>> Hello, young scholars.

My name is Michelle-Anne Spring, and I am a fourth-grade teacher at Hawthorne Park Elementary School in Willingboro Township Public School District.

And I am also the 2019-2020 Burlington County Teacher of the Year.

I am so excited to be joining you today.

I am coming to you from my home in New Jersey, as you can see.

I am in my family room, and here is where my family gets together to have conversations, to fellowship, to hang out, and just to have a really great time.

So, I'm happy that you're joining me.

I am inviting you to become part of my family today, so let's go on a gallery walk.

So, this is my family.

You have my mom, my husband and myself, and also, my two children, whom I adore, of course.

I know that this is a difficult time, but I really want you to understand that we are all in this together.

Today, we're going to be talking about my absolute favorite subject, which is mathematics.

And mathematics has been my favorite subject since I was a child.

I know -- that's a really long time, but I will proudly tell you that I'm a mathematician and I love talking about numbers, because mathematics is a science.

Join me as we get into our lesson for today.

As you can see, we've moved locations.

Welcome to my kitchen.

So, let's pick up where we left off.

By the way, what is your favorite subject?

Did you say it was math also?

If you did, here is an air high five.

But if you didn't, that's okay, too.

So, you might be wondering why it is that I love math so much.

One of the reasons is because math is relevant to what we do every day.

What does that mean?

It means that math is important in everyday life.

For example, let's talk about fractions.

Fractions happens to be one of my favorite concepts in math, and one of the reasons is because fractions will always be a topic that we're going to need forever and ever.

You're going to need fractions for baking and for cooking.

It's going to help you with parts of measurements.

It's going to help you tell the time.

And my personal favorite is -- it's going to help you to figure out discounts when we go shopping.

And there are several other uses.

So, it's interesting because fractions make up a whole.

Let's think of it this way.

I am a whole person, but there are many parts of me.

For example, I am Jamaican by birth.

I was born in Jamaica and went to school in Jamaica.

I graduated high school in Jamaica and then I came to the United States when I was 16 years old to go to college.

So, one part of me is Jamaican.

I'm American also.

I am a wife, a mom, a daughter, and a teacher.

That's six parts of me that, when joined together, make up my whole.

So, separated, there are six parts of me, and let's go over them again.

One part, I am Jamaican.

Second part, I am American by naturalization, which means that I am a citizen by taking a test.

Third, I'm a wife.

Fourth, I'm a mother.

Fifth, I'm a daughter.

And sixth, I'm a teacher.

When you join those together, it makes all of Michelle-Anne Spring.

So, that leads us to our lesson for today.

Our lesson for today will be adding and subtracting fractions.

And our objective is for us to be able to understand addition and subtraction of fractions as joining and separating parts, referring to the same whole.

Let me tell you what I mean.

I am the whole.

Each part of me, if you remember, say it with me.

I'm Jamaican.

I'm an American.

I'm a wife.

I'm a mom.

I'm a daughter.

And I'm a teacher.

So, those six parts -- they make up my whole.

Does that make sense?

For today's lesson, you will need a pencil and paper.

Any paper will do, as long as it's blank.

Maybe something from your cupboard.

I have can and I'm using mixed vegetables and I am using canned corn.

I'm also using some tangerines that are in whole still and Skittles.

I'm sure you love Skittles.

I love Skittles.

Again, today's objective is for us to understand addition and subtraction of fractions as joining and separating parts, referring to the same whole.

Let's start by talking about, what makes up a fraction?

A fraction is made up of a numerator and a denominator.

And it is written this way -- 1/6.

The top number is called the numerator.

The bottom number is called the denominator.

And that line that separates the two numbers, the numerator and denominator -- it's called a fraction bar or a vinculum.

So, the numerator.

The numerator means that that number represents the number of parts we have.

So that 1 means we have one part.

The denominator is the total number of equal parts we have in the whole.

So, in this case, the whole is made up of six parts.

So, for more on that, let's take a look at this Flocabulary video that really shows and explains all about fractions.

♪♪ >> ♪ Yeah ♪ [ Whistling ] [ Bird chirping ] >> ♪ Na na na na ♪ [ Whistling ] ♪ Na na na na ♪ [ Whistling ] [ Whistling ] [ Bird chirping ] [ Whistling ] >> That Flocabulary video gives very clear information on fractions.

So, let's look at several examples of naming the parts.

So, if we look at this fraction, I'm writing 2/6.

Which number is the numerator?

Did you say 2?

If you said 2, then that is correct.

2 is our numerator, and that means there are two parts given.

Let's look at another example.

Which number is our denominator?

Did you say 5?

You are correct.

There are five equal parts in the whole.

Let's look at another one.

What about now?

Can you tell me which part tells you how many equal parts there are in the whole?

Did you say 9?

Yes, that's correct.

In this fraction, there are nine parts in the whole.

What does the 6 mean?

The 6 -- yes, it is our numerator, and it means that we have six parts.

So, our whole fraction tells us we have 6 parts out of 9 equal parts.

Does that make sense?

Let's look at just one more.

This is 11/12.

Can you tell me which number represents the number of parts that we have?

Did you say 11?

Yes, that is correct.

We have 11 parts.

And so we can read this fraction as saying we have 11 parts out of 12 equal parts in the whole.

Does that make sense?

Excellent.

And we're going to look at what exactly a fraction looks like in a model.

We'll be looking at tangerines, some cans, and some Skittles.

Boys and girls, I just realized that when I was showing you the examples of the naming parts, I had the fractions labeled already for you.

So let's try that again.

I have four fractions, and we're going to look at the parts of the fraction.

Fraction 1.

Let's try that again.

Fraction 1.

Fraction 1 is 5/8.

Can you tell me which number is the denominator?

Did you say 8?

That is correct.

8 is the denominator.

Can you tell me what the denominator means?

Yes.

It means that they are eight equal parts in the whole.

What about the 5?

What does the 5 mean?

Yes, we have five parts.

And, so, the fraction means that we have 5 out of 8 equal parts.

Does that make sense?

Let's try another one.

Our second fraction -- how would you say that?

You are correct.

It is 9/10.

What does that 9 mean?

Yes, the 9 means we have nine parts.

And you are correct -- it is the numerator.

What about the denominator?

What does that mean?

Yes, it tells us that we have 10 equal parts in the whole.

You are doing excellent, excellent work.

Now I want you to do these two on your own.

First, name the fraction.

Did you say 4/5?

That is correct.

This fraction is 4/5.

And what does 4/5 mean?

Yes.

It means you have 4 parts out of 5 equal parts of the whole.

You are doing fantastic work.

I am so proud of you.

What about our last fraction?

Can you say that?

You are correct again.

That is 1/7.

And what does that mean?

Yes, you are correct again.

It means you have 1 part out of 7 equal parts of the whole.

Young scholars, you are doing excellent, excellent work.

Now that we have gone through the naming of the parts, so, as a recap, we have looked at the numerator, the denominator, and we looked at the line that separates the two numbers.

Again, the numerator, the top number, tells us how many parts we have.

The denominator, the bottom number, tells us how many equal parts there are in the whole.

So, now, young scholars, that we have looked at the naming of the parts, let's look at some models.

So, now let's look at what a model of a fraction looks like.

And I'm just going to use items I have around the house.

It's not fancy.

This is a tangerine.

And, as you can see, I have already peeled the tangerine, so we just have the pegs.

When you separate the tangerine, you'll see that you have a certain number of the pegs.

And we shall count them.

1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

So we have 10 pegs of this tangerine.

Now, when we look at the fraction, we know that the whole will be out of 10.

So we now have our denominator, which is 10.

So, let's look at how we can show... 10 slices of tangerine.

Our denominator, again, shows us how many equal parts we have in the whole.

These 10 pegs of tangerine show us that there are 10 pegs in the whole.

Now let us look at a fraction of the whole.

Let's see.

What would 2/10 look like?

Well, we have 2 pegs of tangerines out of 10.

So we are modeling 2/10 of our tangerine.

Does that make sense?

How about if we wanted to see what 4/10 of our tangerine would look like?

Remember, these represent the whole.

So, we are taking 1, 2, 3, 4 out of our 10.

So this represents 4/10 of our tangerine.

Does that make sense?

Now you try.

That's our whole.

Our whole has 10 pegs of our tangerine.

What would 6/10 of the tangerine look like?

Yes, you are correct.

Let's go ahead and count.

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

Now we have 6 out of our 10 pegs of tangerines.

That's our 6/10.

Do you have a fraction you would like to try?

Go ahead.

Now it's your turn to try it.

Use your own fraction and model it at home.

Excellent.

What a great job you just did.

Should we try something else?

I agree.

Let's try our cans.

Here are four of our cans.

I just took these from my cupboard.

So, mixed vegetables and corn.

So, now I am going to stack my cans.

I have four cans to make up my whole.

1, 2, 3, and 4.

These four cans -- they represent my whole.

This would be my denominator, which would be four equal parts in my whole.

Hmm.

Young mathematicians, I wonder -- what would 1/4 look like?

Well, I just removed one of my cans from my four cans.

So now I have 1 can out of 4 cans.

This can represents 1/4 of the cans I took from the cupboard.

Does that make sense?

Yes.

I'm glad you agree.

Let's try another faction.

What about if I wanted to keep most of my cans?

Let's model 3/4.

1, 2, 3.

[ Gasps ] Look -- we have just modeled 3/4 of the cans.

I now have 3 cans out of 4 cans.

That is excellent work.

Now it's your turn.

I want you to model the fraction 2/4 using the cans you have at home.

Now we're back to our whole.

Young scholars, what did you do?

Wow!

You stacked two cans to show that you have 2 cans out of 4 cans.

What amazing work you're doing.

Excellent job showing that you understand how to model a fraction.

That is excellent.

Now, why don't you try your own fraction at home.

Go ahead.

How did that go?

Excellent.

Now, don't get discouraged.

I want you to keep practicing how you can model what fractions look like, and use anything that you have at home.

It could be empty water bottles or cans or even pieces of fruit.

You can use almost anything to model the numerator and denominator of a fraction.

Remember, when we were looking at our tangerines, that the numerator was what we had.

For example, remember when we modeled 2/10 of the tangerines.

We had 2 tangerines out of the 10 equal pegs of the tangerine.

Does that make sense?

You have been such great scholars.

You are doing excellent work.

Wonderful.

Our next modeling will get a little more challenging, but that's what learning is.

Excellent work, young scholars.

Young scholars, since our objective is to understand addition and subtraction of fractions as joining and separating parts, referring to the same whole -- If you're wondering why I keep repeating the objective, it's because it's very important for you as mathematicians, as learners to understand what you need to do in order to reach or to achieve your objective for today's lesson.

So, can you tell me what today's objective is?

Yes, today's objective is for us to understand addition and subtraction of fractions as joining and separating parts, referring to the same whole.

Excellent work.

Now, let's look at a video from Math Antics about adding and subtracting fractions before we go to some modeling.

♪♪ >> In this video, we're going to learn the basics about how to add fractions.

Now, a lot of math books will teach you how to add fractions before they teach you how to multiply them, but here at Math Antics, we think you should learn the other way around.

You remember how easy it is to multiply fractions, right?

You just multiply the top numbers together and you multiply the bottom numbers together and you have your answer.

So, you might be wondering, "Well, can't we just do that with addition, too?

Can't we just add the top numbers together and add the bottom numbers together and get our answer?"

Well, alright.

Let's try it and see, but I got a bad feeling about this.

Let's try adding 1/2 to 1/2.

So, if we added the top numbers, we'd get 2, and if we added the bottom numbers, we'd get 4.

But, well, that can't be right, because 2/4 simplifies to 1/2.

And if you add 1/2 and 1/2, you should get a whole, not a half.

[ Alarm blaring ] Uh-oh.

We must have broke some sort of math rule.

I'm out of here.

Okay, here's what we did wrong.

It turns out that there's some important math rules called order of operations that say you have to do multiplication and division before you do addition and subtraction.

Now, because fractions are just division problems, if you just added the top numbers and added the bottom numbers, you'd be breaking those rules, because you would be doing the addition before the division.

So, what are we gonna do instead?

Well, fortunately, there is a trick that lets us work around the order-of-operation rules and add fractions without dividing.

But there's a catch.

It only works for fractions that have the same bottom numbers.

The trick is -- if fractions have the same bottom numbers, we can add them by just adding the top numbers together and keeping the same bottom number in our answer.

For example, to add 1/2 and 1/2, we just add the top numbers, and 1+1 gives us 2.

But we don't add the bottom numbers.

We just use the same bottom number in the answer, which is 2.

So, 2/2 is a whole fraction, and that makes sense, because if you add 1/2 and 1/2, you get a whole.

Let's see a few more examples, like this one.

5/16 plus 2/16.

Again, since the bottom numbers are the same, it's easy to add these fractions.

All we do is add the top numbers together.

5+2=7, and that's the top number of our answer.

Then we just keep 16 as the bottom number of our answer.

So 5/16 plus 2/16 equals 7/16.

Pretty easy, huh?

But what about subtracting fractions?

Does that work the same way?

Yep.

If the bottom numbers are the same, all you have to do is subtract the top numbers and keep the same bottom number in your answer.

Here's an example of subtracting fractions with the same bottom numbers.

5/9 minus 2/9.

First, we subtract the top numbers.

5-2=3.

Then we just write the same bottom number in our answer -- 9.

So 5/9 minus 2/9 is 3/9.

Yep, adding and subtracting fractions with the same bottom numbers is easy.

And there's a special name for problems like this.

It's called adding or subtracting like fractions.

A teacher once told me that they're called like fractions because the bottom numbers are the same or alike, but I think it's because they secretly like each other.

[ Chirping ] Just kidding.

But, seriously, like fractions are easy to add with the trick we just learned.

But what happens if you want to add two unlike fractions?

What do you do if you have fractions with different bottom numbers?

Unfortunately, the only way we can add unlike fractions without doing the division first is to change them so that they do have the same bottom numbers.

In other words, we need to change our unlike fractions into like fractions so we can just use our trick.

In math language, that's called finding a common denominator.

Now, remember that a denominator is just a fancy math word for the bottom number of a fraction, and common just means that they're the same.

So, how do we find a common denominator so that we can add or subtract unlike fractions?

That's what we're going to learn in the next video.

But before you move on, be sure to do the exercises for this section.

♪♪ Learn more at mathantics.com >> Wasn't that great?

Math Antics does such a fantastic job teaching us not only what a fraction is, but also how we add and subtract fractions using like and unlike denominators.

Today, we are going to be focusing on adding and subtracting fractions with like denominators.

So, now let's practice adding and subtraction -- excuse me -- subtracting fractions with models.

Okay, young scholars, so, I did say that we were ready for something more challenging.

So, now we are really going to get into our objective for today.

So, our objective today was for us to be able to understand addition and subtraction of fractions as joining and separating parts, referring to the same whole.

So, remember, at the beginning of our conversation, I talked to you about how I was a whole and the parts of me that made up that whole.

So, again, remember I told you that I was Jamaican, that I was American, that I am a mom, I am a daughter, a wife, and a teacher.

That's six parts of my whole.

So, now we're going to be looking at wholes using these Skittles, but we're going to look at how we join and separate the parts, referring to the same whole.

So, now I can show you what the same whole looks like.

So, you can see that our green Skittles -- there are five pieces, so five parts in that whole.

Does that make sense?

Good.

Our red Skittles -- there are also 1, 2, 3, 4, 5.

And so there are five parts that make up that whole, as well.

So, do you see that, young scholars, that there are five parts in each of these wholes?

So, now let's model the joining of the parts that refer to the same whole.

So, now let us model... 1/5 plus 2/5.

Can you see that?

Is that better?

Excellent.

So, now we're going to model 1/5 plus 2/5.

So, we're going to take one of our Skittles from the green and two from the red.

So we have 1/5 of a green Skittle and 2/5 of the red Skittles.

Let's join those together.

Simple.

We'll just count.

1, 2, 3.

Now we have three Skittles in total out of five.

Now, you might be wondering why we didn't join together all the Skittles.

Remember, we're looking at the same whole.

So, the green Skittles had five parts, five equal parts in the whole, and the red Skittles had five equal parts in the whole.

And, so, we are joining the parts that refer to the same whole.

That means that the denominator is the same, just like in our fraction.

So, we have 1, 2, 3 Skittles out of 5 equal parts.

Look -- what do you notice, boys and girls?

You're correct.

Looking at the numerators, the numerators represent the number of Skittles we have.

So, we joined the one green Skittle to the two red Skittles and now we have 3 out of 5 Skittles.

Does that make sense?

Excellent.

Let's do another.

How about orange this time?

Let's try seven.

Lucky number 7.

So we have seven orange Skittles.

So if we're looking to model out of the same whole, how many brown Skittles should we put down?

Did you say seven?

Oh!

You guys are so amazing.

Absolutely excellent.

Yes, seven brown Skittles, because they're out of the same whole.

Let's make sure we have the correct number.

1, 2, 3, 4, 5, 6, 7.

1, 2, 3, 4, 5, 6, 7.

Perfect.

So now we have two different-colored Skittles that have the same equal parts in the whole.

So... let's add together, or join, 3/7 plus 2/7.

Let's model that.

So, we already have the same whole.

So, our first fraction is 3/7.

So 1, 2, 3.

That's 3 out of our 7 orange Skittles.

Now we're joining that with 2 out of our 7 brown Skittles.

1, 2.

Boys and girls, how many Skittles did we join together?

Did you say 5?

How did you get that answer?

You counted.

That is an excellent answer.

Let's count together.

1, 2, 3, 4, 5.

We have 5 Skittles out of 7 equal parts of the whole.

That is excellent.

Would you like to do one at home?

Go ahead, try it on your own.

Join together... 1/6 and 2/6.

Remember to show that using a model.

You can use Cheerios.

You can use marbles.

You can use anything to model addition of fractions.

Are you working on it?

Excellent.

So, how many of your -- I'm using Skittles.

How many of your object did you make into equal parts?

Six?

You have six equal parts.

That's great.

So, when you joined them together, how many did you have?

Why don't you tell me what you did.

Okay, so, for the first fraction, you had 1 of your objects out of 6, and the second, you joined 2 out of 6.

That is perfect.

So, how many did you have?

So you had a total of 3 out of 6.

You are learning so thoroughly.

That is excellent.

Well, now that you have had practice with joining, let's look at separating.

So... We'll keep working with six.

So, let's start with 5/6.

And let's subtract or separate 1/6.

This is our whole, because our denominator is 6.

But we're starting with 5/6, so let's put this Skittle away.

So, we have our 5/6.

We have to separate 1/6 from our 5/6.

Let's go ahead and do that.

Boys and girls, how many sixths do you have left?

1, 2, 3, 4.

Excellent.

You have 4/6 left when you subtracted 1/6 from 5/6.

Does that make sense?

Let's do one more.

Oops.

My marker fell.

Thank you, Damaris.

1, 2, 3, 4, 5, 6, 7, 8.

Now, our whole is out of 8.

So, let us subtract... 5/8 from 6/8.

So we'll be taking 5/8 from 6/8.

Remember, we're working from the same whole.

So we're starting with 6 out of our 8.

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

Looks like we had nine, so let's start again.

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

So, we will remove our two.

Now we have 6 out of our 8.

So, now we're going to separate 5/8.

1, 2, 3, 4, 5.

How many eighths do we have left?

We have one.

We have 1/8 left.

So 6/8 minus 5/8 is 1/8.

Excellent work, young scholars.

Now... you try your own fraction at home.

Excellent work.

Keep practicing.

Keep practicing.

It is not an easy skill, but I believe you can do it.

Keep up the great work.

Whew!

Scholars, today, we learned a lot.

It's really great to exercise our brains.

It's important for us, as mathematicians, to focus on the objective and to understand what we need to do in order to be successful.

So let's think about today's objective.

Today, we learned to understand addition and subtraction of fractions as joining -- that's adding -- and separating -- that's subtracting -- parts referring to the same whole.

We modeled those ideas using regular household items, like cans and Skittles and tangerines.

That helped us to learn how we picture those fractions in our minds.

Again, it is important for us to remember -- you guessed it -- that fractions will always be a topic that we're going to need.

We're going to need fractions for baking, for cooking.

It's going to help us with parts of measurements.

It's going to help us when we tell the time.

And, of course, you know my personal favorite.

It helps us to figure out the discounts when we go shopping.

Do you want more practice?

Look around your home and ask a trusted adult to help you model various fractions.

Ask your trusted adult to give you simple fractions to add and subtract.

That will sharpen those skills and get you ready for once school reopens.

I know you can't wait.

My students can't wait to start school.

Can you believe that?

I never thought I would hear them say that.

Well, young scholars, it has been my pleasure.

This concludes our lesson for today.

It has been an amazing experience having this conversation with you.

I hope you enjoyed our lesson as much as I did.

Cheers.

Take care, stay safe, and stay well.

Remember, we're all in this together.

Bye-bye.