(upbeat music) Good morning, my magnificent mathematicians.

I'm so excited to be with you this morning.

We are going to have so much fun today learning more about math and growing our brains.

And I have one of my favorite people in the world with me today.

This is my daughter, Hally.

To get us started, I want to tell you a funny story about her.

She thought she was getting away with something, but she wasn't.

Our family was eating sweet baby carrots as part of our dinner.

And Hally was trying to eat the carrots, but she didn't like them, and they were making her gag.

So she picked up her napkin, covered her eyes, and spit the carrots into her napkin.

She was only two.

She thought that because her eyes were covered and she couldn't see herself spitting out the carrots that I couldn't see her either.

But you were busted, weren't you?

Hally: Yes.

Are there any foods that make you gag?

Maybe it's a food that you know is good for you, but you try one bite and you think, "Oh, never again."

Well, let's imagine that you've decided you will try to eat carrots every day until you can eat ten carrots without gagging.

To show the math about this, we are going to need to walk over and get our handy dandy magic whiteboard Perfect.

So let's look at a table of values for the first week.

On the left side, you'll see days one through seven.

And on the right side, that's where we keep track of how many carrots we were able to eat.

So on day one, we ate no carrots.

On day two, Hally, you ate one carrot without gagging.

On day three, you ate one carrot again.

On day four, you did awesome.

You ate three carrots.

On day five, you ate four carrots.

On day six, five carrots and on day seven, you ate five carrots again.

So you're almost halfway there.

It's good to see numbers on a table like this.

But another great tool that helps us make sense of numbers is a graph.

So we're going to graph these numbers from the table and see if we can make a prediction about how long it will take for Hally to eat ten carrots.

Now, a graph is made up of two number lines.

The bottom number line runs from left to right, just like the number line that you have been counting on since kindergarten.

This number line represents which day you're on in the carrot challenge.

We're going to start at zero and go by whole numbers up to 14 for two weeks.

Then we have a second number line for how many carrots we're eating.

This number line is also going to start at zero and go by whole numbers up to ten because that's how many carrots she's trying to eat.

The number line is vertical.

And when you see two number lines put together like this, we call it the coordinate plane.

The number line at the bottom is the horizontal axis, and the number line on the side is the vertical axis.

Now we get to plot the points from our table.

So let's look at the set of numbers that will make our first point.

The point will be 10 because on day one, she didn't eat any carrots.

Look at the day one spot on the horizontal axis and stay at zero on the vertical axis.

OK. Let's plot our second point.

Find day two on the horizontal axis and go up to one carrot on the vertical axis.

Now, we'll need a point where those two values connect, and that's the point (2, 1).

Are you starting to see how it works?

Let's do a few more.

On day three, she ate one carrot.

So we have the point (3, 1).

On day four, she ate three carrots.

So we'll add the point (4, 3).

On day five, she ate four carrots.

So add the point (5, 4), and on day six, she ate five carrots.

So we'll add the point (6, 5).

The last day of the week, she ate five carrots again.

So we'll add the point (7, 5).

The neat thing about points on the coordinate plane is that they let us see trends.

From this graph, we can predict how many more days it will take for Hally to be able to finish those ten carrots at dinner time.

I'm going to grab my pointer and we're going to use this like a line.

If we look at a line through the points, we can make a good prediction and see about how many days it's going to take to eat those ten carrots.

So, Hally, on the vertical axis, go up to day ten.

The point where your finger is should be above the number of days it will take you to eat ten carrots.

So slide over all the way to, yeah to our prediction line.

And then over the days it's going to take you to eat those ten carrots.

What did you land on?

Hally: 13.

OK, so 13 days.

It's going to take about two weeks.

Our prediction point is at (13, 10).

So that tells us about 13 days.

Great job on this.

Graphs can seem a little scary at first, but as long as you think about them like combining two number lines, they are super helpful for making predictions about what could happen in the future.

All right.

Great job today, Hally.

That's all that we've got for today.

I hope that you have a great rest of the day.

We're going to, aren't we?

Hally: Mm, hmm.

And we will see you next time on Rise and Shine.

(upbeat music)