(funky music) ♪ From our house to yours ♪ ♪ From Newark to the Shore ♪ ♪ One big New Jersey fam, and we're learning live ♪ ♪ Learning live, learning live ♪ - [Announcer] Support for this special educational program has been provided in part by RWJBarnabas Health, NJM Insurance Group, the Fuel Merchants Association of New Jersey, and National Oilheat Research Alliance, by New Jersey Realtors, and the New Jersey Education Association, working to make public schools great for every child.

- Hi, New Jersey, it's Miss D. I've had so much fun learning with you over the last few weeks, but I wanted to take some time to review.

I've learned how to read with enthusiasm with my teachers.

I've learned how to make fractions with fruit.

I've made music with household items.

(pot banging) I've learned how to make paint with things in my kitchen.

I've taken notes on moments in history and written letters to all of my friends and family.

There's so much more to learn, and I hope that you've enjoyed these lessons, too.

Monday through Friday, 9:00 AM to 1:00 PM, right here on NJTV, - Pretty awesome, huh?

- Your New Jersey public media station.

You can watch lessons in math, language arts, science, social studies, music, PE, art and more for grades three through six, but all ages are welcome to join.

A bunch of New Jersey teachers, the New Jersey Department of Education, New Jersey Education Association, and NJTV partnered up to make sure you're still learning and make it pretty fun, too.

So now it's time to meet today's teacher and tune it to NJTV "Learning Live".

- Hello, mathematicians.

It's great to be here with you again.

For those joining me for the first time, my name is Mrs.

Correa.

I am a master teacher of mathematics for the West New York School District.

Hi, West New York friends!

Today, I am thankful for students.

You are all so special.

Students from all over the world have taken on learning from home and done such an amazing job.

So I want to say thank you.

It is because of you that we keep learning and growing together.

Your efforts spread joy and positivity, like this rainbow.

Did you know that some children have been making rainbows from home and posting them on their windows, on the sidewalks.

You may have done a rainbow, too.

These rainbows are meant to spread hope and cheer during these trying times.

It also serves as a sign of support for all our frontline workers.

You may have spotted some in your own neighborhood.

Well, today, we will be making a special type of math rainbow.

Do you know what I'm referring to?

I hear some yeses and some nos.

That's okay, don't worry.

Let's go inside and find out more.

But first, here's what you're going to need for today's lesson, pencil and paper; coloring tools, crayons, colored pencils, markers; 20 small objects, it could be Legos, beans, little Cheerios, anything.

I will give you about a minute to gather your supplies.

Okay, mathematicians, do you remember how I get my classroom started?

When I say, all set, you say, "You bet!"

All set, you bet.

You ready?

All set?

You bet!

Awesome, I'll see you in just one minute.

(upbeat dance music) Welcome back, friends.

I am so excited to get started.

Today, we're gonna talk about factors and multiples.

We're gonna be able to identify all the factors of the numbers between one and 100, and we're gonna be able to identify the common multiples of given numbers.

So let's jump right in.

Here, I have a number bond.

Some of you may remember a number bond from first and second grade.

In first and second grade, it was used to represent an addition equation.

These were known as a part-part-whole chart.

These were the parts that gave un the sum up here, which was the whole.

But for today's purpose, we're going to turn this into a chart that will help us with multiplication.

So this is the product, and these are its parts.

Let's see if you can help me fill this out.

Three times what number will give me 15?

There's so many ways you can think about it.

You can use multiplication and the missing factor, or you can use division.

So what do you think.

Five, very good!

How did you figure it out?

You used multiplication?

Okay, so you thought three times five gave you 15.

Did anyone else think of it differently?

You used division, okay.

So you said 15 divided by three will give you five.

Very good, either way, you can figure it out because they are related.

Multiplication and division are its inverse operations.

So you may have remembered learning some fact families, and you can write this equation in several different ways.

Let's try it.

We can say three times five equals 15.

We can also say five times three equals 15.

And now, we can do the division statements.

15 divided by three will give me five.

And 15 divided by five will give me three.

This is known as a fact family.

You're able to see it just by looking at this number bond and how they're related.

Today, we're gonna focus on multiplication, but you can still use division if that helps you.

Today, we're gonna look at these parts.

They actually have a name, and that's part of today's lesson.

These are known as the factors.

This is known as the product, or a multiple.

See, three can go into 15 five times evenly.

That means it's a factor because the definition of a factor is a number that will divide into another number without a remainder, and there was no remainder here.

Five is a factor of 15 because five can go into 15 three times and have no remainders.

Very nice!

We're gonna get into factors a little bit deeper now.

So I'm going to transition from this number bond and just place it here.

Then I'm going to set up my paper or my board.

What I need you to do is get your paper and pencil ready.

And then we are going to create a little T chart, but only that one section's going to be bigger than the other section.

It'll look something like this.

And here, we're gonna title this smaller section number of tiles, or you can say number of toys or number of beans or number of Cheerios, whatever it is that you're using for your manipulative.

And here, we're gonna talk about factor pairs.

In math, one of the most successful tips I can give you is to stay as organized as possible, and I love to use organizational charts like this.

So on your piece of paper, write number of blank, whatever it is you have as a manipulative.

And here on this side, you're going to write factor pairs.

Then gather those manipulatives, 'cause we're going to use them to discover factors of the numbers from one through 100.

(laughs) Just kidding!

We can't do all the numbers one through 100 in this fashion, but don't worry.

I'm going to get you to learn all of those factors from the numbers one through 100, but for the reason of time and I really can't go and on forever, or maybe I could 'cause it is math that I love, but for today's purpose, we're going to just start with these manipulatives, and it's only going to be 20.

But then I'm gonna show you strategies on how you can get what you do know to find the other numbers without the manipulatives.

So stay tuned for that.

Okay, so let's get started.

Here I have one manipulative.

I have the number one.

What two numbers can multiply to equal one?

One times one.

There you go, that is a factor pair of one.

Can you think of any other factor pair for one?

No, that's it.

One and done.

Awesome.

Let's look at the number two.

It's beginning to form some kind of array, is it not?

What can you tell me are the factor pairs of two?

One times two.

That's correct.

You have one group or one row of two.

You can also say here you have two rows of one, because one times two is the same as two times one.

What property allows you to do that?

The commutative property, very good!

Remember our fact families?

Well, that's all it means.

One row of two or two rows of one.

Either way, you're correct, awesome.

Okay, so far I think we've got it simple.

Let's keep going.

What if I had the number three?

How would I write this array or this factor pair?

Three groups of one, or, see like this, if I did it this, three groups, woop, of one, see?

Or I can say I have three rows of one.

So I can write three times one.

But if you wrote one times three, it's all good 'cause you're correct.

Remember the commutative property, awesome.

Okay, now let's look at the number four.

Excuse me, I need my manipulative.

I'm just gonna go here.

Let's look at four, ready?

Here's another array.

What do you think?

One row of four.

Yeah.

Is there another way I can do it?

Ah, I see what you're saying.

(gasps) Look at that.

What can I say about this one?

Two rows of two.

So I can say that two times two also is a factor pair for four.

You see that?

Can you notice something else about this?

It makes a square.

Very nice.

Do you know that when you do make a square, it's known as the perfect square because you have exactly two of two.

I wonder if we're get another perfect square down along the other side of the numbers.

Let's see.

Okay, so now that we've finished four, now let's try the number five.

Uh-oh.

That doesn't make a perfect square or a rectangle.

And if I went like this, now I have a rectangle, or an array.

Okay, so what would I say?

One row of five.

Or if I stacked them on top of each other, I could say five rows of one, but it's still the same factor pair.

So we're just gonna leave it as one times five.

Okay, we're coming down the line.

We erase this just for my sake of purpose, but you continue on your chart all the way down.

You don't need to keep erasing.

That's just for me because I need my space.

Okay, so now I have five, and I'm now up to six.

Let's look at six.

One row of six, anything else?

Two rows of three.

Oh, look at this smart mathematician.

Awesome, you were able to make a rectangle, an array.

So we have two rows of three, correct.

So two times three is also a factor pair of six.

Can you think of another way?

Well, if we put it this way, it would be three rows of two.

So it would be three times two.

But we already have that factor pair, so we can keep going, very nice.

Here we go, number seven.

That does not make a rectangle.

See how you have a remainder?

So we're going to have to find another configuration where there will be no remainders.

What do we have?

One row of seven.

Okay, stack them down and I can say seven rows of one, but, again, it's still the same factor pair.

All right, we're getting there.

What about eight?

Boop!

One row of eight.

Do you know another way?

Yes, okay, yeah, I'm gonna bring these down.

And there we go, another array.

What does this array represent?

Two rows of four.

So two times four.

Very nice, so eight has two factor pairs.

It has one and eight itself, and it has two times four.

Did you notice something yet?

Did you notice that each number has one as a factor?

Yeah, every number has had one, one row of that number.

And did you also notice that that number is also a factor pair of itself every time.

So every number will have one as a factor pair and itself as another factor.

Nice, right?

Let's continue.

Now I have the number nine.

Go ahead and write nine on your paper.

Okay, and I'm going to go ahead and place it, hm, nope.

So I have to move along, and there you go.

One row of nine.

One times nine.

See, there's the one, and there is itself, nice.

Any other way?

Well, let's see.

Okay, yes!

Three rows of three, nice.

Fix that up nicely, okay.

There it is.

Three rows of three.

Do you notice something?

If we line it up correctly, it would make a perfect square.

Three by three, see?

Another perfect square, so that was four is a perfect square, nine is a perfect square.

Hm, I wonder if there's more perfect squares along the line of the numbers.

We'll see.

Okay, so now I'm going to try 10.

Well, this configuration won't work, so let's see what else we could do.

Hm, well, we know we could do one times 10.

This time, I'm going to go up because I'm running out of space horizontally.

So I'm going to lay it out vertically.

This is vertical, and this is horizontal.

10 times one, or one times 10, however you wanna think about it.

Is there another way?

Think of 10.

Hm, yes!

Two times five, so let's see.

(gasps) You got it, there's an array!

Here you go.

You have five rows of two.

Or we can make it like this, and it'll still be the same thing, see?

This one would be two rows of five, two times five.

But we already have the factor pair.

Hey, what does that remind me of?

A 10 frame, that's right!

Awesome work!

Okay, 11.

Hm, nope.

Let's see.

Mm, nope.

Let's see, uh-oh.

Mm, nope.

Mm-hm.

I think we're stuck with this one.

I tried many different ways.

Did you try, too?

Right, all I could find was 11 groups of one or 11 rows of one.

So I'm gonna say 11 times one, or one times 11 if you went horizontally.

That's okay, too.

Okay, let's go with the next number.

Remember, you can keep going.

I just need space, but you could keep going on your list.

We're at 12.

Make sure you have the right manipulatives 'cause as we get to the bigger numbers we start to get a little, we could get it all mixed up.

So make sure your manipulatives are on the side.

Okay, so now, ooh, I see this configuration, there's no remainder.

I made an array, so what can I say?

Four groups of three equals 12.

Awesome.

Do you know another way?

Yeah, I see it, too, right?

I can go like this and like this.

(gasps) And what could that could be?

Six rows of two.

That's another factor pair.

Do you know another one?

What about the one, yeah, the one times itself because they all have one, and they're all factor of themselves.

Oops.

So I could always stack them just like this, and there you have it.

Very good!

I want you to try 13.

Go ahead, I'll give you a second.

(gasps) What'd you get?

(laughs) Yes!

13 times one.

Very nice!

Okay, let's do 14.

Well, we always have 14 times one because we know one times itself is always a factor pair, mm-hm.

You think there's another way?

Let's try two.

Let's go this way.

What if I wanted to do two rows.

Will that be okay?

Sometimes when the numbers get a little big, it might be hard for you to do it in your brain, but you can try.

I'm gonna try, too.

(gasps) It worked out.

Two rows of seven, yeah!

Let's try three.

Mm-mm.

And I can see already that four is not gonna work.

Mm-mm.

Five?

No, no.

That's not gonna work.

Six?

Mm-mm.

Seven, well I already have it there, so that's it.

I know I've gone through all the numbers that it could possibly be.

Okay, let's try the last one for now, which is 15.

Hm.

That's not gonna work.

Go ahead, and go ahead and spend some time with your 15 manipulatives and see what you can come up with.

I'll give you a few seconds while I think, too!

Ooh, I found one, did you?

Yeah!

Did you get it, too?

Awesome!

Three rows of five.

So three times five.

Awesome work!

Can you think of another way?

You could do four rows.

Hm.

No.

Can't do four rows.

If we did five rows, we would have the same, so we don't have to try five.

How about two rows?

Two rows, or, I'm sorry, or two groups.

Hm.

Nope, nothing times two is gonna equal 15, mm-mm.

But we know that if we need a factor pair, there is one pair that's always faithful.

It always be there.

There is one factor pair that you could guarantee every single number has.

One times itself!

So no matter what, every number's gonna have one times itself.

Now, I know we said 20.

I wanna give you a chance now for the last few numbers for you to figure out, what are their factor pairs?

And we're gonna come back and check.

I'll give you a few seconds.

Go ahead and try it.

Try 16, 17, 18, 19, and 20.

Okay, see you in a few seconds.

Go ahead try it!

(upbeat dance music) Okay, so how'd you do?

Awesome, okay!

Let's compare notes.

Here's what I got, and let's see if you got the same.

Okay, so here's 16.

I have one times 16, two times eight, and four times four.

Do you notice something?

A perfect square, yes!

All right, high five!

Yeah, so remember, you had four rows of four.

It makes a perfect square.

So we have four is a perfect square 'cause you have two rows of two.

Nine is a perfect square 'cause you have three rows of three.

16's a perfect square 'cause you have four rows of four.

Can you predict which number will be the next perfect square?

Yes, 25, awesome!

Five rows of five.

I bet you can continue finding a bunch of perfect squares.

Great work!

17, just one times 17.

I tried it so many different ways, just one times 17.

18, one times 18, two times nine, and three times six.

That had a few pairs, huh?

19, one times 19, that's it.

20, (gasps) yes, also had quite a few pairs, one times 20, two times 10, four times five, awesome.

Mathematicians, you can try all the number from one through 100.

But we're not gonna do that today 'cause that would be, whew, too much work for right now.

But as we further along get in this lesson, I will show you different ways and techniques so it can help you when you need to find other factor pairs of any given number.

Awesome!

So I wanna recap.

Let's look at this image.

These were the rectangles that we made.

Here are all the arrays we created out of the factor pairs of the numbers one through 15.

Do you notice anything?

Yes, some of the numbers only have one array, and some of the numbers have multiple arrays.

The numbers with only one array are numbers with only one factor pair, one and itself.

These are known as prime numbers, like the examples in two, three, seven, 13.

See, they're only one and themselves, so that means they are prime numbers.

The other numbers have more than one factor pair, and they're known as composite numbers, like for example, number four.

It has one times four and two times two, or the number nine, one times nine and three times three.

Isn't that awesome?

Well, I think that now is a good time for a brain break.

So I decided, we had so much fun with my brother the last time, I thought maybe we could give him a call and see if he would be willing to give us another fitness brain break, a part two fitness brain break.

What do you think?

Yeah, I should call him, right?

Okay, no problem.

Let me call my brother, and let's see what he's up to.

Come on!

Hi, big bro!

- Hi, my beautiful little sis!

- Guess what?

I have another opportunity to work with the fourth grade students of New Jersey.

- Wow, that's absolutely phenomenal.

- So I was thinking, since we had such a great time the last time, maybe you could help me out with part two of another fitness brain break.

- Absolutely, I'm always ready for a challenge.

Let's bring it up a notch this time.

I think these mathematicians will be ready for this.

- Oh, I love it.

Sounds awesome.

Go get Sebastian.

Go get Evelette.

Let's give these mathematicians one minute to get their sneakers on.

- Let's do this.

- Let's do it!

- Okay, so now we're gonna go a little more active, a little more change of pace.

We're gonna now do these three following exercises.

Well, we got the bear crawls.

We've got the banana to Superman.

Hm, I like Superman.

Third is the crab crawl.

So those are the three exercises.

For the bear crawl, we'll do it for 30 seconds.

The banana-Superman is gonna be a total of 60 seconds, and we're gonna switch midpoint so at the 30-second marker.

And the last one, the bear crawls, 30 seconds.

And we're gonna do the same thing.

We're gonna now do two rounds of that.

And that should be anywhere from three to five minutes.

All right, so the first exercise we're gonna demonstrate is the bear crawl.

All right, so both my kids will now show you the bear crawl.

Controlled movement, guys.

You're gonna go up about two or three.

It's like you're climbing up and then reversing all the way back to start position.

(feet clomping) All right, that is exercise one, you'll be doing that, too, for 30 seconds.

Exercise two, we're gonna hit that core.

You're gonna feel those abs really working.

You're gonna lay on your back.

Okay, hands back, legs straight out, and we're gonna do the first exercise is the banana.

Okay, so you wanna keep your hands extended back there, legs straight out.

You're gonna bring your legs six inches, and your arms off the ground and in a crunch position.

You're gonna make your little banana.

Now, this is a very challenging exercise.

You guys can rest now.

You're going to be doing that for about five-second hold and relax, five second hold, and relax.

If you could do it the whole 30 seconds, you're one strong mathematician.

All right, so that's the 30 seconds, and then we have to flip and do the Superman.

Now the Superman's are my favorite.

I love Superman.

So this is a great exercise.

Now this takes care of your posterior chain here along your back glutes, and what we're gonna do is we're gonna elevate off the floor and we're flying!

All right, that you'll do, same thing, five seconds.

A couple seconds left, come right back, take a little five seconds, all right, and 30 seconds.

So that sequence will be a total of 60 seconds.

You're gonna be doing a banana and a Superman.

Exercise number three will be the crab crawl.

Here we go, guys.

Show the mathematicians how it's done.

You're gonna go down, one or two, three, and then reverse it.

(feet clomping) Okay, so if you don't have the space, you can do it stationary.

So we're gonna pop up, lift our right leg, left leg, right arm, left arm.

And you're gonna keep going around until your time is up.

And here we go.

Evelette and Sebastian will be coming down to the floor to get ready to start the bear crawl.

I'm gonna start my timer.

(electronic beeping) Go, here we go!

They're gonna be going up and down.

Bear crawl for 30 seconds.

This is gonna get a little challenging.

You guys can take your breaks as needed if you feel 30 seconds is too long.

That's okay.

You could stop, take a little break, and then continue.

Remember, it's all about progression.

And progression is when you start building up strength, you're able to last a little longer.

You get stronger.

(electronic beeping) - Rest.

- Awesome job!

Okay, so we're gonna lay down now for the second exercise.

Lay on your backs please.

(electronic beeping) And at the bell, you will begin.

You're gonna bring your arms back, legs straight.

(electronic beeping) - Go.

- Here we go!

Keep those feet about six inches off the ground.

Arms should be extended back.

You start to fatigue, come down, take a break.

Not a problem.

All right, once again, we wanna build up strength for these exercises.

Our goal ultimately need to be up for about 30 seconds, but as you can see, it's challenging.

So they're going and taking their breaks.

It's okay.

Yeah, work those abdomens.

(electronic beeping) - Rest.

- Awesome.

- Woo!

- For our second part of exercise two, we'll be doing the Superman.

So we're gonna get on our bellies.

Arms are straight out, and, at the bell, we're gonna go up.

Ready?

And up!

(electronic beeping) (kids lightly grunting) We're holding that for 30 seconds, and just like we did the banana, all right, we can hold for five seconds and back down and relax.

Take your breaks as needed.

We're trying to build up strength.

So we're flying.

You're keeping your legs up, your arms up, chest off the floor.

(Sebastian pants) (electronic beeping) Amazing!

(electronic beeping) - Three, two, one.

- Here we go, the crab crawl, exercise number three.

Sebastian will be demonstrating going up and down, and Evelette will do it stationary.

Here we go!

(feet clomping) While we do it stationary, we lift the right leg, left leg, right arm, left arm.

Yes.

Getting a nice little workout, getting that blood flowing in the body.

(electronic beeping) - Rest.

- Great job.

Amazing job, we just concluded fitness brain break two!

We had a fantastic time showing you mathematicians how to get in shape.

It's just as important to train our body as it is the mind.

Back to you, sis!

- Thanks, big bro!

That was awesome.

Okay, let's get back to the math.

Look at this.

Pretty cool looking, huh?

Well, it's an activity we're gonna do next, and it was created by someone called Eratosthenes.

Do you know who that is?

I know, it's okay if you don't.

He was around a very long time ago, but he was a famous Greek mathematician, and he had so many awesome discoveries.

He's also known as the father of geography because he was able to calculate the circumference, at least came pretty close to the actual size of the distance around the entire Earth.

Wow!

And you know how he did it?

Through watching the sun and shadows.

You gotta look it up.

It's some great stuff there.

But today, we're gonna talk about one discovery he had called the sieve of Eratosthenes.

Do you know what a sieve is?

This!

See?

You may have seen a trusted adult using it.

Yeah, like this.

Whatever you put in here, the smaller particles fall through.

And the other stuff stays behind.

Well, the sieve of Eratosthenes is a way to discover all the prime numbers from one to 100.

You can actually use it for more than that, but we're just gonna focus on one through 100, and we're gonna sieve out all the prime numbers and keep the composites left behind.

All right, but there's some rules we need to follow in order to get this right.

So what I want you to do is pay attention.

You don't have to write anything.

This one is on me.

But we do have the follow the rules, and you're gonna help me out.

First of all, we have the hundred chart right here, and again, you can go further, but for now, we're gonna just stick to the 100 chart.

Here are my rules that I must follow in order to find all the prime numbers.

I'll use different colors so we can see the different numbers.

Some key words here that I wanna point out, we were talking about factors and multiples.

So multiples are numbers that are the product of any two given numbers.

If I have three times two, you have six.

Six is a multiple of three and a multiple of two because he is the answer to both two, and he is answer in the family of six.

So if you went through all your six times tables, I mean, sorry, if you went through all your two times tables, you would find six in there.

And if you went through your three times tables, you find six in there, too.

So six is a common multiple to both two and three.

So there's so many more patterns that we're gonna be able to discover using the sieve of Eratosthenes.

Let's jump right in.

First, we have to cross out one.

Since prime numbers we heard were greater than one, well, one is not greater than one, so he's the first one that gets crossed out.

Okay, now, let's start with our first row.

It says the first prime number is two.

Cross out all the multiples of two.

Okay, so two is a prime number.

And two also, oh, sorry, two also is the only even prime number.

It's the only one!

Pretty cool, huh?

Okay, so now what we're gonna do is, once we circle him, because he is prime.

He only has one times two, just one times himself, everything else we're going to have to cross out because it'll have one times itself but also two times something.

So, for example, the next multiple of two would be four.

It's like skip counting, two, four, six, eight.

So four is gonna get crossed out because two times two equals four and one times four equals four.

See, it has two factor pairs.

That means it's composite.

It's no longer prime.

Awesome, okay, so we're gonna continue and we're gonna cross out all the multiple of two.

Wrong one, woo, can't be too fast.

Wow, I'm eliminating most of the numbers already.

This is gonna be a lot easier than I thought.

See, all these numbers are multiples of two.

If I kept counting by two, I will continue to find the multiples because multiples can keep going and going and going forever because numbers are infinite, and I could keep counting by two.

See multiples are infinite.

Factors are limited.

Okay, all done!

Now, the next rule says that I have to circle three because he's the next prime number.

He only has one times three.

Then it says, cross out all multiples of three.

So I can go ahead, see six is already crossed out.

That's okay, keep going and think of all the multiples of three.

And there you have it, all the multiples of three.

Okay, let's keep sieving.

We have five is our next prime number, five.

One times five are the only two factors that equal five.

And then, we can cross out all of the multiples of five.

So we can count, five, 10, 15, 20, 25, 30.

Okay, cool, and we're down to the last one.

Here we go, multiples of seven.

Seven, multiples of seven.

Here we go.

Well, first we gotta circle seven because he is, in fact, a prime, only one times seven.

And then we have to cross out all the multiples of seven.

(laughs) See, once you get to 77 and then you get to 84, and you've done all your multiplication tables, you can look up here and I have all the multiples of each number.

So you may only know to 84, but that's okay, 'cause once you know to 84, you could keep going.

You just count by sevens.

So you could say, one, two, three, four, five, six, seven, cross him out.

One, two, three, four, five, six, seven, cross him out.

And then that's it, and you cross it out.

And now supposedly, all the numbers that remain are prime numbers.

So I'm gonna go ahead and circle those.

See, we're left with all the prime numbers.

Here's a closer look at the prime numbers.

There are 25 prime numbers from one through 100.

Thank you, Eratosthenes, that was so awesome even in 2020.

Thanks for the contribution.

So now, we're gonna slow down and start doing a little activity that requires us to just use our colored pencils and some knowledge that we learned today.

We're to do some factor rainbows.

Remember at the beginning of the lesson I talked about the rainbows.

Well, now we're gonna use our knowledge of math and factors to create our very own factor rainbows.

Wanna try?

Okay, awesome.

Let's start with the number 35.

Now, you can use any color.

It doesn't have to be the ROYGBIV colors of the rainbow, red, orange, yellow, blue, green, indigo, violet.

It's okay if you don't have all those colors.

You can make it as colorful as you want, or you can use as limited colors as you want.

It's your factor rainbow, and you can choose whatever order.

Let's look at 35.

Instead of writing the factors as a number sentence or an expression, we're gonna write them a little different so that way we can create a rainbow.

You ready?

Okay, so 35.

What's the first factor pair that you can think of that equals 35?

Yep, one times 35 because every number has one and itself.

So what I want you to do is write it as so.

On one side of your paper, you're going to write the one and on the other side the 35 'cause they will branch together in order to make that rainbow.

But we're not gonna design it just yet.

Okay, then we're gonna put a little comma to separate them.

Now, let's look at the next number.

Maybe you don't have your multiplication facts memorized.

That's okay.

We can use our process of elimination to figure it out.

Let's look at two.

Is this number divisible by two?

No, it's not an even number, so it's not gonna be divisible by two.

We can skip that one.

Three?

Well, let's think of the multiples of three.

And you go all the way, three times 11 is 33, and three times 12 is 36, so it passes this one.

So mm-mm-mm.

Four, can you think of the multiples of four?

We know that eight times four is 32 and eight times five is 40, so we pass it, so mm-mm-mm.

Five?

Five times, think of all the multiples.

Five times seven.

Excellent!

How about six?

Think of all the multiples of six, six, 12, uh-huh, uh-huh, keep going.

Nope, right, it does not have a 35 in there.

So that's it because the next one is seven, and it's already here, so we are done.

Yep, 35 only has two factor pairs.

Okay, so now we're gonna create the rainbow.

So this is what you do.

You make an arch like that and then another one with another color.

Show you in just a second, here you go.

See?

One times 35 and five times seven.

Can you create a factor rainbow for me?

All right, I'm gonna give you the number.

Let's see, hm.

How about the number 42?

Go ahead and try it.

(upbeat dance music) So how'd you do?

Here's how I did.

Let's compare.

So for 42, I have these factor pairs.

I did one and 42 'cause one times itself is always a factor pair.

Two and 21 'cause I knew it was an even number.

So I know it was divisible by two, which really just means take half.

So half of 42 is 21.

Three times 14, you may know three times 12.

That's 36.

And then you just keep using your skip counting to find the other multiples.

So you have 39 then 42.

So I know that 42 is a multiple of three.

So three times 14.

Then four, I didn't find anything.

And five, I knew right away because it doesn't end in zero or five.

42 is not a multiple of five.

And then six times seven, I knew that one.

I bet you did, too, yeah!

Awesome job!

So now I want you to create your own factor rainbows.

Go ahead and choose any number you want.

If you want a rainbow that has multiple colors, then you're gonna have to pick a number that has multiple factors.

So test out a few numbers.

See which ones give you the amount of colors that you want to use in your rainbow.

Yeah, and when you're all set and you've done your rainbow, you can choose to do it however.

You can do it like I did with just one little line, but maybe you wanna make each line thicker.

That's okay, that's your rainbow.

But whatever you do, when you're done, be proud of your work and hang it up for all to see or even if you just wanna see it and let it bring you hope and positivity.

Yeah, you know what?

I have an idea.

I think now I'm gonna go outside and take that rainbow, and I'm going to change it into a factor rainbow.

What do you think?

Yeah!

Let me show off how much I love math!

Do you wanna come see?

Do you wanna join me?

Come with me.

Let's go outside and turn my rainbow into a factor rainbow.

Awesome, let's go.

So here's my rainbow.

I want to find out the factor pairs of the number 60.

Do you think you can help me?

Great, so let's begin.

One times what number is 60?

60, awesome!

How about two?

Two times what number will give me 60?

What do you think?

30, awesome!

How about the number three?

Three times what number will give me 60?

Awesome, 20!

Let's go to the next number.

How about four?

Does four go into 60?

Yes!

How many times?

15 is correct!

How about five?

Does five go into 60?

Yeah, let's try it.

Five times what number goes into 60?

12, awesome!

Okay, what about the number six?

Does six go into 60?

Yes, 10 times!

Wow, thank you for helping me with this beautiful math factor rainbow.

It looks fantastic.

Remember, you can make your own factor rainbow.

Just choose a number and match the colors to the factor pairs, and you have a factor rainbow.

Make sure to display them in your window or wherever you want, on your walls, and remember to always think of hope and positivity every time you see the rainbow.

Continue to smile and show your true colors!

Take care of yourself and stay safe, bye!

(funky music) ♪ From our house to yours ♪ ♪ From Newark to the Shore ♪ ♪ One big New Jersey family and we're learning live ♪ ♪ Learning live, learning live ♪