(playful music) (electric gadgets ringing) - [Children] Math Mights!

- Welcome 3rd grade Math Might friends.

I'm super excited that you joined us today.

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

Are you?

Let's check out our plan for today.

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

And after that, we're gonna learn how equivalent whole numbers are fractions.

But first, let's warm up our math brains with a mystery math mistake.

Oh no!

It looks like our Math Might friends are 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 I have here is 63 divided by 3.

As we can see, Springling is upside down.

She's a little confused.

So using her strategy, we might find our mystery math mistake there.

Our target number is 63 and we want to figure out how many groups of three we can pull out from 63.

So I'm thinking, hmm.

How many groups of three can I pull out from 63?

10 groups of three is a good number.

I'm starting with 10 because 10 groups of three I know equals 30.

And 30 is halfway to 63.

So I'm gonna pull out another 10 groups of three, and that equals 30.

We're almost there.

I know that I only need one more group of three.

So I'm gonna have one group of three.

And that equals three.

When I add these all together, 30 plus 30 plus three, that equals 63.

We've reached our target number.

Now I'm going to add up all of our groups up.

10 plus 10 equals 20.

So 63 divided by 3 equals 20.

Did you use your magnifying glass and find the mystery math mistake?

What do you think about what I did?

Let's take a closer look and let's see what our friends Eric and Maki think.

Eric says, "I know that 20 times three equals 60.

"So I don't think this answer makes sense."

Let's take a look at Eric's thinking.

Eric is using the inverse operation for division by saying 20 times three equals 60.

So if we know that 20 times three equals 60, then that can't be right because our target number is 63.

Let's see what Maki thinks.

Maki says, "It looks like you solved it correctly.

"However, when you added up the groups of three, "you forgot the last group.

"It should be 21."

Let's see what Maki is trying to tell us.

As you can see 3rd graders, Springling is right side up, which means she's feeling a lot better about Maki's thinking.

If we look here at our groups of, Eric said that we added 10 plus 10 and that equals 20, but Maki noticed that we forgot one group of three.

So we need to add those all together.

And now we have 10 plus 10 plus 1, and that equals 21.

So 63 divided by 3 equals 21.

Great job 3rd grade Math Mights using your magnifying glass to find that mystery math mistake.

Now let's take out our I can statement for today.

I can find fractions and whole numbers that are equivalent.

We're gonna take a look at a number line and figure out which fractions are equivalent to whole numbers.

I have a number line that I've partitioned into halves.

Let's use this one whole fraction strip to see if we can find fractions that are equivalent or equal to that.

Let's start with 1/2.

1/2, as we can see, is not equal or equivalent to one hole.

Now we're gonna go to 2/2.

We can see that 2/2 are equivalent to one hole.

So I'm gonna circle that fraction.

As you can see on the number line, we visualize 2/2 equaling one whole number.

I wonder if we continue, if we can find more fractions that equal or are equivalent to a whole number.

Let's take a closer look.

Let's build 3/2.

3/2 is not a whole number.

Let's try 4/2.

4/2 is another whole number.

So I'm gonna circle that.

What whole number is 4/2 equivalent to?

One, two.

It's equivalent to the whole number two.

Let's build 5/2.

5/2 is not equivalent to a whole number.

Let's build 6/2.

6/2 is equivalent to another whole number.

So I'm gonna circle 6/2 What whole number is 6/2 equivalent to?

We have one, two, three.

It's equivalent to the whole number three.

Let's build 7/2.

7/2 is not equivalent to a whole number.

Finally, let's build 8/2.

We can see that 8/2 is equal to a whole number.

Which whole number is it?

One, two, three, four.

8/2 is equivalent to the whole number four.

Now that we've identified the fractions that are equivalent to a whole number, let's put those whole numbers on our number line.

Do you notice a pattern with these numbers?

I sure do.

Hmm, how many times does two go into two?

One time.

So one is that equivalent whole number.

How many times does two go into four?

Two times?

So that equivalent whole number is two.

How many times does two go into six?

Three times.

So three is that equivalent whole number.

And finally, how many times does two go into eight?

Four times, so four is the equivalent whole number.

You're doing an awesome job, 3rd grade Math Mights!

You used those fraction strips to locate fractions on a number line that were equal to whole numbers.

I want to challenge you now.

I want to take away those visual tools and I want to see if you can find those patterns to help us identify even more fractions that are equivalent to whole numbers.

I have a number line that I have partitioned or divided into thirds.

Let's look at these fractions and see which ones are equivalent or equal to a whole number.

1/3 is not equivalent to a whole number.

2/3 is not, but 3/3 is equal to one whole number, the number one.

4/3 is not equivalent to one whole number.

5/3 is not, but 6/3 is.

I know it's equivalent to a whole number because three can go into six two times.

7/3 is not equivalent to a whole number.

Neither is 8/3, but 9/3 is equivalent to a whole number.

And I know this because three goes into nine, three times.

10/3 is not equivalent to a whole number.

11/3 is not equivalent to a whole number, but I do know that 12/3 is equivalent to a whole number because three goes into 12 four times.

And four is that equivalent whole number.

If we look at our number line, we notice that there are some patterns.

If I start with the first fraction and count one, two, three, one, two, three, one, two, three, one, two, three, every third fraction is equivalent to a whole number.

We also know this because each of those denominators can go into the numerator by a whole number.

So we just figured out two separate patterns to help us identify how fractions can be equivalent to whole numbers.

You're really smart, 3rd grade Math Mights.

Let's look at 12/6.

We're gonna decide if the fraction is equivalent to a whole number.

Now you might be wondering how was I able to figure out which fractions were equivalent to whole numbers and which fractions were not?

Let's take a closer look and see what Eric says.

Eric says, "12/6 is equivalent to a whole number "because 6/6 would be one whole, "and six more would make 12, which would make two wholes."

This reminds me of my friend DC.

(playful music) Let's take a closer look at how DC can help us.

He likes to decompose numbers to make things a lot easier.

Well, guess what?

He can also do that with fractions as well.

Let's see how DC is going to decompose 12/6 to help us understand it a little bit better.

It looks like DC took 12/6 and decomposed it into 6/6, which equals one whole, and then another 6/6, and that equals another whole.

So we can make this into two whole numbers.

So 12/6 is equal to or equivalent to the whole number two I really like the way DC decomposed those fractions so that we can easily see how they are equivalent to whole numbers.

Let's try another one.

Let's look at 12/8.

We're going to decide if 12/8 is equivalent to a whole number.

Let's see what Maki says.

Maki says "No, because you need 8/8 "to make a whole number.

"12/8 is more than one, but it's not quite two."

Let's take a closer look at what Maki is thinking using DC's decomposing strategy.

DC decomposed 12/8 into 8/8 and 4/8.

We know that 8/8 and 4/8 equals 12/8.

But looking at our fractions, only 8/8 equals one whole.

Maki was telling us that in order to make another whole number, we would have to add another 4/8.

And that's why 12/8 is not equivalent to a whole number.

Wow DC, thanks for all of your help.

I don't know about you 3rd grade, but using DC's strategy to decompose those fractions really helped me to see how those fractions were equivalent to a whole number.

Now that we have a better understanding, let's try it in a different way.

Let's create a poster.

We'll write the whole numbers as fractions as many ways as we can.

Let's see how many ways we can make fractions that are equivalent to the whole number five.

I've already done the first one for you.

5/1 is equivalent or the same as the whole number five.

If I have two as my denominator, what would my numerator be so that this fraction is equivalent to the whole number five?

Let's think about the pattern that we learned from our previous lesson.

Remember when we were finding those equivalent fractions, we saw a pattern?

When we worked with halves, every other number or every other fraction was a whole number.

With thirds, every third number was equivalent to a whole number.

And with fourths, every fourth number was equivalent to a whole number.

Let's see if we can apply that same pattern to this strategy.

If I have one times five, that equals five.

So I wonder if I take two times five and that equals 10, is that equivalent to the whole number five?

It is because two goes into 10, five times.

So I guess that means if I have three times five, that would give me 15.

I know that's equivalent to five because three goes into 15, five times.

Four times five equals 20.

20/4 is equivalent to the whole number five, because four goes into 20 five times.

Six times five equals 30.

30/6 is equivalent or the same as the whole number five because six goes into 30, five times.

Eight times five is 40.

So that means 40/8 is the same or equivalent to the whole number five because eight goes into 40, five times.

You did a really great job using all those different strategies the find how fractions can be equivalent to whole numbers.

Now you're gonna take everything that we've learned today and apply it to a game called same but different.

You did an awesome job today, 3rd great Math Mights!

First, you used your magnifying glass to find the mystery math mistake using Springling's strategy of multiplying up.

And then you learned how to use different strategies to see how fractions are equivalent to whole numbers.

I hope to see you real soon when we work more with fractions.

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- [Girl] Changing the way you think about math.

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