(upbeat music) - [Children] "Math mights"!

- Welcome, third grade Math Mights.

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

So let's check out our plan for today.

Today, we're going to solve a mystery math mistake.

And after that, we're gonna learn about equivalent fractions.

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

Oh no, it looks like our Math Might friends had their math strategies all mixed up.

I need your help to solve the mystery math mistake.

We're gonna use a magnifying glass to find the error in the math problem.

Here's how it works.

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

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

Make sure you can explain your reasoning.

We have the problem, 48 divided by 4.

We're gonna start with a friendly or a familiar multiplication fact, because 48 is our target number and we wanna pull out groups of four.

I'm gonna start with 10 groups of 4 and I know that that equals 40.

Next, I'm going to do 4 groups of 4 and that equals 8.

When I add them together, that equals 48.

So I'm going to add up my groups of 10 plus 4 and that equals 14.

So 48 divided by 4 equals 14.

Did you notice the mystery math mistake?

What do you think about my math?

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

Let's see what our friends, Eric and Maki think.

Eric says, "I know that 14 groups of 4 equals 56.

"So I'm wondering if this is incorrect."

I think that Eric is thinking about the inverse operation of 14 times 4.

Let's check it and see if he's correct.

If I use an area model and I think about what DC taught us, I can decompose a number 14 into 10 and 4, and we're gonna multiply that by 4.

10 groups of 4 equals 40.

4 groups of 4 equals 16.

So I'm gonna add that together.

40 plus 16 equals 56.

That's what Eric was thinking.

14 times 4 equals 56, not 48.

There must be something wrong here.

Let's see what Maki thinks.

Maki says, "4 times 4 equals 16, not 8.

"So I think you meant to do 4 times 2, "which would make it 12 groups of 4 in 48."

Did that make sense to you what Maki said?

Let's take a closer look.

Maki says that we should have 2 times 4 to equal 8.

Two groups of four is eight.

And if we add 40 plus 8, that does equal 48.

Now that we've turned our multiplication equation, we have to change what we added together.

So 10 plus 2 equals 12, not 14.

So 48 divided by 4 equals 12.

Were you able to find the mystery math mistake?

Third graders, when you are able to explain and find errors in math problems, you know that you are understanding math concepts a whole lot better.

Great job.

Let's check out our I Can statement for today.

I can identify, generate, and locate equivalent fractions.

Let's talk about equivalent fractions.

Now, we're gonna be using these fraction bars but you can use the fraction strips that you made.

Did you keep up with the ones that you cut out a few lessons ago?

Use fraction strips to find as many equivalent fractions as possible.

Let's start off with 1/2.

I'm gonna take my fraction strip and put it down here.

Then I'm gonna look at my first set of fractions which is 1/3s.

How many 1/3s are equivalent to 1/2?

I take 1/3 and I lay it on top of 1/2.

1/3 is too small.

So let's try 2/3.

2/3 is not equivalent because that's too much.

Now let's try with 1/4s.

I'm gonna take 1/4 and lay it on top of my 1/2.

It looks like I still have more room.

Perfect.

2/4 is equivalent, or equal to, or the same as 1/2.

So I'm gonna record that.

2/4 is equivalent to 1/2.

Now let's try it with 1/6s.

1/6, 2/6, 3/6.

3/6 is equivalent or equal to 1/2.

Let's record that as well.

Now let's do 1/8.

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

4/8 is equivalent or equal to 1/2.

4/8.

As we found those equivalent fractions, did you notice a pattern?

I did.

Let's take a look.

If we look at 2/4, I can see that the numerator double the denominator.

3/6, six is three doubled.

4/8, eight is four doubled.

Can you make a prediction?

Do you know what the next fraction would be if the numerator doubled the denominator?

Now we're gonna use the fraction strips to find as many equivalent fractions as possible for 2/3.

Now, I'm not gonna start with 1/2 because we already saw that that's not equivalent.

So let's move to 1/4s.

1/4, 2/4, 3/4 is too much.

So now we know that 1/4s can not be equivalent to 2/3.

Now let's try 1/6s.

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

It looks like 4/6 is equivalent or equal to 2/3.

I'm gonna record that.

4/6 is equal or equivalent to 2/3.

Now let's try it with 1/8s.

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

No, looks like it's too small.

So 1/8s is not equivalent to 2/3.

All right, third grade Math Mights.

How did you feel about finding those equivalent fractions?

I don't know about you, but for me to be able to visualize it and see those fraction strips helped me to see how those fractions can be equivalent or not equivalent to one another.

Let's try some more by using an area model as a visual tool.

We're gonna try to find fractions that are equivalent to 3/4.

Here we have our whole which is red.

Since we're working with 1/4s, I'm gonna cover them with 4/4.

As you can see, 4/4 is equal to one whole.

But since we're only gonna work with 3/4, I'm gonna take one of those 1/4s away, so all we have left is 1/4, 2/4, 3/4.

Now we're gonna use our area model to visualize and see if 1/2s are equivalent to 3/4.

Here I have 1/2s and 2/2, so that makes our whole.

If I take one of those 1/2s away, I'm left with 1/2.

But as you can see, there's still 1/4 left.

So no, 1/2 is not equivalent to 3/4.

Do you think that 1/3s might be equivalent to 3/4?

Let's have a look and see.

1/3, 2/3.

If I try to place three here, it just doesn't work.

That would be too much.

So 1/3s is not equivalent to 3/4.

Now let's try it with 1/6s.

1/6, 2/6, 3/6.

Oh, it looks like it might fit.

4/6, five... No, it doesn't.

It doesn't work.

Ah, third grade Math Mights, we just saw that 1/6s don't work.

How about we try with 1/8s?

Maybe we'll get it this time.

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

Look at that.

It looks like 6/8 is equivalent or equal to 3/4.

Let's record that in our box.

6/8 is equivalent or equal to 3/4.

You're doing such a great job, third grade Math Mights.

Those visual tools are really helping us to understand equivalent fractions.

Let's keep going and practice some more.

Eric and Maki are running on a track.

Eric ran 3/6 of a mile on the track and Maki ran 1/2 of a mile on the track.

Who ran further on the track?

What do you think, third grade Math Mights?

Do you think Eric or Maki ran further?

Let's take a look.

Eric says, "I think I ran further "because my denominator is higher."

Eric was thinking about the two numbers and the denominator.

In 3/6, he thought that the six is bigger than the two in 1/2, so that probably means he ran further.

Hmm, I wonder, does that make sense?

Is that correct?

Let's see what Maki says.

Maki says, "Looking at the number line, "I think we ran the same distance."

Let's check it out here on our number line.

Before, we had a fraction strip.

Now we've taken it and turned it into a number line.

We've divided the number line in half here and here.

As you can see, 1/2 is right in the middle of that number line.

And then we divided it into six, one, two, three, four, five, six.

Eric ran 3/6 of the track, so his point would be here.

It looks like 3/6 is the same distance as 1/2.

And if we think about that pattern, the numerator double the denominator.

As you can see, 3/6 is the same or equivalent to 1/2.

So Maki was right.

As third graders, sometimes we look at just the numbers but we have to make sure we use those visual tools so that we can plot it correctly on our number line.

When we do that, we can see how 3/6 is the same or equivalent to 1/2.

Take a look at these seven fractions.

Do you think we can locate and label these fractions on a number line?

I've already taken and created three different number lines.

The first one I've divided or partitioned into 1/2s, the next one into 1/4s, and the last one into 1/8s.

We're gonna plot these fractions here on our number lines.

1/2 goes here, 3/8 we would find here.

6/8, 1/4, 3/4, 7/8, and 4/8.

Do you think that we can find any fractions that are equivalent on our number lines?

Let's see what Eric thinks.

Eric says, "3/4 and 6/8 are equivalent "because they are on the same point on the number line."

Let's take a look.

Here's 3/4 and here is 6/8.

So Eric is correct.

3/4 and 6/8 are equivalent fractions.

I'm gonna go ahead and circle 3/4 and 6/8 on my number line to show that 3/4 and 6/8 are equivalent.

Did you happen to notice any other fractions that were equivalent on the number lines?

Let's take a look.

I see that 1/2 is also equivalent to 4/8.

I'm gonna circle that in orange.

So far, we found equivalent fractions for the ones that we plotted on a number line.

Did you happen to see an equivalent fraction that we didn't plot?

Let's take a closer look.

We can see that 2/4 is also an equivalent fraction.

So I'm going to circle that in orange as well because it's equivalent to 1/2 and 4/8.

I know that 2/4 is equivalent to 1/2 and 4/8 because of the points they are located on the number line.

We can also see that 1/4 is equivalent or equal to 2/8.

I'm gonna circle those in pink.

I noticed there is one more set of fractions that are equivalent.

Let's take a look on our whiteboard.

We can see that all of these fractions are equivalent to one whole.

2/2, 4/4, and 8/8 all equal one whole.

Awesome job, third grade Math Mights.

Those number lines really helped us to see how we can find equivalent fractions.

You're gonna apply what you learned today to play a game called equivalent fraction roll.

Great job, third grade Math Mights.

You did an awesome job with those fractions.

That can be such a difficult concept for third graders to understand.

But using those visual models really helped us today.

You worked hard with solving that mystery math mistake.

And then we went on to those difficult concepts of fractions and we were able to visualize equivalent fractions using area models, fraction, strips, and number lines.

You should be very proud of yourselves, job well done.

I hope to see you soon so we can do more with math.

(bright upbeat music) (playful upbeat music) - [Child 1] sis4teachers.org.

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

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