(playful music) - [Kids] Math Mights!

- Welcome, third-grade Math Mights.

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

Let's check out our plan for today.

First, we're gonna do a Mystery Math Mistake.

And after that, we're gonna move on to learning about fractions and whole numbers.

But before we begin, let's warm up our brains with a Mystery Math Mistake.

Uh-oh, it looks like our Math Mights' strategies are all mixed up.

It's up to you to use your magnifying glass to figure out what the math mistake is gonna be for today.

Here's how it works.

I'm gonna choose a strategy that you are familiar with, and then it's your job to use your magnifying glass to try and find the Mystery Math Mistake.

Make sure that you are explaining your reasoning.

Our problem for today is 121 minus 85.

Now, Springling was a little bit turned around, so let's figure out what that misery mistake is going to be.

I'm gonna start at 85, and I want to take a friendly hop to a friendly decade number.

That would be 90.

What's the distance between 85 and 90?

Hop, Springling, hop.

It's five.

Now we're gonna take a lover friendly hop to another decade.

120.

What's the distance between 90 and 120?

Let's find out.

Hop, Springling, hop.

It's 20.

Now that we're at 120, we're gonna stop at 121.

What's that distance?

Hop, Springling, hop.

It's one.

When I take five plus 20 plus one, that equals 26.

121 minus 85 equals 26.

Okay, third-grade Math Mights.

Do you, do you use your magnifying glass to find the Mystery Math Mistake?

What do you think about my math?

Do you think I'm correct?

I wonder.

Let's ask our friends Imani and Elise and see what they think.

Imani says, "If I added 85 plus 26, it doesn't equal 121."

Elise says, "The distance between 90 and 120 is 30, not 20.

So the answer would be 36."

Let's go to our white board and make that correction.

Looks like Springling is right side up.

She agrees with Imani and Elise.

So, instead of saying the distance between 90 and 120 is 20, it's actually 30.

So that means five plus 30 plus one equals 36.

121 minus 85 equals 36.

Great job, Imani and Elise finding that Mystery Math Mistake.

How did you do third-grade Math Mights?

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

Notice how the better you become at understanding math concepts, you are able to recognize those errors and easily correct them.

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

I can work with fractions and whole numbers on a number line.

Now let's locate and label fractions on the number line.

Is there something that you notice about all of these fractions?

I do.

They're all halves.

Let's use our number line and locate them and label them.

Our number line starts from zero to five.

We're gonna take each of those sections and partition them into halves because the fraction that we are working with is halves.

Starting with zero to one, we're gonna find the midway point.

I'll put a tick mark there.

From one to two, we're gonna find the midway point and put a tick mark.

From two to three, midway point.

Three to four, midway point, tick mark.

From four to five, midway point, tick mark.

Now we're gonna label these halves.

The first tick mark is 1/2.

Then we have 2/2.

Next we have 3/2, 4/2, which is the same as two, 5/2, 6/2, which is the same as three, 7/2, 8/2, which is the same as four, 9/2, and 10/2, which is the same as five.

Great job locating and labeling halves on that number line.

Now we're gonna practice a little bit more, but this time we're gonna work with thirds.

We're gonna stop at 9/3.

Using our number line, you can see that I already have my tick marks here.

They have been partitioned into three equal parts.

I have two tick marks.

I didn't draw a third one because when making thirds, I only need two.

I'm gonna double-check by using my hopping strategy, like Springling taught me, by starting at zero and taking one, two, three hops.

Now I'm going to label all of these tick marks.

The first tick mark would be 1/3, 2/3, 3/3, which is the same as one whole, 4/3, 5/3, 6/3, which is the same as two, 7/3, 8/3, and 9/3, which is the same as three.

How are you feeling about locating and labeling nine-unit fractions on a number line, third grade?

I'm feeling a little more comfortable.

Being able to see this number line and locate them on it, makes it a lot easier for me to understand.

Let's practice a little bit more by labeling and locating fourths.

We're gonna label these fractions on the number line starting from 1/4 and stopping at 12/4.

Remember when we're using the number line, we know that we're working with fourths.

So from zero to one, we wanna make sure we have partitioned it into four equal parts.

Because we're breaking fourths, we want to have three tick marks.

One, two, three, and the fourth tick mark is already there for us, so we don't have to write it.

I'm gonna double-check to make sure starting at zero and taking my four hops.

One, two, three, and four.

Let's label these tick marks.

This is 1/4, this is 2/4, this is 3/4, and this is 4/4, which is the same as one whole.

Now I'm going to continue to partition this number line into fourths using my tick marks.

Now let's go back and label those tick marks.

We started at 4/4 here, so we're gonna continue on.

5/4, 6/4, 7/4, 8/4, which is the same as two, 9/4, 10/4, 11/4, and 12/4, which is the same as three.

We've been working really hard locating nine-unit fractions on a number line, third grade.

Now let's see which fractions locate the whole numbers looking at the three number lines that we just worked on.

The first number line, we had halves.

When we locate the whole number, we see that 2/2 is the same as one whole.

4/2 is the same as two.

6/2 is the same as three.

8/2 is the same as four.

And 10/2 is the same as five.

If you think back to when we were working with division, third grade Math Mights, do you notice something about those fractions?

I do.

If we take two and divide it by two, that's one, four divided by two is two, six divided by two is three, eight divided by two is four, and 10 divided by two is five.

What a great connection we just made with fractions and division to locate whole numbers.

Let's look at our next number line.

We used thirds.

3/3 is the same as one whole, 6/3 is the same as two, and 9/3 is the same as three.

Let's use that division strategy to check.

Three divided by three is one, six divided by three is two, and nine divided by three is three.

And finally, we're gonna look at our number line tat was partitioned into fourths.

4/4 is the same as one, 8/4 is the same as two, and 12/4 is the same as three.

Four divided by four is one, eight divided by four is two, and 12 divided by four is three.

Awesome job, third-grade Math Mights, using those fractions to locate whole numbers on the number line.

Were there any other thing that you noticed with those fractions and number lines?

What patterns did you notice across the fractions?

Imani says, "For halves, every other fraction was a whole number."

Looking at this number line, we see that Imani is correct.

Every other number is a whole number.

She also noticed, for thirds, every third number was a whole number.

Looking at our second number line, I agree with the Imani's thinking.

Every third fraction is also a whole number.

One, two, three, the whole number one.

One, two, three, whole number two.

One, two, three, the whole number three.

Finally, Imani notices for fourths, every fourth number has a whole number.

I agree with Imani's thinking.

Every fourth fraction is also a whole number.

One, two, three, four.

4/4 is the same as one whole.

One, two, three, four, 8/4, the whole number two.

One, two, three, four, 12/4 is the same as the whole number three.

That was pretty cool.

Now are learning one step further and locate and label one on each number line.

And we're gonna use halves to locate the whole number one on this number line.

We start at zero and we stop at 1/2.

We're gonna use our fingers to estimate what that distance would be.

I know that 2/2 is the same as one whole.

So I have 1/2 here.

I'm gonna estimate with my fingers where the next tick mark would be.

That's about here.

So I would label that as 2/2.

That's the same as one whole.

Now let's see if we can find one whole using fourths.

This number line starts at zero and stops at 1/4.

I'm gonna use my fingers again to try and estimate where the next fourth would be.

Remember, 4/4 is the same as one whole.

So I'm gonna take my fingers and estimate the next tick mark, which would be here.

Let's label that, 2/4.

Using my fingers, we're gonna estimate again.

About here is where the tick mark would go.

This would be 3/4.

Using my fingers, we're gonna estimate about here for the next tick mark, and that would be 4/4.

4/4 is the same as one whole.

Now that we've labeled halves and fourths, et's see if we can extend our thinking a little bit more and label sixths and eighths.

We're gonna start at zero and stop at 1/6.

I know that 6/6 is the same as one whole.

So I'm going to use my fingers to estimate the distance for the next tick mark.

About here is where I would draw it.

Labeling that 2/6.

Using my fingers to estimate the next location of the tick mark, 3/6, 4/6, 5/6, and 6/6, which is the same as one whole.

I think you're getting really good at locating one using fractions on that number line, third-grade Math Mights.

Let's do one more example using eighths.

Our number line starts at zero and it stops at 1/8.

We're gonna estimate where the next tick marks are going to be.

It's about here.

So this would be 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 and 8/8, which is the same as one whole.

Great job, third-grade Math Mights using fractions to locate one on a number nine.

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

Third-grade Math Mights, I am so proud of you.

You worked really hard today.

First you found the Mystery Math Mistake by understanding your math concepts and being able to recognize with your magnifying glass the mistakes that were made.

And then you took a really scary concept of fractions and you were working hard and you were able to identify larger fractions and find fractions that equal one on a number line.

I am so proud, you did a great job, and I hope to see you really soon.

(bright music) (mellow music) - [Kid] sis4teachers.org.

(air whooshing) - [Kid] Changing the way you think about math.

(bright music) - [Narrator] The Michigan Learning Channel is made possible with funding from the Michigan Department of Education, the State of Michigan, and by viewers like you.

(upbeat music)