kowalski project

Solving Multi-Step Equationsby: Mike Kowalski

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Learning Objectives and Standards

To be able to solve multi-step linear equations, and be able to explain the reasoning behind the process used.

CCSS: HSA-REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.


Table of Contents

Warm up

Properties of Equality

Solving Strategies

Time to Balance!

Google form

ReferencesClick for next slideClick for next slide

Warm UpPerform the indicated operation.(click for next problem and answers)

Problems: Answers:

3*-8 -24

-6+7 1

-4-3 -7

-15/-5 3

2+(-2) 0


Warm Up

How’d you do?

If you got most right move on to the next slide.

If you need a little more practice check out this video or this one.


http://www.khanacademy.org/math/arithmetic/absolute-value/adding_subtracting_negatives/v/negative-numbers-introduction

http://www.khanacademy.org/math/arithmetic/absolute-value/mult_div_negatives/v/multiplying-positive-and-negative-numbers


These allow us to solve an equation.

We can think of an equation like a balance.

It’s our job to make sure the balance stays even, so our equations stays equal.



If we don’t use the properties of equality our balance will not be even.

If we don’t keep our balance even, our equation is no longer true.



These are the properties we are going to use today:

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of EqualityClick for next slideClick for next slide


Addition Property of Equality

If a = b then a + c = b + c

In English: If we know an equation is true we can add the same thing to both sides.

As long as we do the same thing to both sides our equation will stay balanced!



Subtraction Property of Equality

If a = b then a - c = b - c

In English: If we know an equation is true we can subtract the same thing from both sides.

As long as we do the same thing to both sides our equation will stay balanced!



Multiplication Property of Equality

If a = b then a*c = b*c

In English: If we know an equation is true we can multiply both sides by the same thing.

As long as we do the same thing to both sides our equation will stay balanced! Click for next slideClick for next slide


Division Property of Equality

If a = b and c≠0 (because you can’t divide by 0), then a/c = b/c

In English: If we know an equation is true we can multiply both sides by the same thing.

As long as we do the same thing to both sides our equation will stay balanced! Click for next slideClick for next slide


Now that we know the Properties of Equality we can put them to work.


Solving Strategies

Like the tools seen here, we need tools to help us solve equations.

Solving strategies are our tools.


Solving Strategies

To solve an equation our goal is to get the variable by itself.

To do that we are going to use the properties of equality discussed earlier and some of these solving strategies.


Solving Strategies

One strategy is to get the variable on one side of the equal sign first.

You may not have to do this for every equation, but it’s a good thing to check.

Variables can be moved from one side of an equation to another by using the addition and subtraction properties of equality.


Solving Strategies

Once the variable is on one side a good strategy to use is to eliminate numbers in the equation by working the order of operations backwards.

Do you remember the order of operations?

PEMDAS which stands for Parenthesis, Exponents, Multiply, Divide, Add, and Subtract! See this video for more


http://www.khanacademy.org/math/arithmetic/multiplication-division/order_of_operations/v/introduction-to-order-of-operations

Solving Strategies

So if we wanted to eliminate pieces from our equations using the order of operations backwards the first thing I should get rid of is addition and subtraction.

We can do that using the addition and subtraction properties of equality.

In order to eliminate addition from my equation I’m going to have to use the subtraction property of equality.

In order to eliminate subtraction from my problem I’m going to have to use the addition property of equality.


Solving Strategies

The next thing we can focus on eliminating is multiplication or division.

We can do that using the multiplication and division properties of equality.

In order to eliminate multiplication from my equation I’m going to have to use the division property of equality.

In order to eliminate division from my problem I’m going to have to use the multiplication property of equality.


Solving Strategies

Remember when you’re using these strategies and the properties of equality, it’s all about balance!

If we don’t do the same thing to both sides, we’re not keeping our equation balanced.

If our equation doesn’t stay balanced, we won’t end up with the right answer.


Time to Balance!


Time to Balance!

For this part we are going to try to solve an equation while keeping our scale balanced.

You are going to need to click on the bullet you think is the correct step in order to solve the equation.

If you make the correct choice you will be directed to the next step.

If you make an incorrect choice you will need to go back and try again.

Ready to balance?!?


Time to Balance!

Solve the following equation: 5x + 3 = 3x -7

I would subtract 3 from the left side

I would divide both sides by 5

I would subtract 3x from both sides

Time to Balance!

Oops!

You forgot to do the same thing on both sides.

Remember the subtraction property of equality says we must subtract the same thing from both sides of the equation.

Click the arrow to take you back to the problem.

Back to the problemBack to the problem

Time to Balance!

Oops!

You forgot our solving strategies.

We want to collect our variable on one side of the equation first.



Time to Balance!

Nice job! You used the subtraction property of equality to get your variable on one side of the equation.

Now for the next step. Continue solving 2x + 3 = -7


I would subtract 3 from both sides

I would add three to both sides

Time to Balance!

Oops!

You forgot our solving strategies.

We want to work the order of operation backwards.

We need to take care of addition and subtraction before division.



Time to Balance!

Oops!

In order to solve we need to undo what’s in our problem.

Since there’s already a + 3 in the problem to get rid of it we would need to do the opposite.



Time to Balance!

Nice job! You used the subtraction property of equality to eliminate the +3

Now for the next step. Continue solving 2x = -10


I would divide the left side by 2

I would divide both sides by -10

Time to Balance!

Oops!

You forgot to do the same thing on both sides.

Remember the division property of equality says we need to divide both sides by the same thing.



Time to Balance!

Oops!

If we’re trying to get the variable by itself we need to focus on the side of the equation with the variable.

Since the -10 is already on the other side of the equation shift your focus back to the other side and see if there’s something you can do.



Time to Balance!

Nice job! You used the division property of equality to eliminate the 2 multiplying the x

You solved the equation

x = -5

Since we got the variable by itself we know we’re done!

You can use these same strategies to solve any equation.


Google Form

Now that you’ve seen the properties of equality in action it’s your turn to try them out.

Solve the problems on this Google Form to practice using the properties of equality to solve equations.

Once you’re done click submit so your results can be collected.


You made it!

Thanks for using my interactive powerpoint.

I hope you learned a lot about solving equations.

Layla’s tuckered out from all this solving. Time for a nap.

References

All images provided by openclipart.org

All video links provided by Khan Academy

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