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

- Welcome, second grade Math Mights.

My name is Mrs. McCartney, and I'm so excited that you joined us for another "Math Might" show.

Let's check out our plan for today.

Today, we're gonna be doing a Mystery Math Mistake and represent data in line plots.

First, we're gonna start off warming up our brain with a Mystery Math Mistake.

Oh, no, all of our Math Might friends are all mixed up.

It looks like Minnie and Subbie are wearing Abracus' hat, and our friend T-Pops has DC's mallet.

What is going on here?

Well, here's how the Mystery Math Mistake works.

One of our friends from Mathville is going to solve a problem.

It's your job to look closely at the problem to see if you can detect the Mystery Math Mistake that they may have made while they're solving the problem.

Let's see who our Math Might friend is that's needing some of our help.

Oh, no, it's Springling, she's all upside down and not sure if she solved this problem right.

She solved 84 minus 46 and put the answer of 39.

She used her process of the open number line counting up to get to her answer.

Let me show you how she solved it to see if you can detect the Mystery Math Mistake.

I'm gonna go ahead and make my open number line starting at 46 and ending at 84, just how Springling told me.

She decided to hop to a friendly decade number of 50.

When Springling made that hop, she knew that she went 5.

Next, Springling we went all the way from 50 up to 80.

With this great big hop, she said it was the distance of 30.

Last, she hopped from 80 to 84, which was 4.

When we add this all together, she has 30 plus 5 plus 4, which gives her the answer of 39.

Did you detect a Mystery Math Mistake in Springling's calculations?

I think I might've seen something there, but let's see what our friends are thinking first.

Our friend Krisha said that she thinks that Springling miscounted.

The distance between 46 and 50 is 4, not 5.

Great catch, Krisha.

Let's see if we can act that out.

Here we have 46 to 50.

Wait a minute, the distance between these two numbers is not 5.

We know from 46 to 50, that that is the distance of 4.

Now let's see what our friend Dawson is thinking.

He said, "I agree.

This would change the answer to be 38, not 39."

When we look here, if we add up what we have, 30 plus 4 plus 4, he's correct.

That equals 38.

So 84 minus 46 equals 38.

Great thinking, and great catch, Dawson and Krisha.

Did you see that Mystery Math Mistake?

Finding a Mystery Math Mistake in somebody else's work helps us to become strong mathematicians.

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

Our I Can Statement is, "I can represent data in line plots."

Let's take a look at this data that you see in front of you.

What do you notice and what do you wonder?

I see a bar graph that I'm familiar with in second grade, but then I see something else.

Let's see what our friends are thinking.

Our friend Krisha says, "I noticed the bar graph only has three bars, and the second one is like a picture graph in inches."

Ooh, we've learned about picture graphs in first grade.

That might be something we wanna think about.

Let's see what Dawson is wondering.

Our friend Dawson says, "I noticed there are 14 x's and the numbers are in inches."

Let's take a look at what the kids are noticing.

Our friend Krisha notices the bar graph only has three bars, and the second one is like a picture graph in inches.

I remember using picture graphs in first grade.

That's a really great notice that Krisha has.

Let's take a closer look at these two graphs to explain what they're noticing.

I see here that I see a bar graph with three bars, which Krisha was correct.

This over here appears to be something more like a picture graph.

Our friend Dawson said he notices 14 x's, 6, 7, 8, 9, 10, 11, 12, 13, 14.

He's correct.

He also says that he sees this here, where it's measuring in inches, so these numbers in the graph must represent inches.

These are really great notices.

Did you notice some of the same things that they did?

Let's check out their wonders.

Our friend Krisha is wondering if the second graph is a picture graph.

She also wonders what the x's are for.

Our friend Dawson says, "I wonder why there are numbers at the bottom?"

These are really great wonders.

Let's take a look at those together.

Our friend Krisha said, "Is the second graph called a picture graph?

And what are these x's for?"

Actually, boys and girls, the graph here that we're looking at is actually called a line plot.

A line plot is another way that we can display data in second grade to be able to draw conclusions or answer questions about.

The x's on here are representing the amount of teachers that have the hand span of six inches.

Over here shows the amount of teachers that have their hand span of eight inches.

So one, two, three, four, five teachers' hand span is eight inches.

Our friend Dawson wonders why there are numbers at the bottom.

Well, we just kind of show that these numbers really represent the inches.

This is a lot about what we're gonna talk about in today's show to help us to get better at understanding this new way of displaying data.

Let's measure our hand span to the nearest inch.

I'm gonna go ahead first and show you how you might want to measure your hand span.

So I'm gonna put my hand on the dry-erase board.

Now, I don't want my fingers squished together.

I wanna see how far if I stretched out all my fingers will my hand span reach.

I'm gonna go ahead with my marker and trace my hand so that I can measure my hand span.

This is something that you can do on a piece of paper or a dry-erase board, and then be able to measure it.

Now that I have my hand span, let's use my inch ruler to see how many inches my hand span is.

Let's go ahead and take the ruler and see if we can measure the length of my hand span.

I'm gonna try to draw a starting line here from my pinky over to my thumb, so I can kind of lay this to figure out the hand span.

I'm going to measure like we always do, starting at zero, and it looks like my hand span is seven inches.

We went ahead and looked at all the students in my class and measured their hand span just the way I showed you.

I created this chart of all the students' hand span, and we recorded their length of their hand span in inches just like we did.

Now, if I had questions for you like, what was the most common hand span?

Or if I asked you a question like, what is the least common hand span?

Do you think from looking at this data that we could answer these mathematical questions?

I mean, we could, but I think if we took this data and put it into a line plot, we could not only answer those questions, but we also could answer some other questions about the data that we collected.

Looking at our data, we need to decide, if we're gonna create a line plot, what numbers we should put.

So I see that I see sixes, sevens.

I see eights, I see a five, and I see a nine.

So if I wanna think of creating a line plot with inches, I think we could start it at five and count each notch until we get to nine 'cause that way we could record the data on our line plot.

Let's go ahead and move our data aside, and I'm gonna go ahead and make this line.

I know that this is going to be inches.

It's very important that when you're creating any kind of a graph that we label what we're talking about.

The top of this graph should really be looking at hand spans, so we wanna put up here Hand Span.

Now we know that we wanna look at those different parts, so I know that we have five, some people had five inches, some had six inches, some were seven inches, some were eight inches, and some were nine.

The next part is we're going to put an x to kind of stack it on top of each other until we have all of the data represented.

If I go back to my chart that I'm looking at here, I know that I could count how many students had five.

I see one and I see two.

Therefore, I would go ahead and put two x's.

The x's on a line plot represent each person, really similar to what Krisha was talking about in a picture graph.

In first grade, we sometimes make a smiley face or a star to represent it.

In a line plot, we mark it just with an x.

Now we're gonna go ahead and figure out how many of our friends had a hand span of six inches.

So now I'm gonna count, one, two, three, four, five, six, seven, eight, nine, ten.

That was really popular.

I'm gonna write 10 x's One, two, three, four, five, six, seven, eight, nine, ten.

We now have the hand spans for everyone that has six inches.

Now let's move on to seven inches.

Looking at the data, one, two, three, four, five.

Five students have the measurement of seven inches, which was the same as mine.

Now let's check our data to see how many people had a hand span of eight inches.

If I'm going down here, one, two.

I know that I'm counting two eights, so I'm gonna go ahead and put 2.

And then last but not least, we're gonna go through and look for nine, one.

We know there's only one.

Even though we didn't put a check mark every time we recorded the data on our line plot, we know we counted the numbers so we know that we have everyone included in our data.

Now we have all of the data displayed.

Do you think you know what the longest hand span is?

Well, that's kind of easy.

We did that when we set that up.

We know that nine is the longest hand span, just like we know the shortest was five.

What else can we draw from by looking at the line plot based on the information we put on?

With this data, I can figure out that six inches was the most common hand span in the class.

The least common hand span was nine inches.

Do you think you could draw the conclusion from our original chart that easily if we didn't have it on a line plot?

I don't think so.

We could have done it, but it would've taken us a while to do tallies and count.

That's the great thing about line plots.

Let's take a look to see if we can answer one more question.

How many more people had the hand span of six inches than seven inches?

Well, we know we can count these like we did before to show that we have 10 students that have six inches for their hand span.

And under seven, we know that we have five students.

So this is a simple problem.

10 minus 5 tells us that five more students had a hand span of six inches versus seven inches.

Wow, a line plot can really help us answer some really great questions about the data that we've represented.

Now it's your turn to try to apply what you've learned today in the show by creating your own line plot with some data that we've provided for you.

Second grade Math Mights, we've had a great show today from our Mystery Math Mistake, helping Springling turn back right side up to doing our measurement, looking at applying it within a line plot in answering questions.

I sure hope that you join us for another "Math Might" episode soon.

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

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