one-step addition/subtraction equations Today’s Lesson: What: one-step addition/subtraction equations Why: . . . so I can explore the meaning of an equation through an equation modeling lab.

How is the Inverse Property of Addition used when solving an equation?

In your own words, describe the Golden Rule of Algebra.

PART ONE: MODELING EQUATIONS

YES! Both sides equal 8 so they are balanced! Think about an equation. Is this a true equation? 3 + 5 = 4 + 4 3 + 5 4 + 4 8 8 YES! Both sides equal 8 so they are balanced!

3 + 2 1 + 3 5 4 3 + 2 = 1 + 3 Is this a true equation? NO! 5 is “heavier” than 4!

What does “x” have to equal in order for the scale to stay balanced? 5 + 5 10 10 x = 2 because 8 + 2 = 10!

Modeling Equations Lab In this lab, we will use algebra tiles in order to model the process of solving equations! Here are the tile pieces we will use . . .

Example: x + (-2) = 3 To solve the above equation, we will isolate “x”. To do this, we need to get rid of the 2 negative tiles that are with “x”. How can we get rid of the 2 negatives? What is the additive inverse (opposite) of -2? So, we will add two positives to BOTH sides of the equation because it needs to STAY BALANCED!! Watch . . . Once the zero pairs are removed, the tiles left are the answer . . . By making zero pairs! +2 x = 5

Let’s do #1 together . . . 2 2 + 3 = 5 Add 3 neg. to both sides. Left: 3 and Right: 3 2 2 + 3 = 5

Change Subtraction to Addition! #2 is subtraction . . . Change Subtraction to Addition! Add 2 pos. to both sides. Left: 2 and Right: 0 x = 7 7 - 2 = 5

Your Turn . . . You will have approximately 8 minutes to finish lab on your own. Ask questions if you have them! We will go over discussion questions together (but answer them on your own first). Tip: Change all SUBTRACTION equations into their ADDITION form (Draw a line, change the sign)!

PART TWO: Solving Equations WITHOUT models!

Solving Equations: GOAL: To get the variable _____________ (“isolating” the variable)!! RULE: What you do to one side of the equals (=) sign, you MUST do to ________________________ (Golden Rule of Algebra”)! by itself the other side

We have to get “x” by itself! Addition Equations: Example: x + 2 = -2 What number is with “x”? We have to get “x” by itself! Paper/Pencil Method: x + 2 = -2 +(-2) +(-2) x = -4

TOGETHER (paper/ pencil method only): 1) x + 40 = -11 x = -51 2) -25 = x + (-75) x = 50

Your turn: 3) -28 + x = -3 x = 25

Change to ADDITION FIRST! x - 3 = -2 Paper/Pencil Method: Subtraction Equations: Example: Change to ADDITION FIRST! x - 3 = -2 + 3 + 3 x = 1

TOGETHER (paper/ pencil method only): 1) x - (-22) = -2 x = -24 2) -3 = x - 34 x = 31

Your turn: 3) x - 64 = 30 x = 94

WRAP IT UP/SUMMARY: How is the inverse property of addition used when solving an equation? In your own words, describe the Golden Rule of Algebra.

END OF LESSON