(playful music) [children] Math Mights Welcome third grade Math Mights.

My name is Ms. Askew and I am super excited to have fun with math with you today.

Let's look at our plan for today.

First, we're gonna solve a mystery math mistake.

After that, we're going to locate unit fractions.

But before we begin, let's warm up our math brains with a mystery math mistake.

Uh-oh, it looks like all of our Math Might friends have their strategies mixed up.

It's your job help us solve the problem.

Here's how it works.

I'm gonna take a concept that you are familiar with, and you're gonna use your magnifying glass to find the Mystery Math Mistake.

Our problem for today is 15 groups of three or 15 times three.

Now, DC is upside down.

He's a little confused, but I'm gonna use the strategies that he taught us to solve this problem, using our area model.

First, we're gonna take the number 15 and decompose it just like DC taught us.

15 decomposes into 10 and five.

10 groups of three equals the product 30.

5 groups of three equals the product 15.

I'm gonna take these two partial products and add them together.

30 plus 15 equals 55.

15 groups of three equals 55.

All right third grade Math Mights.

What do you think of my math?

Were you able to use your magnifying glass and find the mystery math mistake?

Hmm, let's see what our friends Trevor and Marcus think.

Trevor says, "I know that 15 times two equals 30.

"So the product seems too high to be 55.

"When we only have one more group of 15."

Marcus says, "I don't think you added correctly.

"30 plus 15 equals 45, not 55."

Well, let's go back and check our mistake.

As you can see, DC is right side up and he's back on his pencil.

So he figured out the mistake as well.

So, if we look 30 plus 15 does not equal 55.

It equals 45, just like Mark pointed out.

That means 15 groups of three equals 45.

Excellent job, Trevor and Marcus finding that mystery math mistake.

When you are working with math concepts and you're able to catch those mistakes being made.

That means your understanding of that concept is getting a lot better.

Now let's take out our "I can" statement for the day.

I can partition number lines to locate unit fractions.

Now take a look at these four images.

Which one doesn't belong?

I noticed a lot of different things with those images.

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

Trevor notices that A doesn't belong because it isn't a number line, and it has a part that's been shaded.

This kind of reminds me of the fraction strips that we made.

Marcus says that B doesn't belong because there are no fractions labeled.

It has whole numbers.

The number zero and the number one.

The other images have fractions.

Trevor says, "C doesn't belong "because it's not split into equal parts, "and doesn't show partitions."

So here's the number line, and this is not split into equal parts.

And we don't have tick marks to represent the partitions.

Marcus says, "D doesn't belong "because it doesn't show thirds or half."

If we look at this number line, we see a tick Mark and it's been labeled as fourths.

A is thirds C is thirds.

And remember from the last lesson, we have one, two, three tick marks.

So that's thirds as well.

Great job, Trevor and Marcus.

You came up with good notices to find out how each of those images has something about it that doesn't belong.

When I looked at those four images, I thought that A didn't belong, because it looks more like our fraction strips whereas B, C and D, they were all number lines.

When you want to make your reasoning clear while locating and labeling fractions on a number line, what are some important things to include?

The first thing to notice is partitions of equal parts.

Then you wanna notice a dot or point on a number line.

And finally, label at the fraction.

Let's look at image D from those four images we just saw and see if we can apply those three tips.

I know that this number line has been partitioned into fourth, because if I have my starting point which is zero and I take one hop, two hops, three hops, four hops to the whole number one, that tells me that this number line has been partitioned into fourth because I took four hops.

And the dot here represents one fourth or one hop from my starting point.

Great job third grade Math Mights.

Now that we've learned those three great tips at recognizing what's needed on a number line.

Let's take a look at how Claire, Andre and Diego partitioned their number lines into fourths.

Do one of those pictures or images make more sense to you?

Let's check out what Trevor thinks.

Trevor says, "Andre's number line makes the most sense to me "because it shows the first part "from zero to one in four equal parts.

"I could count one fourth, two fourths "then three fourths and four fourths."

Andre's number line starts at zero and ends at the whole number two.

He labeled his fractions from zero to one.

Now remember the strategy that we use.

Our starting point is here, and we're gonna take one, two, three, four hops.

And that's how I know it's been divided into fours.

The first tick mark is one fourth.

Second tick mark is two fourths.

Third tick mark is three fourths.

And the final tick mark at the number one, is also the same as four fourths.

Great job, Trevor, understanding Andre's thinking on how to divide that number line into fours.

Let's see what Marcus's thoughts were.

Marcus says, "Diego's number line has four tick marks "between zero and one, but that is five parts."

Here's the Diego's number line.

It does in fact have, one, two, three four tick marks in between zero and one.

But if we start at zero, which is our starting point and we take one, two, three, four, five hops we know that that is five parts.

So that's fifths not fourths.

If we labeled Diego's number line, the first tick mark is one fifth, two fifths, three fifths, four fifths, and at the whole number one that's the same as five fifths.

Third grade Math Mights, I'm curious.

Did any of you have the same thinking on Diego's number line?

Did you count those four tick marks in between and think that it was fourths?

A lot of times third graders do make that same mistake.

That's why we wanna start at the zero and count those hops.

That's how we know how many partition parts there are on that number line.

Let's take a look at Claire's number line Claire partitioned a whole number line into four parts except, I know the first tick mark represents half because it is only halfway between zero and one.

So that is showing halves not fourths.

Looking at Claire's number line.

It starts at zero and it ends at two.

I understand her thinking because, she does have four tick marks, but, she labeled them half way between zero and one, and halfway between one and two.

That's why she thought it was fourths.

But we know halfway between zero and one is one half.

Halfway between one and two, is one and one half.

So Claire did not partition her number line into fourths.

See third grade Math mights?

That's why it's so very important to be precise when you are labeling partitions on a number line.

let's practice partitioning number lines.

Then lets locate and label each fraction.

Let's try thirds.

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

We wanna partition this number line into thirds.

We can take and make one, two tick marks.

We don't have to make the third tick mark because it's already there.

Now another way of looking at that is to start at the starting point which is zero, and take one, two, three hops.

That's how I know this number line has been partitioned into thirds.

Now I want to label one third on that number line.

I'm going to put my point here at the first tick mark, and label it one third.

Awesome job third grade Math Mights, locating and labeling thirds on that number line.

Now we're gonna take a look at a different number line.

This number line starts at zero but it goes beyond one and stops at four.

We wanna label half.

We know that half is in between zero and one.

So we want to partition this number line so that we have two equal parts.

We're gonna draw one tick mark right in the middle, because the other tick mark is already there.

So that shows us that we have two equal sections.

We also know that this has been divided in half because if we start at zero, we can take one, two hops.

So this tick mark, we're gonna put a point here and label it as one half.

Great job labeling halves on that number line.

Now let's see if we can try it with eighths.

This number line starts at zero goes beyond one and stops at four.

We want to locate eighths on this number line.

Eighths is part of a whole so that we know is less than one.

So we're gonna locate it between zero and one.

First, we wanna partition this number line into eight equal parts.

We wanna have seven tick marks because that eighth tick mark, is already drawn for us.

One, two, three, four, five, six, seven, eight.

Another way of knowing that we've partitioned this correctly, is by starting at zero which is our starting point, and making sure we take eight hops.

One, two, three, four, five, six, seven, eight.

We want to now locate one eighth on the number line.

We're gonna put our point at the first tick Mark, and label it one eighth.

Awesome job third grade Math Mights.

You're really getting the hang of locating fractions on a number line.

Let's take a look at two more number lines.

What do you notice?

Let's see what Trevor thinks.

Trevor says, "the top number line "just has zero to one.

"The bottom number line has zero to two."

Both ones are in the same place.

And so are, the sixths.

Okay third grade this might be a little confusing.

But just remember, even though that number line extends beyond one, the location of that number doesn't change.

So far we have represented fractions in three different ways.

Let's take a closer look at what we remember.

Looking at this first example, we have a piece of paper that has been partitioned into four equal parts.

If we flip over this one part, it's white.

That means this part is one fourth because, one out of the four parts is white.

Another way that we look at fractions is with our fraction strips or our fraction tiles.

We have one, two, three, four fraction tiles.

That means, this part is one out of the four.

So that's one fourth.

And finally we learned about fractions on a number line.

It starts at zero and ends at two.

We know that one fourth is less than one.

So we have to find that point on our number line.

It has been partitioned into four equal parts.

We can count that by hopping, one, two, three, four or by looking at our tick marks.

These are all different ways to represent unit fractions.

How would you describe unit fractions to a friend?

Let's see what Trevor thinks.

Trevor says, "When you split a whole into equal parts, "a unit fraction is one of those parts.

"All of these show, a whole split into four equal parts.

"One fourth is one of those parts."

Looking at these examples, we can see that Trevor's thinking is correct.

They all represent the unit fraction of one fourth.

We know what's a unit fraction because, all unit fractions has one as a numerator.

And here we have one fourth.

Remember third grade Math Mights, when you're thinking about unit fractions if an object is divided into six equal parts, the unit fraction is one sixth.

If it's partitioned into eight equal parts, the unit fraction is one eighth.

Now it's your turn to partition locate and label fractions on a number line.

Whew, third grade Math Mights, that was a lot of hard work you just accomplished with fractions today.

First, with our lesson we talked about how to use your magnifying glass to find that mystery math mistake.

And then we were locating unit fractions on a number line.

You did an awesome job today, and I hope to see you soon so we can work more with fractions.

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Changing the way you think about math.

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