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Algebra : Section 1.1
_________________________________________________________________
Vocabulary
Variable:
Algebraic Expression:
Numerical Expression:
Word Phrase
Model
Expression
1.) 32 more than a number
2.)
3.) 8 times a number
4.)
Correct Terminology:
Product: _______________________
Sum: _______________________
Difference: __________________________
Quotient: ______________________
Practice Problems:
1.) The sum of 3 and
product of 5 and X
2.) 9 less than the quotient
of M and 7
1.) X +7
2.) H – 5
3.) the product of 3 and
the quantity sum of 7 and B
x
3( )
2
3.)

Words
Expression
1.) the product of 9 and F
2.) three more than the quotient of B and 7
3.) 10 less than the quantity of the sum of B and 8
4.) The product of 3 and the quantity sum of a number and 2
Examples:
1.) —The county fair is coming into town. It costs $5 to enter and then $1 per ride ticket. Your parents
want to know the total amount of money you will be spending but you really don’t know. To keep them
quiet you decide to give them an algebraic expression that represents the total amount. What is that
expression?
2.) You are stacking a certain number of 4 inch blocks on top of a 3 foot table. Write an expression for the
total height off the ground for any number of blocks.
3.) You are visiting a farm that has a bunch of cows. The owner tells you that one of the cows was born
with 5 legs and all the rest of his cows were normal. What is an expression that represents the number of
the total legs?
4.) John has $5 and a certain number dimes in his pocket. He wants to place the money into 2 bags where
each bag has an equal amount of money.
5.)Steve works at RadioShack selling TVs. He gets paid $50a day and then $10 for every TV he sells. It is
company policy that everyone works with a partner so the commission that is made needs to be split
evenly between the two. What is an expression that represents the amount Steve makes each day.
6.) The sales tax in Flagstaff is about 10%. Write an expression that represents the total cost of an item
including tax.
6.)
Algebra : Section 1.2
__________________________________
Mathematicians are ______________________________, __________________________________,
_________________________.
Multiplication:
or
5+5+5
Power: ____________________________________________________________________
Example:
Simplified:
________________________________________________________________________________________
Examples:
1.)
23


3+3+3+3+3
2.)
2 3
3.)  
3 
(0.2) 4


ORDER OF OPPERATIONS :
EXAMPLES:
1.)
2  3 5
2.)

(6  2)3  2

3.)
(3 (5  2 32 ) 1)  4
Problem Children:
32 1
1.)
2

2.)
32
4.) 10 
3.)(−3)2
3 15


You Try:
1.)
50  (3  2  4)
3
2.)
20  4 2  2(7  4)3


3.)
(2 4  4) 10
22  2

Variable Expressions: X=3 Y = 5 Z= 2
1.)

y 2
2.)

(y  z) 4
3.)

2x 2  3y

4.)
(2x) y  z
2
22  (13  (32  23 )
5.)
4 2  (7  2)
x

Practice:
1.) It is a major misconception that (𝑥 + 2)2 equals 𝑥 2 +22 . Why is this not true?
2.)Use parenthesis so that the following is true. 9+3-2+4 = 6
Algebra: Section 1.3
_________________________________________
Start Thinking: What is a square root?
Vocabulary:
Parts of a Radical:
Square Roots: ____________________________________________________
√64
Examples:
1.) √16
2.) √121
3.) √−9
4
4.) √27
5.) √9
Perfect Squares:
Plotting on a Number Line:
1.) √10
2.) √78
3
3.) Arrange the following numbers on a number line. √5, − 2 , 0.2, √16
4.)List the following numbers from least to greatest.
1
√11, 3, 0.3, 3 , −18
Real World:
1.) You are going to create a square concrete pad. The only requirement is that the area must be
115 sq. ft.. What is the approximate length of one of the sides in feet and inches.
Set: _______________________________________________
Subset: ____________________________________________
Element:____________________________________________
Classification of Numbers:
Rational Numbers: ____________________________________________
Examples
Natural Numbers: ____________________________________________
Whole Numbers: ______________________________________________
Integers: __________________________________________________
Irrational Numbers: ___________________________________________
Real Numbers: ________________________________________________
Create the Diagram to describe the relationship between the categories of numbers.
Easy Example
Types of Numbers
Practice problems:
Determine which type of numbers each of the following is.
R = real I= Integers W =Whole N = Natural Ir= irrational Ra= Rational
1.) √25,
2.) .045
3.) √10
4.) −√16
5.) 4.52389……
Thought Provoking:
Is there a smallest positive rational number? Why or why not?
You Try:
Classify the following numbers as Rational/ Irrational/ Natural/Integer/Real/ and or Whole.
1.)√25
2.)5.326
3.) √28
4.)-8
5.)1.828282…
Algebra: Section 1.4
_________________________________________
John is trying to find the sum of the following numbers. He says that he just can’t do it because
he is bad at adding decimals. How could you explain to him that the problem is actually very easy
to do in his head?
Problem: 7.75 + 4.4 + 2.25
Properties:
Commutative property: ________________________________________________
Associative property: __________________________________________________
Identity Property:_____________ ________________________________________
Zero Property of Multiplication: ________________________________________
Multiplication Property of -1: _____________________________________________
Practice: Explain which property is being shown.
1.) (9 ∙ 𝑛) ∙ 5 = 9 ∙ (𝑛 ∙ 5)
2.)𝛽 ∙ 0 = 0
4.) 3(5n)=15n
5.) ∆ + 𝛾 = 𝛾 + ∆
3.) (10 + 𝑏) + 𝑚 = 10 + (𝑚 + 𝑏)
6.) (4+7b)+3 = (3+4) +7b
Practice:
1.) Andy says that he is so smart and that he has come up with another property. He says that
𝑎 ∙ 𝑏 = 𝑎 + 𝑏. Is his reasoning correct? How do you know this?
2.) Determine the properties that justify each step.
6𝑥𝑦
𝑦
=
6𝑥 ∙ 𝑦
1∙𝑦
=
6𝑥 𝑦
∙
1 𝑦
=
6𝑥
∙1 =
1
6𝑥
Algebra Section 1.5
_______________________________________________________________
Review of Fractions and Decimals
Fractions:
Adding
Subtracting
Multiplying
Dividing
Subtracting
Multiplying
Dividing
Decimals:
Adding
FLAVORS OF ADDING AND SUBTRACTING:
1.)The sum of a Positive and a Negative
-Rule:
a.) 21 +(– 53)
b.) 19+ (- 7)
c.) 2.1 +(– 4.5)
d.)

1
4
 ( )
3
5
2.) The Difference of Positives
-Rule:
a.) 23- 17
b.) 7- 81
c.) 5.7 – 20.2
d.)
1 3

4 2

3.) THE FUNKY ONES
- Positive minus a Negative
-Negative minus a negative
- Negative minus a Positive
Rule:
a.) 10 – (-3)
b.) (-9) – 10
c.) (-6) – (-10)
1.) -10 – 9
2.) 20 – 54
3.) -9 – (-6)
4.) 3.2 – 9.7
5.)
Practice:

2
1
 ( )
3
6
6.) 10.3 – 1.9
Vocabulary:
Absolute Values: ________________________________________________________________________________
Examples:
1.) 3
2.) 2  5


3.) 9  3

Critical Thinking:
1) A scuba diver dives 25 ft to photograph brain coral and then rises 16 ft to travel over a ridge before diving
47 ft to survey the base of the reef. Then the diver rises 29 ft to see an underwater cavern. What is the
location of the cavern in relation to sea level?
2) Atoms contain particles called protons and electrons. Each proton has a charge of +1 and each electron
has a charge of -1. A certain sulfur ion has 18 electrons and 16 protons. The charge on an ion is the sum
of the charges of its protons and electrons. What is the sulfur ion’s charge?
3) Without calculating, tell which is greater: the sum of -227 and 319 OR the sum of 227 and -319?
EXPLAIN.
4) If R is the opposite of T on a number line, which of the points has the greatest absolute value? Why?
5) Is |a - b| always equal to |b - a|? Use examples to explain your answer.
Algebra Section 1.6
______________________________________________________
Properties of Products and Quotients:
-The Product or Quotient of numbers with the same sign will be ______________________________________.
-The Product or Quotient of Numbers with opposite signs will be _____________________________________.
Two Ways To Remember the Properties
GOOD AND BAD PEOPLE
TRIANGLE
Concept Practice: Assume that making money is considered a positive and losing money is considered
a negative. Also assume that it is possible to go back in time. For each situation
explain if the result will be positive or negative and explain your mathematical
reasoning.
EX 1: You end up losing several hands of poker all in a row.
Ex 2: You go back in time and undo the loss of several hands of poker.
EX 3: You go back in time and undo several won hands of poker.
EX 4:You end up winning several hands of poker.
Practice:
2 1
2.)   
5 3
1.) 2.34 (1.2)


3.) 10.8  (1.2)

Practice:
2
1.)  (0.8)
5
2.)

1 2 3
 
8 3 4
3
2
3.)1 4 ÷ 5

𝑋
3
2
3.)𝑌 where x = 4 and y = 5
2 3
3.)(− 3)
Application: Use the recipe below to answer the questions.
1.) How many cups of cheese to you
need if you are going to triple
the recipe?
2.)You only have 5 peperoni slices.
What will you have to do to the recipe?
How much diced tomatoes will
you need?
3.)You have a 16oz bag of chips and you want to use all of them. If you adjust your recipe so that you
can use all of them….
a.) How much cheese will you need?
b.)How many grams of fat will there be?
b.) How much diced tomatoes will you need?
Algebra Section 1.7
____________________________________________________________
Essential Understanding:
Distributive Property:
***A different view of the distributive property
VISUAL
ALGEBRAIC
2 (3X + 4)
PRACTICE:
1.) 3 (5x +2)
4.) – (5x+2)
2.) -5 (-4x +1)
3.) 8 (x – 3 )
3
5.) – –4 (-2x – 3)
Vocabulary:
Term: __________________________________________________________________________________
Constant: ______________________________________________________________________________
Coefficient: ______________________________________________________________________________
Like Terms: ____________________________________________________________________________
PRACTICE:
Determine the number of terms, what the coefficient is of each term, and what the constant is.
2
2.) x yz
1.) 3xy  4 x 1

3
3.) 3x  5  6x


Combining the two:
1.) 3(2x 1)  7x

2.) 2(5x 1)  3(2x  7)

3.) 2x  5(x  2)

4.) 7x  (3x  2)

YOUR TURN!!!!
1.) 3x  7(5x  4)

2.) 6(3x 1)  2(3x  4)


TRY TO MULTIPLY THE FOLLOWING IN YOUR HEAD.
1.) 16 9

2.) 15 11

3.) Rewrite the following using the distributive property.
3x  5
2

3.) 7x  (5x  2)
Algebra Section 1.9
______________________________________________________
Start Thinking: Tim’s family decides to go on a cross-country road trip. It is Tim’s job to document the mileage as
they go. He finds that on day one they were 210 miles from home. The next he sees that they are 420 miles from
home. The following day he sees that they are 630 miles from home. Since he had Mr. Gallagher the year before
he sees a pattern. What is that pattern?
Concept:
Three different methods of representing a relationship between two different variables are through
__________________________________, __________________________________,
____________________________.
Setting up an equation:
Practice problems:
1.) John was born in 2001 on September 20th and his brother Todd was also born the same day but in 2003.
Write an equation for John’s age in relation to Todd’s.
2.) Floppy the rabbit is known for having 3 bunnies each season. Write an equation that relates the numbers of
seasons and number of total bunnies.
3.) Peter ate deep fried twinkies, dip and dots, a turkey leg and 3 Indian fry breads. As a result he threw up 2
times each time he went on the zipper. Write an equation that represents the relationship between the number
of times he rode the zipper and the number of times he threw up.
EQUATIONS
True
False
Open
Solution: _________________________________________________________________________________
SINGLE VARIABLE:
1.)10 =– 2 – x
1
2.)2 𝑥 = 6
-12
4.) 1.32 ∙ 𝑥 = 0.792
2
5
𝟏
3.) 3 + 𝑥 = 12
12
1
42
𝟓
3
15
𝟔
5.) 2 ÷ 𝑥 =
0.7
𝟒
Practice: Determine if the following are solutions.
1.) y = 3x
(6, 18)
4.) y 


2.) y = -2x +5
3
x
4
(1, 7)
2 3
( , )
5 10
3.) y = 0.25x
5.) y 

1
2
x
4
5

(16, 4)
(2,
9
)
10
Tables/ Graphs:
1.)John was born in 2001 on September 20th and his brother Todd was
also born the same day but in 2003. Write an equation for John’s age in
relation to Todd’s.
2.) Floppy the rabbit is known for having 3 bunnies each season. Write an
equation that relates the numbers of seasons and number of total bunnies.
Using Tables:
1.) The table shows the number of words a secretary types in terms of minutes. How
words can he type in 60 minutes?
2.) The table shows the cost of staying at a certain hotel. How much does 30 nights cost?
many
Algebra Section 1.9B
_________________________________________________
1.) Amy said that she makes $25 per day and $1.25 for every doughnut she sells. She then starts telling you a
story about how one day she made $140. You don’t believe her. She says that she is positive that she did because
she remembers it very clearly that she sold 85 doughnuts. You decide to use your Algebra 1 skills
to test her story.
Step 1: Write in words a way to express how much total money she makes per day
when selling a certain number of doughnuts.
Step 2: Convert the words into an equation using the variables x and y.
Step 3: Determine what her story of making $140 and selling 85 doughnuts looks like
as a ordered pair (x,y).
Step 4: Determine if the ordered pair is a solution to the equation. What does your
answer tell you about her story?
3.) Bob decides to open a business selling chairs. He has to buy tools before he can start the business.
The cost of the tools is $600. He is able to sell chairs for a profit of $30 a piece after accounting for the
cost of the wood and screws.
a.) Write a word phrase that describes the total amount he will make accounting for the fact that there
is a start up fee (aka. Cost of tools).
b.) What is an equation that models the words in part a.) using the variables x and y.
c.) How much will he make after selling 100 chairs?
d.) He says that he is going to sell 50 chairs and will make $900. Is this true?