(delightful music) - [Children Speaking in Unison] Math Might.

- Welcome, third grade Math Might, my friends.

My name is Ms. Eskew, and it's time to have fun with math.

So let's check out our plan for today.

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

After that, we're going to compare fractions with the same numerator.

Before we begin, let's warm up our math brain.

Oh-oh, it looks like our math might friends had their strategies all mixed up.

We need your help to solve the mystery math mistake.

Here's how it works.

I'm going to act out a problem with a concept you are familiar with.

You need to use your magnifying glass to find the error.

Make sure that you can explain your thinking.

Sprinkling is all turned upside down.

So I think our misery math mistake might be with our multiplying up strategy.

Our target number is 96.

So we wanna figure out how many groups of six are in 96.

I think I'm gonna start with 10 groups of six because I know that 10 groups of six equals 60.

Next, I'm going to figure out how many more groups of six I need.

I think I'm going to try six groups of six because I know six groups of six equals 36.

And finally, I think I only need one more group of six and that's going to equal six.

When I add these altogether 60 + 36 + 6 = 96.

Now I'm going to add all of my groups 10 + 6 + 1 = 17.

So 96 divided by 6 equals 17.

Let's see what our friends Nora and Laila think.

Nora says, "I know 17 groups of six equals 102.

So I think something isn't correct."

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

Nora used the inverse operation of 17 x 6.

And that equals 102.

It doesn't equal 96.

So I agree with Nora's thinking.

Let's see what Laila says.

Laila says, "It looks like you have one extra group of six in 96.

It should be 16 because 10 groups of six is 60, then six of six is 36, which would be 16 groups of six in 96."

Let's take a closer look at what Laila is saying.

She told us that we had an extra group because if we take 60 and add it to 36, it does equal 96.

So that extra group of six is not needed.

Let's go ahead and take that away.

And once we do that, we have 10 groups of six plus six groups of six and that equals 16.

Thanks, Nora and Laila for helping us solve that misery math mistake.

Third graders, were you able to use your magnifying glass and solve the mystery math mistake?

Now let's move on to our 'I can' statement for today.

I can compare fractions with the same numerator.

Let's take a look at these two fractions, 5/6 and 5/8.

Priya says, "5/6 is greater than 5/8."

Tyler says, "5/8 is greater than 5/6."

Who do you agree with?

Can you show your thinking?

Let's see what our friends Nora and Laila think.

Nora says, "I agree with Priya because sixth are bigger than eighths.

So 5/6 is greater than 5/8."

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

It looks like the sixths, one, two, three, four, five, six is greater than the eighth.

Sometimes as third graders, we'll look at the numerator and the denominator.

And if the denominator is bigger in one fraction than the other, we automatically think that that fraction is bigger.

But as you can see with our fraction strips, the six are divided into larger parts.

That's a great way to look at fractions with the same numerator.

I wonder if there's a different way of looking at that.

Let's see what Laila thinks.

Laila says, "I also agree with Priya because I drew it on a number line and saw 5/6 is to the right of 5/8."

Let's take a closer look at what Laila is saying.

We have two number lines.

The first one has been divided into eighths.

And the second one has been divided into sixths.

When we plot our fractions 5/8, we count 1/8, 2/8, 3/8, 4/8, 5/8, and that's our point.

We also plant five six by counting 1/6, 2/6, 3/6, 4/6, 5/6.

We can clearly see that 5/6 is further down the number line than 5/8.

And that's why 5/6 is greater than 5/8.

What do you think the difference was?

What did you notice about the way Nora explained it using the fraction strips, and how Laila described it using the number line?

When we look at the two different representations, we can see that Nora was looking at the fraction strips.

She can see that the size of each of the parts can be compared, and 1/6 is bigger in size as compared to the part that's 1/8.

Laila looked at it from using a number lines perspective.

5/6 is further down the number line than 5/8.

And that's how she knew that 5/6 is larger than 5/8.

Great job, third grade Math Mights using what you know about fractions to compare them using the numbers trips and the number line.

I have another little trick that I like to help my students when they are trying to figure out which is greater.

Think about if you had a chocolate bar.

Now, if you had to share that chocolate bar with some friends, would you want to share six or eights?

I love chocolate.

So I would like to have a greater size of chocolate.

So I think between six friends and eight friends, I would rather share my chocolate bar with six friends because then that piece would be a lot larger or greater than the piece that was broken up and share with the eight friends.

Does that help you make a little more sense about this concept?

Let's apply that knowledge which fraction is greater 3/4 or 3/8?

Now, when I look at those fractions, I see that the numerator is the same but the denominator is different.

Think about that chocolate bar.

Would you want to share a chocolate bar that's divided into fourths or into eighths?

Let's see what Nora thinks.

Nora says, "I think 3/4 is greater than 3/8 because when I use the area model papers, I can visualize which one is greater."

Let's take a closer look at Nora's thinking using our whiteboard.

Here I have a hole and I'm going to divide it into fourth.

The fraction that we are comparing is 3/4.

So I'm gonna take away one of those fourths.

So we have 3/4; 1/4, 2/4, 3/4.

Now the question is, is 3/4 greater than 3/8?

Let's compare using our eighths.

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

It looks like 3/4 is greater than 3/8.

Let's write that out.

3/4 is greater than 3/8.

Even though the numerators were the same, the denominators were different and we can see using our area model that the fourths were a lot larger or greater than the eighths.

Great job there are great Math Mights.

Now that you were able to figure out which fraction is greater, Let's try figuring out which fraction is less than.

We're gonna look at the fractions 5/3 and 5/6.

which one is less?

Laila says, "I know 5/6 is less 5/3 because 5/3 is greater than one because the numerator is larger than the denominator."

I had the fractions, 5/3 and 5/6.

Let's build 5/3.

1/3, 2/3, 3/3, 4/3, 5/3.

Now let's build 5/6.

1/6, 2/6, 3/6, 4/6, 5/6.

Now that I've built 5/3 and 5/6, let's take a closer look and see what Laila's thinking.

If we look at the 5/3, I can take my one whole fraction strip and put it over and see that it is more than one whole.

We know that because the denominator is smaller than the numerator.

Now we can understand better what Laila was saying.

We saw that the five thirds was more than one whole, which means that 5/6 is less than 5/3.

So I can say that 5/3 is greater than 5/6 or 5/6 is is less than 5/3.

How are you feeling about comparing fractions third grade Math Mights?

I think you've been doing a great job.

So let's kick it up a notch and see if we can figure out what the missing denominator might be to make a statement true.

We have the fraction 4/4.

Let's think about another fraction that has a numerator of 4 that would be greater than 4/4.

Laila says, "I think you could make the second fraction 4/2 and make the statement true."

Let's model that using our fraction strips.

First, let's create the fraction 4/4.

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

Now we're going to create 4/2.

1/2, 2/2, 3/2, and 4/2.

Now that we've created our fractions, let's check and see if 4/4 is less than 4/2 by using what we know with whole numbers.

As we can see, 4/4 is equivalent to one whole.

And if we look at the fraction 4/2, we can see that four halves is made up of one whole and another whole.

And that makes two wholes.

One is less than two.

Therefore, I know that 4/4 is less than 4/2.

Nora has a different idea.

Nora says, "I think you could make the second fraction 4/3 and make the statement true."

Let's take a closer look and model that on our white board.

We're gonna create 4/4 again.

And now we're gonna create 4/3.

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

Thinking about our whole numbers, we see that 4/4 is the same or equivalent to one whole.

When we have 4/3, we see that 3/3 is equivalent to one whole and we have another 1/3 left.

So 1 is less that 1 and 1/3.

Therefore, we know 4/4 is less than 4/3.

Third grade Math Mights, you have been doing an awesome job comparing fractions.

Now I think it's time for me to give you a challenge.

I want you to compare fractions but this time they're gonna be no visual tools.

Let's take a look at our whiteboard and compare these two fractions.

We have 5/4 and 5/3.

Now, remember whenever we have fractions that have like numerators, we wanna focus on the size of the denominator.

Think about that chocolate bar.

If you had to share it with four friends versus three friends, which size do you think would be bigger for that chocolate bar?

I think at the chocolate bar that has me sharing with only three friends would be a lot bigger because I would have fewer friends to see we are with.

So that means 5/4 is less than 5/3.

How are you feeling about comparing those fractions there, third grade Math Mights.

Let's try another example.

We're gonna compare the fries actions 3/8 and 3/6.

Now remember when we have common numerators, which we see here is the numerator three, we wanna focus our attention on the denominators.

Think about a pizza.

If you have a whole pizza that was divided in eighths and you had another whole pizza that was divided into sixth, which pizza would have the larger pieces?

3/8 would be smaller or less than 3/6.

All right, third grade Math Mights, I have one more challenge for you.

Let's look at 7/3 and 7/2.

Remember when we have common numerators, which we see here is seven, we wanna focus our attention on the denominator.

If we have thirds and halves, which one is bigger or greater?

We know that halves are more than thirds.

So our fraction would be 7/3 is less than 7/2.

Third grade Math Mights, You have been working really hard comparing fractions.

Now it's your turn to take what you've learned today and apply it to a game called spin to win.

I have enjoyed my time with you today working with fractions.

I hope to see you real soon where we have more fun with math.

(delightful music) (enchanted music) - [Elementary student 1] Sis4teachers.org.

- [Elementary student 2] Changing the way you think about math.

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