Solving Equations A Stand-ALONE INSTRUCTIONAL RESOURCE Audience: The intended learners are 7th grade pre-algebra students who are learning how to solve equations. It will also serve as a review for 8th grade and higher. The review will prepare students so they can expand on their knowledge of how to solve equations. In both cases the exercises will be helpful learning tools. This could be beneficial for hearing impaired students, as auditory learning is not necessary. Goals/Standards: Solving Equations is the basis for almost all algebraic concepts. If students struggle with this area, they will struggle with other areas in math as well. It is important that students have a strong foundation solving equations before they move on to higher levels of math. This concept is introduced in 7th grade and built upon as students progress.   7th grade Michigan Grade Level Content Standards (GLCS): A.FO.07.13 Students are to “…generate and solve linear equations…and interpret solutions” Michigan GLCS: A1.2.1 High School math students are to, “write equations with one or two variables to represent mathematical or applied situations, and solve” Click the ‘NEXT’ button to continue NEXT

introduction Today, in Ms. Stechschulte’s 7th grade class, we will be learning how to solve one-step equations. To navigate through this presentation, click on the arrows and buttons at the bottom of the screen. The arrow labeled ‘NEXT’, will take you to the next slide. The arrow labeled ‘BACK’, will take you back to the previous slide. When you get to the Main Menu, click on the first link to begin the lesson. If you need to go back to the previous lessons to clarify concepts, please do so. Click the arrow below to continue. NEXT

Goal Your goal is to learn the concept of solving equations so you are successful answering the quiz questions. You must know the concepts well enough to solve two-step equations for tomorrow’s class. When you are finished with the first 2 Lessons, go to Lesson 3 and play the online math games for the remainder of the class period. Good luck and have fun  BACK NEXT

What is an equation? “An equation is a written statement indicating the equality of two expressions” It consists of a sequence of symbols that are split into left and right sides joined by an equal sign. For example, 2 + 4 = 6 is an equation. http://dictionary.reference.com/browse/equation Left side Right side BACK NEXT

2x + 3 = 5 Parts of an equation * Remember * Left side Right side Coefficient: the number that is in front of the x. This means that 2 and x are multiplied. Variable: the letter you are solving for; it needs to be isolated on one side of the equation. A variable can be any letter. BACK NEXT

Main menu Solving equations Lesson 1: Using adding & subtracting Lesson 2: Using multiplication & division Lesson 3: Online Math Games Click on the link for Lesson 1 to begin. When finished with Lesson 1, continue with Lesson 2 then 3.

Online math games Hoop Shoot Equation Buster Easy Algebra Equations Say the ‘2 – steps’: Rags to Riches BACK

Solving Equations is like balancing a scale: x + 1 = 3 To solve an equation you must get x by itself on one side of the equal sign, while keeping the scale balanced 1 1 1 x 1 BACK NEXT =

Solving Equations is like balancing a scale: To get x by itself you have to take away (subtract) 1. However, this will cause the scale to become unbalanced, so you also have to take away 1 from the other side of the equal sign. 1 1 x 1 1 BACK = NEXT

Solving Equations is like balancing a scale: x + 1 = 3 -1 -1 x = 2 After you subtract 1 from both sides of the equal sign, you are left with x = 2 1 1 1 x 1 BACK NEXT =

inverse operation “Two operations are said to be inverse to each other if one operation undoes the effect of the other operation.” Addition and Subtraction are inverse operations Multiplication and Division are inverse operations http://www.icoachmath.com/Sitemap/InverseOperation.html BACK NEXT

Solving equations To solve x – 5 = 3, Inverse operations must be used when solving equations. In the previous example we SUBTRACTED to undo the ADDITION to get x by itself. To solve x – 5 = 3, what operation must you use to get x by itself? BACK NEXT

x – 5 = 3 +5 +5 x = 8 Solving equations To solve If you said ADDITION you are correct! To undo SUBTRACTION you must ADD. To solve x – 5 = 3 +5 +5 x = 8 Add 5 to both sides to keep the equation balanced. BACK Begin Quiz 1 MORE EXAMPLES

More examples x + 2 = 4 To solve an equation get rid of whatever is with the variable (x). What you do to one side, you must also do to the other side. 1 1 1 1 1 x 1 NEXT =

Subtract 2 from both sides to keep the scale balanced More examples x + 2 = 4 Subtract 2 from both sides to keep the scale balanced 1 1 x = 2 1 1 1 To Quiz 1 x 1 BACK NEXT =

Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve More examples Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve x – 2 = 3 +2 +2 x = 5 Add 2 to both sides to keep the equation balanced. To Quiz 1 BACK NEXT

-1 = 7 + x -7 -7 -8 = x x = -8 More examples -1 = 7 + x is the same as saying 7 + x = -1 Since 7 is ADDED to x, you must SUBTRACT 7 from both sides to solve -1 = 7 + x -7 -7 -8 = x x = -8 Subtract 7 from both sides to keep the equation balanced. To Quiz 1 BACK

Solve x + 4 = 9 A. x = 13 B. x = 5 C. x = 9 Quiz 1 Question 1: Click on a letter to continue.

Solve x – 5 = 2 A. x = -3 B. x = 2 C. x = 7 Quiz 1 Question 2: Click on a letter to continue.

Solve – 5 = 4 + x A. x = -9 B. x = -1 C. x = 9 Quiz 1 Question 3: Click on a letter to continue.

Correct!! Nice Work! NEXT

Correct!! Great Job! NEXT

Correct!! Fabulous! NEXT

Let’s look at another example Incorrect Try Again Let’s look at another example NEXT

More examples x + 2 = 4 To solve an equation get rid of whatever is with the variable (x). What you do to one side, you must also do to the other side. 1 1 1 1 1 x 1 NEXT =

Subtract 2 from both sides to keep the scale balanced More examples x + 2 = 4 Subtract 2 from both sides to keep the scale balanced 1 1 x = 2 1 1 1 x 1 To Quiz 1 BACK =

Let’s look at another example Incorrect Try Again Let’s look at another example NEXT

Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve More examples Since 2 is SUBTRACTED from x, you must ADD 2 to both sides to solve x – 2 = 3 +2 +2 x = 5 Add 2 to both sides to keep the equation balanced. To Quiz 1

Let’s look at another example Incorrect Try Again Let’s look at another example NEXT

-1 = 7 + x -7 -7 -8 = x x = -8 More examples -1 = 7 + x is the same as saying 7 + x = -1 Since 7 is ADDED to x, you must SUBTRACT 7 from both sides to solve -1 = 7 + x -7 -7 -8 = x x = -8 Subtract 7 from both sides to keep the equation balanced. To Quiz 1

What is the inverse operation of MULTIPLICATION? SOLVING EQUATIONS What is the inverse operation of MULTIPLICATION? BACK NEXT

The answer is… DIVISION SOLVING EQUATIONS The answer is… DIVISION BACK NEXT

What is the inverse operation of DIVISION? SOLVING EQUATIONS What is the inverse operation of DIVISION? BACK NEXT

The answer is… MULTIPLICATION SOLVING EQUATIONS The answer is… MULTIPLICATION BACK NEXT

SOLVING EQUATIONS When you have an equation with multiplication or division, you will do the inverse operation to solve! BACK NEXT

Since 6 and x are multiplied, to solve, we divide by 6. examples Since 6 and x are multiplied, to solve, we divide by 6. 6x = 48 6 6 x = 8 Divide by 6 on both sides to keep the equation balanced. BACK NEXT Reminder: When a number is divided by itself, it equals 1.

Since x is divided by 4, to solve, we multiply by 4. examples Since x is divided by 4, to solve, we multiply by 4. x = 5 4 (4)x = 5(4) x = 20 Multiply by 4 on both sides to keep the equation balanced. To Quiz 2 BACK MORE EXAMPLES

More examples The inverse operation of MULTIPLICATION is DIVISION, so we divide by 10. 10x = 30 10 10 x = 3 Divide by 10 on both sides to keep the equation balanced. To Quiz 2 BACK NEXT

x = 3 -5 (-5)x = 3(-5) x = -15 More examples The inverse operation of DIVISION is MULTIPLICATION, so we multiply by -5. x = 3 -5 (-5)x = 3(-5) x = -15 Multiply by -5 on both sides to keep the equation balanced. To Quiz 2 BACK NEXT ** Remember: Negative times a positive = negative

-2x = -10 -2 -2 x = 5 More examples The inverse operation of MULTIPLICATION is DIVISION, so we divide by -2. -2x = -10 -2 -2 x = 5 Divide by -2 on both sides to keep the equation balanced. To Quiz 2 BACK ** Remember: Negative times a negative = positive

Solve 5x = 35 A. x = 175 B. x = 30 C. x = 7 Quiz 2 Question 1: Click on a letter to continue.

Let’s look at another example Incorrect Try Again Let’s look at another example NEXT

Correct!! Super! NEXT

Solve x = 4 -2 A. x = -8 B. x = 6 C. x = -2 Quiz 2 Question 2: Click on a letter to continue.

Let’s look at another example Incorrect Try Again Let’s look at another example NEXT

Correct!! Fantastic! NEXT

Solve -3x = 6 A. x = 2 B. x = -2 C. x = -18 Quiz 2 Question 3: Click on a letter to continue.

Let’s look at another example Incorrect Try Again Let’s look at another example NEXT

Correct!! Great Job! NEXT

More examples The inverse operation of MULTIPLICATION is DIVISION, so we divide by 10. 10x = 30 10 10 x = 3 Divide by 10 on both sides to keep the equation balanced. To Quiz 2

x = 3 -5 (-5)x = 3(-5) x = -15 More examples The inverse operation of DIVISION is MULTIPLICATION, so we multiply by -5. x = 3 -5 (-5)x = 3(-5) x = -15 Multiply by -5 on both sides to keep the equation balanced. To Quiz 2 ** Remember: Negative times a positive = negative

-2x = -10 -2 -2 x = 5 More examples The inverse operation of MULTIPLICATION is DIVISION, so we divide by -2. -2x = -10 -2 -2 x = 5 Divide by -2 on both sides to keep the equation balanced. To Quiz 2 ** Remember: Negative times a negative = positive