Algebra

ALGEBRA Algebra is finding the unknown It uses letters for numbers Algebraic equation - has a letter - has an equal sign - eg. 5 + y = 8

ALGEBRA one side of the equal sign must equal the other.

Using Variables VARIABLES You can use any letter to represent a variable without changing the meaning of the equation or expression Use a short cut to show multiplication 3n = 3 x n When you solve an equation you find the value of the variable Short cut Wherever there is a pencil that means they have to write out the notes. We have gone over 2(3) and how that can be written many different ways but they will probably forget!!!

2y-7 Coefficient Constant Variable

Reading Equations and Expressions The cup contains an unknown amount of counters Write the expression 1. X + I would like them to write it ALL even the instructions. They have to draw the cup on the paper. Then have them try to figure out what the equation/expression is. The answer will be on the last click of the button. X + 4

X X 2X + 2 X+X + 2 2. + + Write the expression The coefficient is . . . The constant is … 2X + 2 X+X + 2 There is a text box hiding behind the 2x+2 it says x + x+ 2. Have them try to figure out a different way to write it, then the next click has 2x +2

X X + 3 = 7 3. = + Write the equation How many counters must be in the cup to make both sides equal? X + 3 = 7 They should write it all down on their paper. If they are being good the last questions they don’t have to write but just put the answer

Do – Reading Equations and Expressions practice.

BIG IDEAS… so far In ALGEBRA we are trying to find out how much the UNKNOWN is Both sides of the equal sign are in balance Variables represent the part that is unknown in the equation

When we Know what “x” is Equal To When we have a value for the variable and we put it into the equation or expression and solve. Called SUBSTITUTION eg #1. Solve if x = 5 x + 8 = Write the equation down Substitute the value in for the variable 5 + 8 = 5 + 8 = 13 Solve – Find the answer

Ratio Tables We can use a RATIO TABLE to solve equations when we know the value of “x” eg. 5 + x = Input (x) Output (Answer) 1 6 5 + x = 20 2 5 1 6 10 25 7 2 7 5 10 20 25

eg. 2x + 1 = 2 x + 1 = (4) (2) (3) (1) 3 5 7 9 1 3 2 5 3 7 4 9 BEDMAS Multiply Input (x) Output (Answer) 1 3 2 x + 1 = (4) (2) (3) (1) 3 5 7 9 2 5 BEDMAS 3 7 4 9

Do – Substitution Practice.

X – 1 = 3 x What is the equation? x Modeling Algebra -1 1 PRESERVATION OF EQUALITY x -1 1 1 1 What is the equation? X – 1 = 3

What is the equation? 3X + 7 = -6

What is the equation? X - 3 = 3

What is the equation? -3 = 2x - 2

When we do not know the value of “x” What is the equation? X + 1 = 2

The Equality UNBALANCED Goal – Get “x” by itself What happens when we move ? x 1 1 1 x 1 1 1 The Equality UNBALANCED

BUT We have to do something that keeps the balance AND gets “x” by itself 1 -1 x x 1 -1 1 1 X + 0 What can you do to +1 that will leave “x” by itself? What can we do to this side to balance it? WHAT YOU DO TO ONE SIDE YOU MUST DO TO THE OTHER We want X + 0 on one side. What can we do to balance the scale? x 1 -1

How much is “x” ? x 1 -1 X = 1

Remember what you do to one side you must do to the other What is the equation? We want x alone – What do we have to do? 1 1 x -1 1 1 1 1 1 1 1 1 x + 0 Want this to equal zero x = 2 X -5= -3 Remember what you do to one side you must do to the other

Modeling Algebra – Finding “x” Goal – - to get “x” alone on one side of the equal sign - What you do to one side of the equal sign you must do to the other

Do Modeling Algebra: Finding “x”