(playful music) (magical music) (glass squeaking) - [Children] Math Mights!

- Welcome, third grade Math Might friends.

I'm so excited that you joined us today.

My name is Ms. Askew.

Are you ready to have fun with math?

I sure am.

So let's check out our plan for today.

Today, we're going to do a number talk, and after our number talk, we'll be measuring with halves and fourths.

Before we begin, let's warm up our math brains with a number talk.

A number talk has three parts.

First, I'm going to pose a problem today using fractions.

Second, you are going to solve the problem mentally without pencil or paper.

And finally, we're gonna share out how you solved and explain your strategy.

I want you to take a look at these fraction area model papers.

What fraction of space is occupied by color?

Let's think about that for a minute.

Can you come up with multiple fractions that occupy each color?

Let's see what our friends Landon and Myles think.

Landon says, "I think 4/8 are blue and 2/4 are yellow."

Let's take a closer look at that on our whiteboard.

We have our area model here, and we see that one, two, three, four are blue.

What Landon is saying is if we added the additional blue fraction strips and covered up the yellow, we would have a whole.

And if we count them all together, we have eight parts.

That's where the eighths come in.

When Landon initially saw it, he saw that four out of those eight were blue.

So that fraction is 4/8.

We're gonna write that here and record it.

Landon also said that 2/4 are yellow.

If I continue to cover my area model with these yellow strips, I can see that the whole area model has been covered.

What Landon initially saw was that out of those four, two of them were yellow.

So that fraction makes 2/4.

I'm gonna record that underneath yellow.

Now let's see what Myles thinks.

Myles says, "I think half are yellow and half are blue."

What Myles is saying is that if we take our half fraction strips and cover up our area model, and take 1/2 away, we're gonna move the yellow so that we can see how half of that area model is covered.

And that's why Myles said half are yellow.

We're gonna record that as well.

1/2.

Myles also noticed that half are blue.

We're gonna take these blue fraction strips and put them here, and we're gonna look at our half fraction strip again and see that we have half here, and if we cover up the blue, we also have half.

And that's how Myles was able to see that half of the strips were blue.

Now, that's interesting.

Myles came up with different fractions from Landon to represent those colors.

Let's take a closer look at that.

Let's take a look at the yellow area first.

Landon said 2/4 were yellow, and Myles said that 1/2 is yellow.

Do you see that right away, boys and girls?

Remember when we talked about equivalent fractions in our previous lessons?

If I look at that area model, I can see how those 2/4 can be the same as that 1/2.

So that was some pretty good thinking from Landon and Myles.

Now let's look at the blue area.

Landon said 4/8 are blue, and Myles said 1/2 is blue.

That goes again with those equivalent fractions.

Another way to say the same thing.

Here's Landon's area model, and this is what Myles was thinking, 1/2.

That was some really great thinking, Myles and Landon.

Do you think you can come up with other fractions to represent those colors?

Let's take a closer look.

Landon says, "I also think 4/8 are yellow."

Myles says, "I also think 2/4 are blue."

All right, third graders.

That might be a little confusing to you just by hearing it, so let's take a closer look at what they're saying.

Landon said 4/8 are yellow.

So if I take one, two, three, four of these eighths, and place them over the yellow, I can see that yes, they are the same.

Now that we see how 4/8 is the same as the yellow, let's record that, 4/8.

Now, Myles said that 2/4 are blue.

Let's take a look at that.

If I see my 2/4 here, and here's my blue area here, I can take these fraction strips and cover up this area, and we can see how it's the same.

So we're gonna record that as well.

2/4 are also blue.

Wow, third grade math mights, that's pretty cool.

We were able to see three different ways to represent the yellow area and the blue area of our area model.

Let's take a closer look at that.

When we looked at the yellow area, we saw that 2/4, 1/2, and 4/8 all mean the same thing.

When we looked at the blue area, we saw that 4/8, 1/2, and 2/4 all mean the same thing.

These fractions are considered equivalent to one another.

Great job noticing that all of those fractions were equivalent to the yellow area, and all of those fractions were equivalent to the blue area.

Now we're going to work more with fractions, but this time we're gonna use it with measurement.

Now let's check out our I can statement for the day.

I can measure length in halves or quarters of an inch.

First, we're gonna think about what do you already know about inches?

Let's see what some of our friends say.

One of our friends says, "Inches are used to measure length."

Another friend says, "There are inch marks on rulers, yard sticks, and tape measures."

Another friend says, "Inches are shorter than feet."

And finally, a friend says, "Inches are longer than centimeters."

Third graders, were there some things on that list that you already knew?

I wonder, can you add more to that list?

Now I want to take a look at this slide.

Ask yourself, how many inches is the paperclip?

I have a ruler, and it's not to scale.

I've blown it up nice and big so that we can see it.

When I look at this ruler, I see that it starts at zero, and we count by whole numbers and it ends at six.

Now, remember when you were learning about measurement and you had an object to measure, you measured it from one end point to another end point.

If we look at our paperclip here, we see that it starts at zero and it ends at the one inch mark.

So now we know the paperclip is one inch long.

Now that we were able to see how that paperclip measured to the whole inch, let's take a closer look at another object that measures just a little bit longer than an inch.

Now we have another object.

Ask yourself the question, what is the length of this object?

Myles says, "It is between three and four inches.

It is more than three, but less than four.

It is 3 1/2 inches."

That's pretty interesting, Myles.

Now I can see that we're measuring to the 1/2 inch.

Let's take a closer look at that.

We're gonna partition one ruler to show half of an inch.

This ruler isn't to scale.

I've blown it up so that we can see it a lot better.

It starts at zero and ends at nine.

We want to partition it by showing the 1/2 inch tick marks.

So I'm gonna start between zero and one, find the halfway point, and partition it with my 1/2 inch tick mark.

Now between one and two, two and three, three and four, four and five, five and six, six and seven, seven and eight, and eight and nine.

Now that we have our rulers set up in half inches, let's explore it some more.

How would we record the length of this pencil?

Landon says, "We could record it as 6 1/2 inches."

Myles says, "We could also record it as 13/2 if we counted all the halves."

Let's take a look at what Landon and Myles are thinking.

I have a representation of what Myles and Landon were talking about.

Our ruler here, remember, isn't to scale.

It's blown up so that you can see it a lot better.

We're gonna measure our pencil from end point to end point, and just like Landon says, we start at zero and it ends at the half mark, so that makes it 6 1/2 inches long.

I found it very interesting that Myles said it was 13/2 and not 6 1/2.

Let's take a look at what Myles is thinking.

If I look at our ruler, we can see that each of those tick marks represents half inches.

If we counted all those half inches, we should end up with 13/2, just like Myles said.

We're gonna start at zero and begin to count.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13.

Oh, now I see what Myles is talking about.

When he counted all the tick marks, there were 13 together, and that makes 13/2.

Landon measured the length of the pencil as 6 1/2 inches, and that is equal to or equivalent to 13/2, which is what Myles measured the pencil as.

You're doing a fantastic job, third grade math mights.

Now that we've looked at how to measure with whole and halves, let's take a look at it in a different way.

Take a look at this picture here.

What do you notice?

What do you wonder?

This paperclip looks a little bit different from the last paperclip that we saw on the ruler.

Let's see what the boys think.

Landon says, "I notice the length of this paperclip looks close to one, but not quite to half."

Myles says, "I wonder how we can precisely measure the paperclip."

Landon and Myles, you have some great notices and wonders.

That brings me to a great thought.

Why don't we partition this ruler in a different way?

This ruler is not to scale, it has been blown up so that you can see it a lot better.

It starts at zero and it ends at four.

We partitioned it into fourths, or 1/4 inch marks.

I've already done the first one for you.

Remember, when we show fourths, we want to have three tick marks.

One, two, three, one, two, three, one, two, three.

Now that we partitioned our ruler into fourths, let's see how we can measure that paperclip to show that how it's a little bit past the one, what would it measure?

I'm gonna measure from one end point the next end point.

Starting at zero, I see that I have my tick marks, and I can label those tick marks as 1/4, 2/4, 3/4, and 4/4.

We know that 4/4 is equivalent or equal to a whole.

When we look at our paperclip, it's one tick mark past the one inch mark.

So if we continue to count, we have one whole, and then we're gonna count our quarter or 1/4 inch marks, and that's 1/4.

So that means this paperclip measures 1 1/4 inches.

Now that we say that the paperclip measures 1 1/4 inches, is there another way that we can record that measurement?

Let's take a look.

On my ruler, we have partitioned it into 1/4 inches or fourths.

Let's label that.

The first tick mark represents 1/4.

Then we have 2/4, 3/4, and 4/4, which is the same as one whole, and 5/4.

So if I were to name this paperclip measurement, I would say that it is 5/4 inches long.

1 1/4 is equivalent or equal to 5/4.

When we look at the measurement of the paperclip, we notice that the numerator in 5/4 is bigger than the denominator.

In our previous lesson, we understood that to mean that whenever the numerator is greater than the denominator, it means that that measurement is greater than one, and we saw that with the paperclip.

It went just a little bit past the one inch mark.

Now it's your turn to take everything that we've learned today and do an activity where you are going to create one ruler that is partitioned into half inches and another ruler that is partitioned into quarter inches.

You're gonna find objects and measure them.

Awesome job, third grade math mights!

You were working really hard today!

First, we did our number talk where we talked about lots of fractions, and then we were able to measure things to the whole inch, the half inch, and the quarter inch.

I hope to see you soon, when we talk more about measurement.

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