>> Hi, everyone.

Welcome to math class.

My name is Toni-Ann Palmisano, and I'm going to be your teacher for today's math class.

I currently teach middle school mathematics at a school in Hudson County.

I love my job, and I look forward to seeing the bright faces every single morning in my classroom.

During today's lesson, we are going to learn about one-step equations.

We are going to be able to activate prior knowledge of applying the skills of expressions, variables, coefficients, inverse operations, all to solving one-step equation problems, also involving real-world application word problems.

In addition, I'm going to throw in a little challenge where you will be able to apply the distributive property with solving equations.

I am so excited for this lesson to start.

In order for you to be successful during this class, you're going to need a few items.

Please get out a piece of paper and pencil, if you have it.

You can even use the back of the packet that your teacher sent you home before going off to virtual learning.

If you have a highlighter, that would be great.

We're going to highlight a lot of key words during today's lesson.

And also, don't forget your smile, and most of all, confidence.

You can never be a successful math student if you don't have both of these items.

You must always be happy, smiling, even in the worst of times when you don't understand something, and your confidence must shine.

We all are human.

We make mistakes.

Even though I'm a teacher, I make plenty of them.

So make sure that you're ready to make mistakes during this class.

Before we actually dive into the lesson, I wanted to tell you a little bit about myself.

As I said earlier, teachers are human.

I'm a human being.

I go out to the store.

I see my students in real life.

But, most of all, you want to go about life, doing what you love, and teaching is what I love to do.

Going into work every day and seeing my students really brings so much joy to my life.

A couple of years back, I won an award called the Milken Educator Award.

During the notification ceremony, I was surprised in front of my entire school filled with so many of the students that I adore, and I was awarded this prize.

Later I came to find out that it was a very special award, and I am so incredibly thankful to have been awarded.

I hold a photo close to me to recognize the importance of how my students matter in my life, and I'd like to share that with you.

Okay.

This was the moment I was awarded three years ago.

A lot of the students pictured here are now in high school, but you could see the expression on my face.

I nowhere ever imagined that it would be me.

So in case you're holding on to any memories or you have something near and dear to your heart -- maybe something you got from a grandparent or parent or a sibling.

Just remember that those items are what sometimes get us through a day.

I also got a gift once from a student, which showed -- A couple of students together and myself as their advisor, and, you know what, it's an everyday candle on one side, but on the other side it reminds me why I love my job.

So, just as we get ready to dive into the lesson, I wanted to show you that I'm a human being, too.

I have emotions.

I go through life.

So if there's any time that you're sitting there struggling with school, know that you're not alone because even adults have some things that they go through on their own that they have to get over.

I wish you the best of luck in today's lesson, and I cannot wait to get into it with you.

Here we go.

Get out your pencil paper and get ready to enter the world of algebra.

>> Hi, boys and girls!

Ready to enter the world of algebra?

Here we go.

Do you have that pencil and paper out?

In case you need another second to get it, let's also go through what else we need for today's class.

If you have a highlighter, don't forget to pull that out.

If you're used to using a calculator in school, feel free to use it during today's lesson.

If you never use a calculator, then you won't need it.

Luckily, today we're going to deal with numbers that aren't too large.

Turn on your thinking caps and remember that it's okay to make mistakes today.

Also, don't forget that smile and that confidence.

Remember I was telling you a little bit about myself earlier?

One thing I forgot to add is just how much I love the sunshine.

Sunshine makes me so happy.

I love being outside.

I love spending time at the beach or by the pool.

I guess you could say I love summer in general.

What's your favorite season?

Give you something to think about.

Okay, so, as we go through this lesson here, we are going to think about what prior knowledge can we activate?

Now, the activation of prior knowledge means that you were taught some skills, either earlier this year or last year, that will allow you to learn this lesson on equations a little bit easier, okay?

So here on the board, I have 4X minus 7 equals 5.

Now, this is an equation.

It's an equation because it has an equal sign.

It also has an operation of subtraction.

Some other operations, as you know, are addition, multiplication, or division.

Here we happen to see subtraction.

We also have something called constants, which are just numbers that are usually in equations, expressions, inequalities.

Just the numbers.

We also have something called 4X.

Now, I want to take a second to look at 4X because they have two important vocabulary terms that would be able to describe that combination.

Before I see whether or not you know them, I have a visual here, okay?

4X.

Together, it reads 4X.

If I was to separate it, they stand alone.

Let's look at the X first.

Does anyone know what we call a letter that stands for an unknown in algebra?

Start with a V. Very good.

A variable.

So wherever we see this X, let's write variable.

Okay, so when it stands alone, it's a variable.

It could be X, Y, Z. It could be A, B, C. Any variable -- Any letter, rather, can stand for a variable.

Now, when I bring in the number 4, okay?

4 is right next to the variable.

The number in front of any variable has a special name.

It's called the coefficient.

Can everyone say that?

Coefficient.

Okay?

If you don't know how to spell that, no worries, just follow along on the screen.

So together, I call this 4X.

The X alone, a variable.

The 4 in front of the X, coefficient.

I'm taking some time to go through these important vocabulary terms because you're going to hear me say a lot of them during today's lessons.

So, this lesson is on equations.

As I stated earlier, an equation has an equal sign.

It states that both sides are equal to one another.

To help you with this understanding, I have two important pictures on the screen.

One is in green, and the other is in red.

Okay?

Let's focus our attention to the photo in green.

If you haven't already noticed, it's a photo of a balance scale.

The green photo shows both sides having equality.

Each side is equal.

How do I know that?

They're at level with one another.

If I direct my attention to the next one, which is the photo in red, I see that the right side is slightly higher than the left side.

Would you say that that is balanced?

You are correct.

That is not balanced.

So the goal here for equations is to balance the equation.

How do you do that?

You do something called isolating the variable.

So your goal here is to isolate the variable.

What does it mean to isolate the variable?

In order to isolate the variable, we want to have the variable by itself -- either X equals, Y equals, Z equals.

Whatever variable we have, We want it to equal a number.

Now, whether that number is a whole number, a fraction, or a decimal, or a negative number, it doesn't matter.

What does matter is that we recognize that equations have one solution.

That's also important to write down.

Now, you're probably thinking, wait, how would it not have one solution?

Well, when you get into the seventh grade next year, you're going to learn something called inequalities, where you have the solution being multiple solutions, meaning that instead of just having X equals something, you can have X being greater or less than a quantity.

You'll get into that next year.

Going back to equations, equations have one solution.

So your final answer will be X equals quantity.

Good so far?

All right.

So equal sign, isolating the variable, and being able to know that equations have one solution.

Doing great so far.

As mentioned earlier, we have a lot of operations in the world of math.

We're going to learn about two operations right now -- addition and subtraction.

I call addition and subtraction best friends, in a sense.

They go hand-in-hand with one another.

In order to solve equations, we need to apply inverse operations.

Inverse operations undo each other.

So let's write that down.

Inverse Operations.

And inverse operations undo one another.

So what does that really mean?

Well, here's a real-life example.

Imagine you were eating M&Ms.

You took two M&Ms and you put them in a pile to save them for later.

So you took two M&Ms, you added them to a pile.

Then you realized you didn't want them there anymore.

So to undo the adding of two M&Ms to the pile, you are now going to take the M&Ms away.

"Take away" in mathematics is known as subtracting.

So addition and subtraction undo each other.

Those are inverse operations.

You're going to need to know that for this lesson.

And it's an easy to remember the M&Ms problem because I don't know about you, but I love chocolate.

So anything that has to do with food or chocolate, I'm right there.

Okay.

Here is our first example.

Whenever I'm teaching my lessons, I always tell the students just how important it is to rewrite the problem.

When you're rewriting the problem, it gives you the ability to understand and kind of read in your mind what's being asked of you instead of just rushing to get it done.

So let's rewrite this problem together.

C plus 2 equals 5.

So that was the first step.

Re-write.

Now let's think about the purpose of solving an equation.

The purpose is to isolate the variable.

Before we go into another step, get out your handy-dandy highlighter.

I want you to take your highlighter and I want you to draw a line down the equals sign.

Just like that.

The purpose of this is to create a visual for you.

When I look at this equation, I see two sides now.

I see a side to the left of the highlighter, and I see a side to the right of the highlighting.

The next step is thinking to yourself, I need to isolate the variable.

In order to do that, eyeball it.

"Eyeball the variable."

What does that mean?

That means take your eyeballs, take your mind, and focus it on that variable, whether it's an X, Y, a Z, or an A -- whatever it may be.

So that's step two, eyeball the variable.

Now, in this case, it's a C. What's near the C?

C plus 2 Because I'm adding 2 -- it's a positive-2 -- you want to think to yourself, what will undo that quantity?

Think back to those inverse operations.

So if I have addition, I'm going to use subtraction.

Now, this isn't really something that you have to worry about, thinking hard about because you're going to subtract the quantity away of what you're adding.

So if you're adding 2, you're going to subtract 2 on each side.

With me so far?

Again, there is that beauty of the balance scale.

What I did to one side of that highlighter, I'm doing to the other side of that highlighted part.

Again, there's your balance coming into play.

Now you want to think to yourself, did I isolate the variable on the left side?

Well, let's see.

Positive-2 minus 2 goes away.

We show that it goes away by canceling out the quantities, and usually you put a light line through that to do so.

Okay.

So bring down my variable, line up my equal sign, and I'm going to evaluate my right side in this case, which is 5 minus 2, which is 3.

Did I get the variable alone?

Yes.

Because you got the variable alone, you can say that you are done, and you can box up your answer.

So let's go through those steps again.

Rewrite, eye the variable... Step three is going to be apply.

inverse operation.

In this case, it was subtraction.

Then I'm going to think about canceling out the quantities and then, finally, box up your answer.

So those are five important steps to take when solving a one-step equation.

Now, luckily, there is a way to check your work.

Whether it's required of you or not on a test, I still recommend you to do it, and I recommend you do it because it's an easy way to see whether you're right or wrong.

What you do is you rewrite the problem -- C plus two equals 5.

I'm boxing up that variable because that's going to make me realize that I need to plug in the value that I found as a solution.

So C is no longer C. I could replace it with the number 3.

And it's at this point you're asking yourself if both sides are going to balance 3 plus 2 is 5.

5 equals 5.

Because both sides balance, I could put a checkmark, and I know I did the problem right.

So I highly recommend checking in the future.

Good so far?

Good.

Let's try another.

I love Example 2.

I love Example 2 because the order in which the equation is presented to you looks a little different than what we saw in Example 1.

First step, rewrite the problem.

4 equals Y minus 8.

Go ahead and get your highlighter.

Highlight down that equal sign.

Eyeball the variable.

Now that I see two different sides created in the equation -- the left of the highlighted area, the right of the highlight -- I then can go in and eyeball the variable.

The variable is Y. Y is found on the right side of the highlight.

What's in the way of Y?

What's in the way of Y is a minus-8.

Now, you can look at it as saying minus-8 or negative-8.

I know at this point you're not used to negatives so much and positives, but sometimes you can look at that as being a negative-8.

But for right now, let's say subtracting 8, and what will undo subtracting?

You said it.

Adding.

What am I going to add?

I'm going to add exactly what I subtracted away.

So if I subtracted 8, I'm going to add 8.

Think of that balance scale.

What I do to one side, I have to do to the...?

Other.

Good.

4 plus 8 gives me 12.

Bring down my equals sign, line it up, and I get 12 equals Y as a solution.

Did I isolate the variable?

Yes, I did.

Then I'm done.

Box up your answer.

Let's check our answer.

Rewrite the problem, leaving a space for the solution to be added in.

Where you saw a Y, you're going to replace it with a 12.

And you're going to think to yourself, do both sides equal each other?

If they do, you did a good job.

If they don't, we got to go back and look at what we did wrong.

So 4 equals 12 minus 8 is in fact 4.

I put a checkmark and I'm done.

Feeling good so far?

Good.

Example 3.

Let's rewrite the problem.

3.5 plus Y equals 12.75.

Get your highlighter.

Put a line down the equals sign.

See the visual?

See the two sides?

I now have a left side of the equal side.

I now have a right side of the equal side.

Eyeball that variable.

That variable's on the left.

What's in the way of the variable?

What's in the way the variable is 3.5.

You're adding 3.5 to Y. What would be the inverse operation of adding?

Anybody say subtraction out there?

You're right.

So I'm going to subtract 3.5 to each side.

What I do to one side, I have to do to the other.

Now, be careful here, because, if you haven't already recognized, we are dealing with decimals.

Decimals are different from whole numbers.

Decimals have place values.

So as I subtract that 3.5, I want to be sure to put the 3 in the whole column and the 5 in that tenths column.

So, what I like to say in class is that when we're dealing with decimals, you want to be sure to line up the dot and give it all you got.

So we say, "Line up the dot and give it all you got."

I said, "Line up dot and give it all you got."

So that's a way to realize that when you're doing either addition or subtraction with decimals, that decimal point needs to be lined up all the way.

♪ Line it up, up, up ♪ Okay.

So now when we solve here, we can insert a place holder.

5 minus zero is 5.

7 minus 5 is 2.

Bring down that decimal, 12 minus 3 is 9.

>> So I didn't mean for that to actually look like a -- time.

So I wanted to get rid of that, but my answer is Y equals 9.25.

So, you see, sometimes when you're dealing with problems that involve numbers that may not be whole, you may have an extra step there, meaning you have to be extra careful to keep the decimal points lined up when adding or subtracting decimals.

How you feeling so far?

It's your turn to try one.

Go ahead and copy down this equation.

I'll read it aloud.

Y minus 6 equals 8.

I'll give you about a minute to try it.

Let's see what we get as an answer.

Remember those steps!

Get your highlighter.

Draw a line down the equals sign.

Create two sides for yourself.

Left and right.

Eyeball that variable.

What's in the way of the variable?

Then you can go ahead and apply your inverse operations.

How you doing so far?

All right.

Let's compare answers.

Y minus 6 equals 8.

When you eyeball the variable, you should have noticed that we were subtracting 6.

To undo that, I needed to add 6 to each side.

My final answer... Y equals 14.

Done.

Last step I forgot to do was to think to myself, if I have a minus-6 and I have a plus 6 and I add them together, they disappear and they go away because I have zero.

How many of you got Y equals 14?

Good job.

And for those of you who didn't, don't worry, it's going to get easier.

Okay.

Let's try a word problem.

It takes 43 facial muscles to frown.

This is 26 more muscles than it takes to smile.

Write and solve an equation to find the number of muscles it takes to smile.

When you're dealing with word problems, you are going to have to do something called defining a variable before you begin the problem.

By defining the variable, it's going to allow you to understand what is unknown.

So if I read the end of this sentence, I see that I'm trying to find the number of muscles it takes to smile.

That's what I have to write as I'm defining the variable.

So the number of muscles it takes to smile.

You know how much I love this problem already.

It involves smiling, something you know I love to do, and I know every one of you out there loves to do it, also.

Once you define the variable, that's going to help you.

Put our equals sign.

Think to ourself, if I'm trying to find the number of muscles needed to smile, what number in my word problem has to do with the number of muscles that it takes to smile?

Hmm.

I don't know that, you're right, but I do know that 43 is how many muscles it takes to frown.

So that's going to be my total that I'm going to compare my other information to.

>> Now it says this is -- So 43 is... "Is" is actually a key word because "is," for the most part, signifies that equal sign or replaces that equals sign.

You'll see that a lot in math.

So 43 is 26 more muscles than it takes to smile.

How would you translate "26 more muscles than it takes to smile" into algebra?

Well, this here is my unknown.

I don't know this.

Okay.

That's my unknown.

But I do know that "more" can be associated with what operation?

Correct.

Addition.

So my unknown plus -- My unknown plus 26 equals 43.

That is my one-step equation.

Now let's take our steps.

Think about eyeballing the variables on the left side.

I'm going to add 26 in my initial equation.

So that means to solve, I'm going to subtract 26 from each side.

Bring down your isolated variable.

Bring down your equals sign.

43 minus 26.

I'm going to borrow.

And I get a final answer of 17.

Now, you can always look to see whether or not your answer makes sense because these are real-life problems.

So if it takes 43 muscles to frown and that's 26 more than the muscles it takes to smile, well, we just found out that it takes 17 muscles to smile.

So 17 plus 26, working backwards, would give you back that 43.

So you can always relate it to real life, luckily.

Questions so far on a word problem?

Notice how I'm doing a lot of marking up to the words in the word problem.

I'm doing circling, I'm doing underlining, I'm using my highlighter.

So those are some shortcuts to help you understand the problem instead of just rushing into setting it up and trying to get it done, okay?

So take a little extra minute or so to even reread it another time to hopefully have you understand it better.

Okay.

Let's look at this next word problem.

Raheem's roller blades costs $70.25 less than his bicycle.

Ooh!

That right there, before I move on, I'm going to highlight this sentence.

I think that's important.

And I think what's really important is for me to bring out the word "less" because that might signify a operation.

His roller blades cost $43.50.

How much did his bicycle cost?

So let's define our variable.

Remember, when we're defining our variable, we're deciding what is unknown.

And that's always usually in the last part of the word problem.

What we don't know is how much the bicycle costs.

Okay?

And you can abbreviate.

So you want to think to yourself, we don't know how much the bicycle cost, but we do know that the roller blades cost $43.50.

How many of you out there think that that is our total, meaning that that will be the number after the equals sign?

You are correct, because that's our total for the roller blades.

Now, the bicycle, we still need to figure out what it's going to cost, but we do know that the roller blades cost $70.25 less than the bicycle.

Do I know the bicycle?

You do not.

Always start with your unknown, boys and girls, when writing an equation from a word problem.

It's the easiest way to go.

From there, you can think to yourself, how can I take $70.25 less than his bicycle and write it as a expression that will be part of my full equation?

X less than the bicycle, $70.25.

So "less" -- Is it addition, subtraction, multiplication, or division?

Good job.

Subtraction.

And we put the $70.25.

So before we start to solve it, see if you understand the setup and why we chose subtraction and why we should chose the placement of the numbers.

Good?

Okay.

Put your highlighter.

If I'm subtracting $70.25, what would be the inverse operation of that?

Very good, adding.

I'm going to add that same quantity -- no thought needed.

So if I'm adding $70.25 to one side, I'm doing it to the other.

Now, an important point to bring out here.

See where we said that we're adding?

Most oftentimes, some students tend to put the addition sign on the other side and they tend to, like, put it in crazy places.

Remember, rule of thumb.

Line up your operations with each other, okay?

That's gonna help you especially see how to cancel it out.

Negative-$70.25 or minus $70.25, and then adding it makes the quantity go away.

I'm left with X equals.

And this final answer of adding 5, 7, 3, 11... gives me an answer of $113.75.

Again, does your answer make sense?

Put yourself in the situation.

Pretend you had roller blades that cost $43.50 and then a bicycle, okay?

Think about this.

The bicycle has to be more money than the roller blades because it's telling you in the first sentence that the roller blades cost this amount less than the bicycle.

So that's an indication that the bicycle price is going to be more.

How are you feeling so far?

I hope not overwhelmed.

This is the first part of the lesson dealing with addition and subtraction as inverse operations.

We're going to move on now to multiplication and division.

Go ahead and take one second, and we'll pick up in one second.

See you in a second!

>> Hello, boys and girls!

Now we're going to learn how multiplication and division are also inverse operations that can be used to solve equations since we can use those to isolate the variable.

So on the screen here we see two properties of equality, and we do see a little reminder here that inverse operations undo each other.

So we have addition canceling subtraction out, and now we have multiplication canceling out division and vise versa.

Let's get into the first example here.

Remember the first step, rewrite the problem.

3X equals 6.

Get out your highlighter.

Highlight the equal sign.

What we're going to do here is now focus in on eyeballing the variable.

When I eyeball the variable, I see that it's on the left side of the equal sign.

I also notice that it is not added to or subtracted from any other number.

Instead, it's really close to a number.

It's like it's hugging it, I say.

If you remember earlier in the lesson, I let you know about coefficients and variables.

This is where we need to remember those.

If I look at 3X, 3 is being multiplied to X, meaning that if I wanted to isolate X, I would need to apply the inverse operation for multiplication.

The inverse operation for multiplication is division, but not by writing the division sign that you learned in the 5th grade.

Instead, we're going to use a fraction bar to signify division in the world of algebra.

I'm dividing out by the number which I'm multiplying by.

Remember, a coefficient is the number being multiplied by the variable.

So if I'm multiplying the X by 3, I want to divide by 3.

What I do to one side, I do to the other.

And what I like to do in class, I tell the students, is to always box up that coefficient because if you box it up, that will allow you to see what you then need to divide by.

So our step there is going to be to divide out by the coefficient.

Now, when you get into higher grades, maybe next year in the 7th grade, your coefficient may be a fraction.

It may be a decimal.

We call those rational coefficients.

But just for the sake of this lesson, we're gonna deal with whole numbers.

3 divided by 3 doesn't give you zero.

What's 3 divided by 3 give you?

1 is correct.

3 divided by 3 gives you 1.

So 3 divided by 3 gives me 1.

I can cancel out those 3s, drop down that X. Because if I think about 3 dividing by 3 giving me 1 watch here.

X is the same as 1X.

I like to call it a phantom 1 in class.

Sometimes you need to see it, sometimes you don't.

So whether or not you write 1X or X, X is isolated.

Keep that in mind.

6 divided by 3 gives me 2.

So my final answer is X equals 2.

Good?

That's why dividing by the coefficient is an important step.

The vocabulary term of coefficient will allow you to understand that you only need to go ahead and divide out by that number that is in front of the variable.

If I was to check this solution, I would rewrite my problem, leaving a box for what I need to substitute, and I'm going to plug in my solution that I found, which is 2.

3 times 2 -- Remember, when numbers are very, very close to each other, it's signifying the operation of multiplication, okay?

You can have parentheses signify that also.

3 times 2 is 6.

6 equals 6, and we're good to go.

Good job.

Moving along here, I have rewriting the problem of 2.25 times N equals 6.75.

Whoop!

Skipping a little bit there.

Remember when I just said we might have a rational co-efficient?

Here we go.

2.25 is my coefficient here.

Put down the highlight.

Eyeball the variable.

2.25 multiplying by N. If I'm multiplying, I need to divide to undo the multiplication.

What's the coefficient here?

Again, coefficient -- vocabulary term.

What's the number in front of the variable?

Good job.

It's 2.25.

I'm gonna box it up.

I'm gonna divide each side by that 2.25.

2.25 divided by 2.25 -- Cancels out.

Why?

It gives me 1.

1N is the same as N. Now, when I tackle the right side, I want to pull it out.

Pull out that right side.

Why?

Because we have to divide it.

So we're gonna need to give ourselves some extra room.

Wow, this is really going to activate some prior knowledge -- dividing decimals.

Can we divide decimals?

It's not that we really can't divide decimals, it's just that we have to make sure that that divisor, which is our number outside of the house, becomes a whole number.

So in this case, I have to do two scoops on the outside, which is your divisor.

Whatever I do to the outside, you must do on the inside.

So put your pencil on the decimal on the inside and also move two.

Okay?

This ringing a bell?

Your new problem -- 275 into 225.

How many times does 225 go into 675?

Okay.

You want to try 3?

There you go.

3.

Final answer, N equals 3.

Questions on that?

I like that problem because we were able to not only see a coefficient that's a decimal, but also review dividing decimals.

I'm impressed.

That one was a hard one.

And moving along here to one of our close to last problems, rewrite the problem.

A divided 3 by equals 7.

Okay?

Here we go.

What we're going to do here is we're going to put our highlighter down the equals sign.

We can now see two sides.

Mm Hmm.

Eyeball the variable.

It's on the left side.

But think about it -- What is in the way of the variable?

What's in the way of the variable -- look -- is dividing by 3.

I'm going to bold that.

Okay?

So if I'm dividing by 3, what will one do dividing by 3?

I hope you said multiplying by 3, because if you did, you're correct.

What I do to one side, I do to the other.

Now, a couple of things here to note -- Notice how I used a dot to signify a multiplication.

Here in the sixth grade, we're learning alternate ways to write multiplication.

Not only are we going to be using the X to signify multiplication, but now we're going to learn how to apply the dog to signify multiplication.

3 -- When we multiply 3 to each side, we want to think about how 3 has a denominator of 1.

Having a denominator of 1 does not change the value of the number.

I'm going to simplify out here, 3 goes into 3.

The both have a common factor of 3, leaving 1.

Isolating that A equals 7 times 3 is 21.

With me so far?

Remember, these problems are not impossible.

Talk to yourself.

Say them out loud.

Don't think you're crazy.

Sometimes you understand things easier when you say them aloud.

So when I say the problem A divided by 3, by hearing "divided by" 3, I'm then able to recognize that I need to apply the inverse operation of multiplication.

Good job.

Part of now is your turn.

You're going to take a second to try this one.

Rewrite the problem and go for it.

Good luck.

Remember, you want to be able to apply inverse operations.

How many of you are thinking of multiplying to each side?

You are correct.

Okay.

Let's see your final answer.

Okay.

Go ahead and check your work.

I'm going to isolate the A by multiplying each side by 29.

Those cancel out.

I get A is equal to 29 times 5.

It's 145.

Okay.

Who got that answer?

Excellent.

Good.

Okay.

So I'm going to actually leave these word problems for you to try on your own.

And before I close the lesson, I want to let you in on a challenge, if you will.

And that's being able to apply the distributive property.

Now, how many of you have ever heard of the distributive property?

Okay.

So the distributive property is a way to simplify using multiplication in a sense.

And on the left side here, what I want to do is I want you to think about that term that you see.

I can see that left side is two times the quantity of 3 plus 5, okay?

And I can read the right side here as four times the quantity of X plus 6.

Now the question here is -- Okay.

I have this term on the outside.

Let's deal with the the right side that I'm on.

I have this term 4 on the outside of parentheses.

How I like to explain it is this.

You have 4 on the outside that needs to be distributed to every term on the inside.

Well, what does it mean to be distributed?

I think of it this way.

You have a friend on the outside.

He's knocking on the door.

The 4 is knocking.

He's knocking, knocking.

They're letting him in.

It's pouring outside.

The 4 says, "Okay, hi!

Can you let me in?"

The four meets the X. The X lets him in.

By meeting each other, it's signified by multiplication 4 times X. You then drop down your operation in this case, which is plus.

The 4 is knock again.

He not only needed to make friends with the X, he also needed to make friends with the 6.

When they meet, it signifies multiplication.

4 times 6.

Then we simplify what we can.

4 times X. I just leave it as 4X.

4 times six, plus 24.

4X and 24 are not like terms, so I need to stop here, and that's my final answer.

So I'm using the distributive property here.

And what I like to bring up is that the distributive property, we always use colors and create happy rainbows.

Okay?

Because the arrows will help us keep track of taking that outside term and helping it to meet everything on the inside.

So that's just a little introduction.

And here's a challenge problem.

3 times the quantity -- Whoa!

Sorry about that.

Of X plus 5 equals 45.

So, before we can even solve this one, we really need to be able to simplify that left side.

So if I eyeball that variable, I see that that variable is in between parentheses.

Okay?

And I cannot break out of those parentheses until I get that term on the outside away.

I'm gonna apply the distributive property.

3 meets the X, 3 meets the 5.

When 3 meets the X, you're going to multiply.

I'm going to drop down my addition.

3 meets the 5.

3 times 5, equals 45.

Simplify where you can.

3X is the same as 3X.

3 times 5 is 15, equals 45.

Now it's at this step where I'm going to leave it as-is because this is something we call a two-step equation.

Which I promise you'll see next year.

But I wanted to bring in the distributive property because I know earlier this year in the 6th grade, you dealt with it when you were dealing with the expressions.

Okay.

In my classroom, I love singing songs.

So I wanted to share a song with you before we part ways.

It sings to the tune of "If You're Happy and You Know It."

So how many of you know that song?

I knew you would.

So it goes a little something like this.

♪ If you want to solve equations, here is how ♪ ♪ If you want to solve equations, here is how ♪ ♪ Just undo the operations by applying the inverse ♪ ♪ Do the opposite ♪ ♪ That's what is allowed ♪ >> Good so far?

♪ If you see a negative, you must add ♪ ♪ If you see a positive, then you must subtract ♪ ♪ Multiply will get undone by dividing everyone ♪ ♪ And divide gets multiply or the answer's wrong ♪ Last verse!

♪ Oh, equation's must stay balanced to be true ♪ ♪ What you do to one side, you must do to two ♪ ♪ And to solve for the unknown, you must get it all alone ♪ ♪ Using every single step you know to do ♪ So I'm going to leave that with you in case you want to sing it on your own as a way to apply inverse operations when solving equations.

I had so much fun in today's lesson.

I really hope that you were able to learn something from our math lesson, whether it was important math vocabulary -- coefficient, variable, inverse operations -- or whether it was the simple importance of using a highlighter when doing word problems or even solving equations to visually see two sides.

It was a pleasure getting to know everyone, and I hope that you do wonderful for the rest of the year.