(playful music) (metal spring vibrating) - [Children] Math Mights!

- Welcome, third grade Math Mights.

My name is Ms. Askew and I'm ready to have fun with math.

Before we begin let's check out our plan for today.

Today we're gonna do a mystery math mistake and after that we're going to compare fractions.

Let's get started with our mystery math mistake.

Oh no!

All our Math Might friends have their math strategies all mixed up.

I 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 that you are familiar with.

You have to use your magnifying glass to see where I made my mistake.

Make sure you can explain your reasoning.

The problem that we have is 84 divided by seven.

Now it looks like springling is all turned upside-down because we are going to make a mistake somewhere.

It's up to you to use your magnifying glass to find that error.

Our target number is 84.

We wanna figure out how many groups of seven are in 84.

I'm gonna start with 10 groups of seven because I know 10 times seven equals 70.

Now I'm going to do one group of seven, and that equals seven.

If I add these all together 70 plus seven equals 84.

Now, I'm going to count up my groups, 10 plus one equals 11.

84 divided by seven equals 11.

What do you think about my math third grade Math Mights?

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

Let's take a look at what our friend Nora thinks.

Nora says, "I know 11 times seven equals 77, so I think something isn't correct."

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

She used the inverse operation and knows that 11 times seven equals 77, not 84.

Let's see what our friend Laila says.

Laila says, "It looks like you started solving it correctly, but then you didn't finish.

You only have 11 groups of seven which is 77.

You need one more group of seven to get to 84."

Third grade Math Mights, were you able to use your magnifying glass and find that same mystery math mistake?

Let's take a closer look and check out what Laila was saying.

Laila is correct.

If I add 70 plus seven, that equals 77, not 84.

So, I do need to add another group of seven.

So, I'm gonna erase my 84 and I'm going to add another group of seven, which equals seven.

Now, when I add 70 plus seven plus seven that equals 84.

So that means I have to change my number of groups.

10 plus one plus one, all together, equals 12.

So, 84 divided by seven equals 12.

Great job third grade Math Mights, using your magnifying glass to find that mystery math mistake.

Now, let's move on to our "I can" state for today.

I can represent and compare fractions.

Let's take a look at these two fraction strips, what do you notice?

What do you wonder?

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

Nora says, "I notice the strips are the same size.

One strip is covered."

Laila says, "I notice half of one is shaded.

We don't know how many parts are on the second strip."

Let's see what you wonder.

Nora wonders, "why is the bottom strip covered?"

Laila wonders, "How many parts are shaded on the bottom strip?

What fraction does the bottom strip show?"

Those were some really great notices and wonders.

Let's explore this a little bit more.

Do the fraction strips represent equivalent fractions?

How do you know?

Looking at these two fraction strips, I can tell that they're not equivalent.

Even though part of the second fraction strip is covered with a cloud, I can see a tiny bit peeking out which is not equivalent, or equal, to the top fraction strip.

Great job, third grade Math Mights using what you know about fractions to solve that.

Let's do some more practice with comparing fractions.

Let's look at 1/2 and 1/3.

Are these fractions equivalent?

Nora says, "No, If I look at these on the number line they are not equivalent."

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

I have two number lines here.

One has been partitioned into half, and the other one has been partitioned into thirds.

If I plot those fractions on the number line: Here's 1/2 and here's 1/3.

As we can see, by looking at the number lines and comparing where those fractions are, we can tell the 1/2 is greater than 1/3, because as you know, when you plot numbers or fractions on a number line, the further down the number line it goes, the bigger the number is.

So that's why 1/2 is greater than 1/3.

Using a number line is a great way to see if fractions are equivalent.

Let's try another visual tool to see if we can find more fractions and if they're equivalent to one another.

We have 4/6 and 5/6.

Are these fractions equivalent?

Laila says, "No.

If I look at these with my fraction strips, they are not equivalent.

4/6 is less than 5/6."

Here we have our fraction strips and we have one whole.

We can see that 5/6 is more than 4/6.

We can see that Laila is correct, they are not equivalent.

4/6 is less than 5/6.

Third grade Math Mights, you're getting really good at this.

You've seen how fractions can be equivalent or not equivalent by using a number line and fraction strips.

Let's try one more way, the area model.

We have 3/4 and 6/8, are these fractions equivalent?

Laila says, "Yes.

If I build these fractions, they are the same size.

3/4 is equal to 6/8."

Do you think 3/4 is equal to 6/8?

Let's take a closer look.

We have our area model and it's been divided into fourths, but because we are working with 3/4, I'm going to take one of those fourths away.

We wan to see if 6/8 is equal, or equivalent, to 3/4.

So, I'm gong to begin to place my eighths on top of my fourths.

1/8, 2/8, 3/8, 4/8, 5/8, and 6/8.

Looks like Laila was correct.

3/4 is equal to 6/8.

What does that look like as a number?

3/4 is equal to 6/8.

You did a fantastic job third grade Math Might using those visual tools to see if fractions were equivalent.

Let's take look at this.

Han says 4/6 is less than 5/6.

His work is shown, let's take closer look at what he's thinking.

We see he has two number lines.

Both number lines have been divided into sixths.

1/6, 2/6, 3/6, 4/6, 5/6, and 6/6 which is the same as one whole.

On the first number line Han has plotted 4/6 and on the second number line he has plotted 5/6.

So, looking at his work, what do you think?

Do you think 4/6 is less than 5/6?

Let's see what Lin says.

Lin says 4/6 is greater than 5/6.

Her work is shown here.

Let's take a closer look.

Lin has also drawn two number lines.

Both number lines have been divided in sixths.

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

6/6 is the same as one whole.

And she plotted 4/6.

The second number line is also divided into six, and she plotted 5/6.

Lin says 4/6 is greater then 5/6.

Do you agree or disagree with her?

How can Han and Lin make different comparison statements for the same fractions?

Nora notices that Lin's number lines are not the same length.

Laila notices that Lin drew the top number line longer, so it makes it look like 4/6 is greater than 5/6.

Did you have the same notices as Nora and Laila?

Let's take a closer look at Lin's number line.

If we look at Lin's two number lines it does seem as though 4/6 is greater than 5/6, but when we are drawing number lines we have to make sure that they are equal in length so that we are comparing the same whole.

Lin's number line doesn't have the same length, so yes it does look as if 4/6 is greater than 5/6.

Did you make those same discoveries?

Let's take what we learned and apply it to a game called "Fractions take Actions".

With this game I have a stack of number cards.

One player is going to pull a card and decide whether it's going to be the like numerator or the like denominator.

I have pulled the number three and I'm deciding to use that number for my like denominator.

So we're gonna go ahead and circle that, and myself and the other player will write the number three for the denominator.

Now, player one, which is me, will draw a card.

This is the number five.

I'm going to put five as my numerator.

The second player will pull a card, and that number is two.

That will be their numerator.

Now, we're going to compare.

Is 5/3 greater than, less than, or equal to 2/3?

Let's act that out using our fraction strips.

First, let's create 5/3.

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

Now let's build 2/3.

1/3, 2/3.

As you can see 5/3 is greater than 2/3.

So, on my game board I'm going to draw the symbol for greater than.

5/3 is greater than 2/3.

According to this round, player one has earned two points because their fraction was greater.

Let's try another round.

I'm gonna pull a card, it's the number two, and I'm choosing number two to be the like numerator.

So I'll write a two and player two will write two for the like numerator.

Now I'm gonna pull a card to determine what my denominator is going to be.

It's four.

Player two will pull a card and their like denominator is six.

Now that we've created our fractions 2/4 and 2/6, which one do you think will be greater?

First, let's build 2/4.

1/4, 2/4.

Now let's build 2/6.

1/6, 2/6.

As we can see 2/4 is greater than 2/6.

Lets record that on our card.

2/4 is greater than 2/6.

It looks like player one has another two points.

Let's record two points for player one.

I don't know player two, could this round be your turn to get on the scoreboard?

Let's try and see.

The first card is an eight.

Eight is going to be our like numerator.

So I'm gonna write that down for myself and player two.

And we're going to circle "like numerator".

Okay, now we're going to pull another card, and it's a six.

Six will be my denominator.

And for player two, the number is four, 4/8.

We have the fractions 8/6 and 8/4.

Because the numerator is larger than the denominator, I think I'm gonna need DC's help to figure out which one is greater.

Hey DC can you help us with that?

We know that DC likes to decompose numbers to make them friendlier.

So, we're gonna take 8/6 and decompose it to 6/6 and 2/6.

Because 6/6 and 2/6 equals 8/6.

Now we're going to decompose 8/4 into 4/4 and 4/4 again, because 4/4 plus 4/4 equals 8/4.

Now, we understand that 6/6 is the same, or equivalent, to one whole.

So we have one whole number and our 2/6.

Let's take a look at our other fraction.

4/4 is equivalent to one whole, and we have another 4/4, which is a whole, so that gives us two.

Now we know that 8/4 is greater than 8/6.

Looks like player 2 finally made it on the board.

When we have a fraction that is greater, they earn two points.

So, two points for you player two.

Let's record that on our card.

8/6 is less than 8/4.

Now you will continue to play the rest of the round.

At the end of five rounds the player who has the most points wins.

Now it's your turn to play "Fractions take Action".

Thanks for joining us third grade Math Mights.

We had such a good time working with fractions today, I hope to see you back real soon.

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Changing the way you think about math.

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