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 ExpressionWrite 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 ExpressionDefine a variable and write an algebraic expression for each phrase.

a. Two times a number plus fiveDefine the variable: _____________________Write the expression: _____________________

b. Seven less than three times a numberDefine the variable: _____________________Write the expression: _____________________

c. Nine less than a numberDefine the variable: _____________________Write the expression: _____________________

d. The sum of twice a number and 31Define 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 = 10.99n What could this represent?

Example 4: Real World Problem SolvingWrite an equation for the data in the

table1. Relate: ________ equals $20.00 minus

________

Define: Let c = ___________________________

Let a = ___________________________Write: ___________________

2.Fill in the table and write an equationRelate: ___________= _______/__Define: Let e = ____________

Let s = ____________

Write: ___________________

Cost of Purchase

Change From $20

20.00 $0$19.00 $1.00$17.50 $2.50$11.59 $8.41

$ Earned $ Saved

$ $$ $$ $$ $

Lesson 2-5 : Properties of Numbers

Example 1: Identifying PropertiesName the property each illustrates.

a. 9 + 7 = 7 + 9 _________________b. (d4) 3 = d(43) _________________c. (3+4) + 7 = 7 + (3 + 4) _________________d. 6(a + b) = 6a + 6b _________________e. (23)5 = 2(35) _________________f. (-3 + 4) + 5 = -3 + (4 + 5) _________________g. (38)0 = 3(80) _________________h. 2(15 + 4)= 30 + 8 _________________i. np=pn _________________j. (p + q) + r = q + (p + r) _________________

Example 3: Justifying steps

Properties of Real Numbers

Commutative Property of Addition/Multiplicationa + b = b + a a•b = b•aEx. 2 + 3 = 3 + 2 Ex. 2•3=3•2

Associative Property of Addition/Multiplication(a + b) + c = a + (b + c) Ex. (2 + 3) + 4 = 2 + (3 + 4) (a • b)•c = a•(b •c) Ex.(2•3)•4 = 2•(3•4)

Distributive Property a(b + c)= ab + aca(b – c)= ab – acEx. 2(3 + 4) = 2•3 + 2•4Ex. 2(3 – 4) = 2•3 - 2•4

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 Reasons____________________ ________________________________________ ________________________________________ ____________________

d. 2(3t – 1) + 2

Steps Reasons____________________ ________________________________________ ________________________________________ ________________________________________ ____________________

Lesson 2-4: Distributive Property

DefineTerm: ________________________________________Constant:_____________________________________Coefficient:____________________________________Like Terms: ____________________________________

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)

Distributive Property (Pass it out)For every real number a,b,and c.

a(b + c) = ab + ac (b + c)a = ba + caa(b – c) = ab – ac (b – c)a = ba – ca

Examples 5(20 + 6) = 5(20) + 5(6) (20 + 6)5 = 20(5) + 6(5)

9(30-2) = 9(30) – 9(2) (30 – 2)9 = 30(9) – 2(9)

c. 2(3 – 7t) d. (0.4 + 1.1c) (3)

Example 4: Using the Multiplication Property of -1To 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. 3x2 + 5x2 ____________________________b. -5c + c ____________________________c. 7y + 6y ____________________________d. 3t – t ____________________________e. -9w3 – 3w3 ____________________________f. 8d + d ____________________________g. 3t + 4t2 – 2t2 + 7t ____________________________h. 4xy + 3y2 – 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 _________

Lesson 5-7: Describing Number PatternsDefine:Sequence: ____________________________________Term: ________________________________________Inductive Reasoning: ____________________________

Example 1: Using Inductive ReasoningUse 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 sequencesYou 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 _______________.

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 11th term in this sequence? __________

X Y

B. Which expression best represents the following pattern?

a. 2x -1b. 3x c. x2 – x + 1d. x2

What would f(6) = ___________

Draw the next pattern:

How many blocks would be in the pattern for the 15th term?

X Y

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Lesson # 3 –1 : Solving Two – Step EquationsDefineVariable___________________________________Solve_____________________________________

Review: Order of OperationsP _______________E _______________M/D _______________A/S _______________

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

Solve: 10 = + 2 Check:

Solve: 7 = 2y – 3 Check:

Steps to Solve an Equation

1. Distribute2. Combine like Terms3. Letters to the Left and in

Front4. What’s happening5. Unwrap the steps6. Check your answer using

substitution

Solve: -x + 15 = 12 Check:

Example 2: Real World Problem Solvinga. 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 FunctionIn 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?: