's check out the next line.

Line D, as we lined it up from endpoint to endpoint, we can see that this one is 8 centimeters long.

And then our last one, E, if we measure it from endpoint to endpoint, I can see that it's 11 centimeters long.

Excellent job measuring.

Does that make sense, measuring from endpoint to endpoint?

We may not be accurate at first with our guess, but with practice checking with a ruler, we can be more precise.

Now it's your turn to practice measuring with a centimeter ruler.

You're going to be using objects that you can find, do an estimate and then measure for the actual length to the nearest centimeter.

Second grade Math Mights, we've had an awesome time together with helping Abracus in our Mystery Math Mistake and then applying our knowledge to create a centimeter ruler and learning how to measure.

I sure hope to see you on another Math Might episode soon.

(cheerful music) (bouncy music) - [Kid] Sis4teachers.org.

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

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