(bright upbeat music) - [Students] Math Mights.

- Welcome third grade Math Mights friends.

My name is Ms. Askew, are you ready to have fun with math?

I sure am.

So let's take a look at our plan for today.

Today, we're gonna do a number talk, and after our number talk, we're going to interpret line plots.

Before we get started, we need to warm-up our math brains with a number talk.

First, we are going to pose a problem using fractions.

Then you are going to solve it mentally without using paper and pencil.

And finally, we're going to share out our strategies.

Take a look at these six fractions.

Which fractions are less than 1/2, equal to 1/2 or more than 1/2?

Do you think you can give me reasons why each of those fractions can be sorted into those columns?

Let's see what our friends and Mia and Ava think.

Mia says, I think 2/4 and 4/8 are equal to 1/2.

Let's take a closer look at what Mia is thinking.

I have 1/2 fraction strip, and we're gonna take 2/4 and see if it's equal to 1/2.

1/4, 2/4 is equal or equivalent to 1/2.

I'm going to record that in my column.

Then I'm gonna cross it out because I've already looked at that fraction.

Mia also says that 4/8 are equal to 1/2.

1/8, 2/8, 3/8, 4/8.

4/8 is also equal to or equivalent to 1/2.

Great job looking at those fractions and seeing how they're equivalent or equal to 1/2.

Now, let's see what Ava thinks.

Ava says, I think 8/8 and 2/2 are more than 1/2.

They are equal to a whole.

First let's look at 8/8, and we can clearly see that 8/8 is more than 1/2.

I'm going to record that.

And then I'm gonna cross it out because I've already looked at it.

Ava also said that 2/2 are more than 1/2.

So let's take a look at that.

We have 1/2 and 2/2.

She's right.

2/2 is more than 1/2.

I'm going to record that as well and cross it out.

Great job ladies finding those fractions that are greater than 1/2 and equal to 1/2.

I wonder what fractions are less than 1/2.

Let's take a look.

Mia says I know 1/4 is less than 1/2.

If I take my 1/4 fraction strip and place it underneath.

I can see that.

yes, she's correct.

1/4 is less than 1/2.

So I'm gonna record that in my lesson 1/2 column.

I'm gonna cross that out.

Ava says, I know 1/3 is less than 1/2 because thirds is smaller than halves.

We can see that 1/3 is in fact less than 1/2.

So I'm gonna record that in my lesson 1/2 column.

Great job taking everything that you know about fractions and using that to sort them in the appropriate column.

Now let's take a look at our, I can statement for today.

I can make sense of line plots with length in halves and quarter inches.

Take a look at this chart in line plot.

What do you notice?

What did you wonder?

It looks like the data on the chart is represented on the line plot.

Let's see what our friends, Ava and Mia think.

Mia notices the length of the shortest twig is three inches.

And the length of the longest twig is seven inches.

Let's take a closer look at what Mia notices.

We see that the twigs have been listed, and the length of those twigs have also been listed in inches.

We take this data or information and put this on our line plot.

These numbers represent the length of the twigs.

For example, twig one measures three inches.

That's why the X is put here above the three.

They Xs actually represent the twigs.

That is how Mia was able to see that twig one is the shortest twig because there are no other twigs listed that are less than three.

She also knows that twigs seven here on our chart was represented with an X here.

She knows that it is the longest because no other twigs on our chart has a length that's greater than seven.

Ava says three twigs had the length of six inches.

Twigs with four inches make up the largest group.

Let's take a closer look at what Ava noticed.

She says that's three twigs had the length of six inches.

So using our line plot we're gonna find the six that represents the inches.

And remember the Xs represent the twigs.

So if we count the Xs, one, two, three of those twigs had a length of six inches.

We can also find this on our chart here at the bottom.

Here's one twig, twig number six that measured six inches, twig number 13, measured six inches, and twig number 14, measured six inches.

Ava also notice that four inches make up the largest group.

If we look at our line plot, four inches has the most Xs which represents the twigs.

One, two, three, four, five to be exact.

Great job Ava and Mia.

You were able to take that information and easily notice it on the line plot.

Now let's look at some of the things that you might be wondering.

Mia wonders were any of the twigs in between whole number lengths?

Ava wonders why did you measure the length of twigs?

Where was this data collected?

Those were some great wonders.

Now I wanna talk more about Ava's wonder.

How will we adjust the line plot if a twig was six and 1/2 inches long?

I wonder how we're gonna represent that.

It reminds me of when we were working with rulers.

Let's see what Ava thinks.

Ava says we would have to add 1/2 inch marks to the scale.

So we know where to put the X. I'm going to use my line plot and I'm going to mark where the 1/2 tick marks would be located.

Remember when you're doing 1/2 it's in between the two numbers.

So in between zero and one, and between one and two, two and three, three and four, four and five, five and six, and six and seven.

Now that I've labeled the 1/2 tick marks I'm gonna show you where I would plot the X on that line plot.

Here's the six, here's my 1/2 mark so I'm gonna put my X right above it.

You're doing an awesome job third grade Math Mights taking what you know about fractions and using them to put them on a line plot.

Third graders, I would like you to take a look at this line plot.

Ask yourself what could the data on this line plot represent?

I see lots of plots and whole numbers.

Let's see what Mia thinks.

Mia says, maybe it's the length of leaves or maybe even rocks.

Wow, third grade Math Mights, we don't even know what it represents.

It wasn't labeled.

It could represent multiple things.

Let's review this line plot and what it actually represents.

It is a line plot of seedlings.

Third grade Math Mights.

You might be asking yourself, what is a seedling?

Well, when you plant a seed and it starts to grow, a seedling appears.

Seedlings grow at different lengths.

So the information on our chart is measuring the length of those seedlings as they begin to grow.

What do we know about the seedlings based on the line plot?

Is there anything that you could share with a friend about what you see on that line plot?

There sure is a lot of information there.

Let's see what our friend Ava says.

Ava says the tallest seedling is five inches.

The shortest seedling is 1/2 an inch.

Looking at our line plot, we can see that the tallest seedling is five inches because remember these numbers represent the height of the seedlings in inches and the Xs represent the seedlings.

We see the X is above five and there are no other Xs that are greater than five so that means five is the highest or tallest seedling.

Now how would we figure out which seedling is the shortest?

Let's take a look at our line plot.

We see that the Xs that represent the seedlings are right here above this 1/2 inch tick mark.

There are no other seedlings that are less than 1/2.

So that's how Ava knows the shortest seedling is 1/2 inch.

Let's see what Mia thinks.

Mia says 22 seedlings were measured.

But how does she know that?

Let's take a look closer look at our information and see if we can't answer that question.

I guess I can start to count all of the Xs that represent the seedlings.

One, two, three, four, five, six, man, there sure are a lot of Xs.

That would take me forever.

But if I look at my data chart, I can quickly see that there were two 22 seedlings measured.

Excellent work.

I bet there's more information that we can take from that line plot.

Looking at my line plot let's determine how many seedlings were an inch and 1/2 versus how many were only one inch.

Remember the Xs represent the seedlings.

When I look at the tick mark that's right in between the one and the two, I know that that measures one and 1/2 inches and I can count them.

One, two, three, four, five, six seedlings.

Six seedlings were one and 1/2 inches long.

If I count the Xs that are above just the one inch tick mark, I see that only one, two three seedlings were three inches long.

So when I compare the two, I see that there were three more seedlings that were one and 1/2 inches versus the three that were only one inch.

Let's see if we can determine how many seedlings were three inches and shorter versus three inches and taller.

I'm gonna start at the three inch mark.

Do I see more Xs here that are three inches and less, or do I see more Xs that are three inches and more?

It looks like there are more Xs that are three inches and less.

Using the line plot, I was able to draw conclusions.

It was very easy to see without even counting how many seats we're three inches or less versus the seedlings that were three inches or more.

How is displaying the measurements on a line plot different from displaying the measurements in a table.

Ava says the line plot is more organized because you can see all the same measurements that are the same length together.

Mia says it is also nice because it goes from smallest to largest along the bottom.

It's also nice to know instead of writing the numbers, you can represent it with an X. I agree with Ava and Mia, don't you?

A line plot makes it so much easier to see the data that's being represented.

What questions could you answer more easily with the line plot than the table?

Ava says I could answer how many seedlings were three inches tall because I just counted the marks instead of searching through the table.

Great thinking that line plot does help to answer so many questions quickly.

Now let's take a look at this line plot where students have measured the length of twigs in inches.

How could we discover how many twig links are represented on the line plot?

When we look at this line plot we see that it starts at zero and it ends at eight.

It has been labeled as the length of twigs in inches.

We know that the Xs represent the twigs.

So in order to find out how many twigs were measured we would just need to count all of the Xs on our line plot.

Two, four, six, seven eight, 10, 12, 14, 15, 16, 17, 18, 19 twigs we're measured.

How many twigs were less than six inches long?

Looking at our line plot, we're gonna find the tick mark that has the six inch mark.

To answer the question how many were less than six inches long?

All we would have to do is count all of the Xs that are less than six.

One, two, three, four.

Four twigs measure a length that was less than six inches.

We can also answer the question, what is the most common twig length?

I can determine which twig had the most common twig length by finding the tick mark that has the most Xs.

I can see that this tick mark here has the majority of the Xs plotted.

But now I have to determine what is the length of that tick mark?

It's in between the six and the seven.

So I know it's more than six.

Thinking back to my fractions, I know that if my number line is divided into one, two, three four tick marks, I'm working with fourths.

So this tick mark represents six and 1/4.

So the most common twig length is six and 1/4 inches.

Third grade Math Mights you are doing an awesome job at plotting information on a line plot.

Now it's your turn to interpret data from a line plot just like we did today.

Third grade Math Mights I'm so proud of all of the hard work that you did today.

I hope you join me again real soon where we'll learn more with math.

(bright upbeat music) - [Girl] sis4teachers.org.

(bright upbeat music) Changing the way you think about math.

(bright upbeat music) - [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.

(bright upbeat music)