Algebra I 2011-2012

Lesson # 1 – 1: Using Variables
Define and give an example of the following
Variable:______________________________________
Expression: ____________________________________
Equation:______________________________________
Key words for writing expressions:
Addition Subtraction Multiplication Division
Certain terms are clues that we need to switch the order that the terms are given to us in a word problem. We call these terms _______________. Star (*) the switches listed above
Example 1: Writing an Algebraic Expression
Write an algebraic expression for each phrase. a. Seven more than a number ‘n’ __________ b. The difference of a number
, ‘n’, and seven
__________ c. The product of seven and a number, ‘n’ d.
The quotient of a number,’n’, and seven e. The quotient of 4.2 and a number, ‘c’ f. A number,’t’, minus 15
__________
__________
__________
__________ g. *five less than a number, x h. *Twelve subtracted from a number, b
__________
__________ i. *A number, n, added to ten __________

Example 2: Writing an Algebraic Expression
Define a variable and write an algebraic expression for each phrase. a. Two times a number plus five
Define the variable: _____________________
Write the expression: _____________________ b. Seven less than three times a number
Define the variable: _____________________
Write the expression: _____________________ c. Nine less than a number
Define the variable: _____________________
Write the expression: _____________________ d. The sum of twice a number and 31
Define the variable: _____________________
Write the expression: _____________________
Example 3: Writing an equation
What does the word “is” suggest? _______________________
Track One Media sells all CDs for $12 each. Which equation best represents the cost c of a given number of n CDs? a. 12 + c = n b. n + 12 = c c. 12c = n d. c =12n
Relate: _____________ is _______ times ________________
Define: Let n = _______________________
Let c = _______________________
Write: ___________________

a. Suppose the manager at Track One Media raises the price of each SD to $15. Rewrite the equation to now find the cost of n CDs. b. Suppose the manager at Track One Media uses the equation c = 10.99
n What could this represent?
Example 4: Real World Problem Solving
Write an equation for the data in the table
1. Relate: ________ equals $20.00 minus
________
Cost of
Purchase
Change From
$20
20.00 $0
$19.00 $1.00
$17.50 $2.50
Define: Let c =
___________________________
$11.59 $8.41
Let a = ___________________________
Write: ___________________
2.Fill in the table and write an equation
Relate: ___________= _______/__
Define: Let e = ____________
Let s = ____________
Write: ___________________
$
$ Earned
$
$ Saved
$ $
$
$
$
$

Lesson 2-5 : Properties of Numbers
Properties of Real Numbers
Commutative Property of Addition/Multiplication a + b = b + a a
•b = b•a
Ex. 2 + 3 = 3 + 2 Ex. 2 •3=3•2
Associative Property of Addition/Multiplication
(a + b) + c = a + (b + c)
(a • b)•c = a•(b •c)
Distributive Property
Ex.
(2 + 3) + 4 = 2 + (3 + 4)
Ex.(2 •3)•4 = 2•(3•4) a(b + c)= ab + ac a(b
– c)= ab – ac
Ex. 2(3 + 4) = 2 •3 + 2•4
Ex. 2(3
– 4) = 2•3 - 2•4
Example 1: Identifying Properties
Name the property each illustrates. a. 9 + 7 = 7 + 9 b. (d

4)

3 = d

(4

3) c. (3+4) + 7 = 7 + (3 + 4) d. 6(a + b) = 6a + 6b e. (2

3)5 = 2(3

5) f. (-3 + 4) + 5 = -3 + (4 + 5) g. (3

8)0 = 3(8

0) h. 2(15 + 4)= 30 + 8 i. np=pn j. (p + q) + r = q + (p + r)
_________________
_________________
_________________
_________________
_________________
_________________
_________________
_________________
_________________
_________________

Example 3: Justifying steps
Simplify each expression and justify each step using a property or a basic operation. a. -4b + 9 + b
Steps
____________________
____________________
____________________
____________________
Reasons
____________________
____________________
____________________
____________________ b. 7z – 5(3 + z)
Steps
____________________
____________________
____________________
____________________
____________________
____________________
Reasons
____________________
____________________
____________________
____________________
____________________
____________________ c. 5a + 6 + a
Steps
____________________
____________________
____________________ d. 2(3t – 1) + 2
Reasons
____________________
____________________
____________________
Steps
____________________
____________________
____________________
____________________
Reasons
____________________
____________________
____________________
____________________

Lesson 2-4: Distributive Property
Define
Term: ________________________________________
Constant:_____________________________________
Coefficient:____________________________________
Like Terms: ____________________________________
Distributive Property (Pass it out)
For every real number a,b,and c. a(b + c) = ab + ac (b + c)a = ba + ca a(b – c) = ab – ac (b – c)a = ba – ca
Examples 5(20 + 6) = 5(20) + 5(6)
9(30-2) = 9(30) – 9(2)
(20 + 6)5 = 20(5) + 6(5)
(30 – 2)9 = 30(9) – 2(9)
Example 3: Simplifying an Expression
* an Algebraic expression in simplest form has no grouping symbols (parentheses)
Simplify each expression using the Distributive Property a. 2(5x + 3) b. (3b – 2)(1/3)

c. 2(3 – 7t) d. (0.4 + 1.1c) (3)
Example 4: Using the Multiplication Property of -1
To simplify
–(6x + 4) rewrite it as -1(6x + 4) and use the
Multiplication property of -1 and the distributive property to simplify
Simplify –(6x + 4) a. –(2x + 1) b. (3 – 8a) (-1)
Example 5: Combining Like terms (shape it up)
Examples of like terms: _______________________________
Examples of not like terms:_____________________________ a. 3x 2 + 5x 2 ____________________________ b. -5c + c ____________________________ c. 7y + 6y ____________________________ d. 3t – t ____________________________ e. -9w 3 – 3w 3 ____________________________ f. 8d + d ____________________________ g. 3t + 4t 2 – 2t 2 + 7t ____________________________ h. 4xy + 3y 2 – 2xy – 5 ____________________________

These phrases include two different operations so we must represent both of those operations in our expression. This represents the distributive property in word form.
“times the sum”, “times the difference”, times the quantity” a. Four times the sum of a number and 5 _________ b.Two times the difference of a number and 16 _________ c.Three times the quantity of a number added to 12 _________ d. 5 times the quantity of a number minus 10 _________

Define:
Sequence: ____________________________________
Term: ________________________________________
Inductive Reasoning: ____________________________
Example 1: Using Inductive Reasoning
Use Inductive reasoning to describe each pattern. Then find the next two numbers. a.
2, 5, 8, 11… b.
2, 4, 8, 16… c.
1, 4, 9, 16… d.
9, 15, 21, 27…

Example 2: Using your calculator for multiple choice sequences
You can use the y= button on your calculator to help you determine the correct choice for a function representing a sequence.
A.
Which of the following function represents the sequence below?
{ 10, 12, 14, 16…}
First, build a table. The x variable represents the _________, and the y variable is the _______________.
X Y
Then check to see which function has a matching table set of values on the calculator. a.
F(x) = 3x + 7 b. F(x)= -2x + 12 c. F(x)= 2x + 8 d. F(x)=x + 9
What would be the value of f(8)= ________
What would the value of x if f(x)= 20? ____________
What would be the 11 th term in this sequence? __________

B.
Which expression best represents the following pattern?
X Y a.
2x -1 b.
3x c.
x 2 – x + 1 d.
x 2
What would f(6) = ___________
Draw the next pattern:
How many blocks would be in the pattern for the 15 th term?

Lesson # 3 –1 : Solving Two – Step Equations
Define
Review: Order of Operations
Steps to Solve an Equation
1. Distribute
2. Combine like Terms
3. Letters to the Left and in
Front
4. What’s happening
5. Unwrap the steps
6. Check your answer using substitution
When we solve an equation we must look at the variable, decide what is happening to that variable using the order of operations, and then unwrap those steps.
Example 1: Solving a Two-Step Equation m
Solve: 10 = + 2 Check:
Solve: 7 = 2y – 3 Check:

Solve: -x + 15 = 12 Check:
Example 2: Real World Problem Solving a. A music store sells a copy of a deluxe electric guitar for $295. This is $30 more than 1/3 the cost of the electric guitar it is modeled after. What is the cost of the original deluxe electric guitar?
Relate:_____________ is _____ more than ____( _____________)
Define: Let c = _____________________________
Write: ____________________________________
Solve: Check: b. Suppose the Panther’s baseball team scored 5 runs Saturday’s game.this was four more than ½ the runs scored by the Lions’ team. How many runs did the Lions’ team score?
Relate: ____________ is ___ more than ___ (____________)
Define: Let L = ____________________
Write: ___________________________
Solve: Check:

Example 3: Writing a Function
In a catalog, tulips cost $0.75 each and shipping costs are $3.00. Write a rule that describes the amount of $ spent as a function of the number of tulip bulbs ordered.Then determine the greatest number of bulbs you can order for $14.
Relate: _______ = ______ ●_________ + ___________
Define: Let a = _________________
Write:___________________
Let b = _________________
If I can only spend $14, I need to substitute that number in for which variable and solve? ____________
Solve: Reasonable?: a. Suppose you have $25 to spend on tulips. What is the greatest number of bulbs you can order? b. Mrs. Simmons works at a furniture store. Her base salary is $125 a week plus 1/12 of her sales. Write a rule that describes her total weekly salary as a function of her sales. Then find the amount of her sales if her total weekly salary was $225.
Relate: _________ = ___________ plus _____ ( _____________)
Define: Let s = ___________________
Let p = ___________________
Write:___________________
If $225 is her pay, which variable do I need to substitute it for and solve?
________
Solve: Reasonable?: