(upbeat music) - [Narrator] Math Mights!

- Welcome, third grade math might friends.

My name is Ms. Askew.

Are you ready to have fun with math today?

I sure am.

So let's check out our plan for today.

First, we're going to do a mystery math mistake.

After that, we're gonna have fun learning about fractions on a number line.

But before we begin, let's warm up our math brains.

Oh no, all of our math might strategies are all mixed up!

It's your job to help unscramble and unmix those strategies, and help us solve a mystery math mistake.

Okay, boys and girls, this is how it works.

We're gonna work out a math problem that you are familiar with, and it's your job to use your magnifying glass to find the mystery math mistake.

Here we have to DC, and he's gonna help us with this.

Remember how DC taught us how to decompose numbers to help make multiplying easier?

Well, he took 12 and decomposed it into 10 and two.

We're gonna use our area model to solve that.

Nine times 10 and nine times two.

Nine times 10 equals nine, and nine times two equals 18.

We add these two numbers together, nine plus 18, and that equals 27.

12 times nine equals 27.

Okay, boys and girls, what do you think about that mystery math mistake?

Do you agree with what DC did, or did you use your magnifying glass to find a mistake?

Let's see what our friends, Trevor and Marcus thought.

Trevor says, "The product seems too small to me.

"How can you have only 27 if you have 12 groups of nine?"

Marcus says, "I think you were supposed to do nine times 10, "not nine times one.

"Then the answer would be 108."

All right, boys and girls, did you find that same mystery math mistake like Trevor and Marcus?

Let's take a look at our whiteboard.

Marcus is correct, 10 groups of nine or 10 times nine does equal 90.

We also have to make that correction with our addition number sentence.

Instead of nine plus 18, we have to correct that to 90 plus 18.

That means our sum is also going to change to 108.

So, 12 groups of nine does not equal 27, it equals 108.

Good job, third grade math might friends, Marcus and Trevor, you caught the mystery math mistake.

Boys and girls, were you able to catch that mistake?

If you did, give yourself a pat on the back.

Awesome job.

Let's check out our, I can statement for the day.

I can learn about fractions using a number line.

Take a look at these two number lines.

What do you notice?

What do you wonder?

Trevor notices that one number line starts at zero and goes up to 10.

He also notices a number line that starts at zero and goes up to one.

Marcus notices that only zero and 10, and zero and one are labeled, and they both have a mark in the middle of the number line.

Trevor wonders, what numbers are on the tick marks?

Marcus wonders, why are the number lines split in half?

Could we put more numbers on the number line?

Boys and girls, that mark that you saw in the middle of the number line, that is what we call a tick mark.

What do you know about the number each tick mark represents?

If we look at this first number line that starts at zero and goes up to 10, that tick mark is right in the middle.

So that means it's halfway.

What's half of 10?

It's five.

So we're gonna label that tick mark as five.

Looking at that second number line, it starts at zero and it goes up to one.

What is halfway from zero to one?

That would be, one half.

So we're gonna label that tick mark one half.

Great job with those notices and wonders, third grade math mights.

Now we're gonna do some more work with fractions and number lines.

And if you're anything like Ms. Askew, you're gonna pay close attention to this lesson because fractions can be a little confusing for third graders.

It's my job today to make you feel a little more at ease, and become more comfortable with learning about fractions.

Are you ready to learn?

Let's go.

Let's take a look at these number lines.

Boys and girls, those were a lot of number lines.

And as you can see, they have been created in many different ways.

I wonder if we can sort them.

Let's take a look at what Trevor thinks.

Trevor says number lines A, E and G have tick marks at the whole numbers.

I have number lines A, E and G, blown up so that you can see them a little better.

Number line A shows zero to eight.

So that means this tick mark represents the number four, because four is halfway in between zero and eight.

Number line E shows zero and four.

So Trevor must label the tick marks, one, two, three, and then four.

Number line G starts at zero and ends at six.

We have two tick marks.

So Trevor labels those tick marks as two, four, six.

Great job sorting those number lines, Trevor.

You notice that each of those tick marks had whole numbers on them.

Now let's see how Marcus sorted those number lines.

Marcus says, "These number lines have tick marks "that are fractions."

I have the number lines that Marcus was talking about blown up, so that you can get a better look at them.

Let's talk about some of them.

Let's look at number line B.

It starts at zero and it ends at one, but we see tick marks that are in between zero and one.

That tells me that these tick marks represents fractions or parts of a whole because they're in between the zero and the one, which is a whole number.

If we look at number line F, we also see it starts at zero and ends at one.

There are those tick marks again that are in between the whole number.

That means those tick marks represents parts of a whole or fractions.

One more number line.

Let's look at D. It starts at zero and we go to one, and then there's two.

But if I notice the tick mark here, it's in between the whole number one.

So that tells me this tick mark is less than one whole number, which means it's a fraction.

Great job, third grade math math mights, that was a lot of hard work.

But as you can see, using a number line helps you to see how it's been partitioned, and what the value of each part is.

Now we're gonna do some more work with fractions on a number line with our friends, Clare and Andre.

Andre and Clare are talking about how to label fractions on a number line.

Andre says half can be labeled like this.

We have the number line that starts at zero and ends at one.

And he goes from zero to halfway, then we have a tick mark, then halfway, and then to the whole number one.

Clare says half can be labeled this way, starting at zero and ending at one, and her point is right in between, and she labels it half.

How could both students labeling makes sense?

Let's see what Trevor thinks.

Trevor says, "Andre was thinking about the parts "that had a length of half, "so he labeled the parts zero to one half, "and one half to one with half."

This is what Andre was thinking.

Here's our number line.

It starts at zero and it ends at one.

And in between this tick mark and the zero, he was thinking about the length of the line.

So that's why he labeled it half.

Then he started from the tick mark and went to the whole number one.

And he said, the length of that is half.

Hm, that kinda reminds me of the fraction strips that we made before in a previous lesson.

Did you guys keep up with your fraction strips envelope?

Let's take a look at that again.

This is half, and this is also half.

So I understand why Andre was thinking that was the correct way to label that number line.

Looking at Clare's number line that starts at zero and ends at the whole number one, Clare put her tick mark right in the middle, which is the midway point between zero and one.

And that's halfway, so she labeled it one half.

Okay, third grade math mights, were you anything like Ms. Askew?

Were you able to make sense of how Trevor and Clare labeled those number lines?

I sure hope so.

Now let's do some more work with labeling fractions on a number line by folding them.

Let's label five number lines.

All right, third grade math mights, we're going to work with halves on the number line.

So we have our number line that starts at zero and ends at the whole number one.

In order to make halves, we're gonna take this number line and fold it in half.

We have partitioned the number line into two equal parts.

We're gonna put our tick mark right in the middle, and we're gonna label it two, because we have two equal parts, and it's in the halfway point in between zero and one.

Third grade math mights, you just learned how to divide the number line into halves.

Now let's try thirds.

Our number line still starts at zero and ends at one.

We're gonna fold our number line first.

We're gonna fold it into thirds, and then we're gonna label it.

Notice that we have one, two, three equal parts.

So that means we're working with thirds.

We're gonna label our number line with our tick marks at each of those points.

This would be one third.

This tick mark is two thirds, and then whole number one is the same as three thirds.

And that's how we label thirds on a number line.

Now we're gonna do an even harder one and label fourths.

We're gonna take our number line and we're going to partition it so that we have four parts.

First, we're gonna fold it in half, and then we're gonna fold it in half again.

Now we have partitioned our number line into four equal parts.

Let's label them.

The first tick mark would represent one fourth.

The second tick mark, two fourths.

The third tick mark, three fourths, and at the whole number one, that is the same as four, fourths.

Is this becoming easier to understand and visualize, third grade?

I sure hope so.

Let's move on to folding our number line into sixths.

Our number line starts at zero and ends at one.

We wanna partition it into six equal parts.

So first we're gonna fold it into thirds.

So we're gonna fold it and fold it again, and then fold it in half.

Now we have six equal parts.

Let's label it on the number line.

The first tick mark is one sixth.

The second tick mark, two sixth.

Third tick mark, three sixth, fourth tick mark, four sixth.

The fifth tick mark, five sixth.

And at the whole number one, that's the same as six, sixth.

Awesome job, third grade math mights, we have one more number line to label.

I'm just curious, did any of you run and get your fraction strips from your envelope to try and match it up with Ms. Askew?

All right, this time we're gonna divide our number line into eighths.

Our number line starts at zero and ends at the whole number one.

We want eighth, so first we're gonna fold it in half, we're gonna fold it in half again, and one more time.

Now we've partitioned our number line into eight equal parts.

Let's label it.

The first tick mark is one eighth, second, two eighths.

The third tick mark, three eighths.

Fourth is four eighths.

The fifth tick mark is five eighths, sixth tick mark, six eighths, seventh tick mark is seven eighths.

And finally at the whole number one, we have eight, eighths.

Great job making those number lines.

So now it's your turn to create partitioned number lines on your own.

I had so much fun with you today, third grade math mights.

First, you helped me with your magnifying glass to locate DC's mystery math mistake.

And then we moved on to that scary, but not so scary topic of fractions, where we were able to partition number lines and label those fractions.

You did an awesome job, and I hope to see you soon.

(upbeat music) - [Narrator] Sis4teachers.org, changing the way you think about math.

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