Essential Questions: Algebra I
1.1.3 Evaluating Algebraic Expressions
1.) What choices should you make from the mastery choice page on LL?
2.) What is the difference between an expression and an equation?
3.) What does “evaluate the expression” mean to do?
1.l.4 Introduction to the Number Line
1.) How many subsets of the real number system are there?
2.) How many ways can we compare numbers in mathematics and what are those
1.1.5 Absolute Value
1.) What does absolute value represent?
2.) What’s special about absolute value?
1.1.8 Commutative and Associative Properties
1.) What is a quick and easy way to tell the difference between the commutative
and associative properties?
1.1.9 Distributive Property
1.) Why do we need the distributive property in mathematics?
PA #1: Practice Time vs. Performance
1.) What is the purpose of a scatter plot?
2.) What do you have to decide before you can create a scatter plot?
1.2.9 Unary Operation: Exponentiation
1.) What is the difference between 5 4 and ( 5) 4 ?
1.2.10 Order of Operations
1.) What mnemonic device do we use to help remember the order of operations
and what does each letter in it represent?
1.3.2 Writing Equations
1.) When defining the variable, can you let the same variable represent two
different numbers? Why or why not?
1.3.4 Combining Like Terms
1.) What are like terms?
2.) What property allows us to combine like terms?
1.3.5 Solving Equations Using the Addition Property of Equality
1.) What does “isolate the variable” mean to do?
2.) How do you “undo” an operation?
3.) What is the first step to solving x 25 12 ? What will the answer be?
1.3.6 Solving Equations Using the Multiplication Property of Equality
1.) How do you know which operation to use to solve a one-step equation?
(when do you add, when do you subtract, when do you multiply, when do you
divide, when do you multiply by the reciprocal?)
1.3.13 Solving Equations Using Two Steps
1.) Which operation do you “undo” first when solving a two step equation?
2.) What is meant by “isolate the variable”?
1.3.14 Solving Equations Using Three Steps
1.) What steps do you follow when you solve equations with variables on both
1.3.15 Solving Equations with Four Steps
1.) How is solving two-step, three-step, and four-step equations related? (Give
and example of each type and solve each example)
1.3.16 Special Cases and Applications: Equations
1.) How can you tell if an equation has one solution, no solution, or infinitely
1.3.8 Absolute Value Equations
1.) What is absolute value?
2.) How is solving an absolute value equation different from solving a regular
3.) When will the solution to an absolute value equation be null or empty set?
1.3.9 Ratio and Proportion
1.) What is a ratio?
2.) How do you solve a proportion?
3.) How do you know to use a proportion to help you solve a word problem?
1.) What does “percent” mean?
2.) What are the two methods used to solve a percent problem?
3.) What is the formula for percent of change and what is it used for?
Chapter 6: Day 1 (offline)
1.) What is the difference in the Product of Powers and the Power of a Power
Chapter 6: Day 2 (offline)
1.) How is the rule for multiplying monomials and the rule for dividing
2.) How do you make a negative exponent positive?
Chapter 6: Day 3 (offline)
1.) Why is it important to be able to write a number in scientific notation?
2.) How do you decide if the exponent will be positive or negative?
3.) How do you use the calculator to evaluate expressions involving scientific
Chapter 6: Day 4 (offline)
1.) How do you determine the degree of a monomial? Of a polynomial?
2.) What is the degree of a nonzero constant? Why?
3.) Which order are polynomials usually written?
Chapter 6: Day 5 (offline)
1.) How should you study for a math test? Why?
1.9.1 The Cartesian Coordinate System
1.) Why is an ordered pair called an ordered pair?
2.) How would you plot the point (- 3 , 5 ) on the coordinate plane?
1.) What is a relation and what are the five ways you can show a relation? (Give
an example of each one.)
2.) What do the domain and range of a relation represent?
1.) What is the difference between a relation and a function?
2.) When you evaluate a function for a given value, what does your answer tell
you? How should your answer be written?
1.9.4 Equations in Two Variables
1.) How many solutions does an equation in two variables have? Explain in
2.) When you graph a linear equation in two variables, what does the graph look
3.) How can you tell the difference between a nonlinear and a linear equation
from its equation? From its graph?
4.) Are all linear equations also linear functions? Explain.
1.) When you hear the word “slope”, what should you think?
2.) How do you find the slope of a line when given the graph of the line?
3.) How do you find the slope of a line when given two points on the line?
1.) What have you found when you find the x-intercept and the y-intercept?
2.) Is it possible for the x- and y-intercepts to be the same? If so, when?
1.9.7 Graphing Linear Equations
1.) What is slope-intercept form and how do you graph an equation in slope-
2.) What is standard form and how do you graph an equation in standard form?
3.) What does the equation for a vertical line look like? Is it a function? Explain.
4.) What does the equation for a horizontal line look like? Is it a function?
1.9.10 Writing Equations in Slope-Intercept Form
1.) What must you know before you can write an equation in slope-intercept
form? If they don’t give you the necessary information, how can you find it?
2.) How can you check your equation when you get it to see if it’s right?
1.9.11 Writing Equations in Standard Form
1.) How do you convert an equation from Slope-Intercept Form into Standard
Form? Explain in detail.
2.) When you check your answer, why is it important to check BOTH equations?
1.9.12 Parallel Lines
1.) When you hear the words “parallel lines”, what should you think?
2.) What steps do you follow to write an equation for a line parallel to a given
line and through a given point?
1.9.13 Perpendicular Lines
1.) What should you think when you hear the words, “perpendicular lines”?
2.) What steps do you follow to write an equation for a line perpendicular to a
given line and through a given point?
1.10.1 Solving Systems of Linear Equations by Graphing
1.) When you graph a system of equations, how do you know where the solution
to the system is?
2.) When you get the solution to a system of equations, how can you check to see
3.) Will you always get one solution for each system of equations? Explain.
1.10.2 Solving Systems of Equations by Substitution
1.) Why is graphing not the best method to use to solve a system of equations?
2.) When is it appropriate to use substitution to solve a system of equations?
3.) How do you know which variable to solve for first? What do you do next?
How do you know when you have solved the system? (Explain the steps used
to solve a system by substitution.)
4.) How can you check your solution to see if it’s right?
1.10.3 Solving Systems of Equations by Addition
1.) When you solve a system of equations (by any method), what are you looking
2.) What has to be true before you can solve a system by addition?
3.) How do you know when you have the system solved?
4.) How can you check your solution?
1.4.1 Introduction to Inequalities
1.) How can you tell the difference between the comparison property of
inequality and the transitive property of inequality?
2.) When you graph an inequality, how do you determine the symbol and
direction of shading?
1.4.2 Writing Inequalities
1.) What are some key phrases that indicate inequality symbols? (give the phrase
and the symbol it indicates)
1.4.3 Multiplication Property of Inequality
1.) When you solve an inequality, when does the inequality sign reverse?
2.) Compare and Contrast solving equations vs. solving inequalities.
1.4.4 Addition Property of Inequality
1.) How is checking an inequality and checking an equation different?
1.7.1/1.7.2 Vocabulary of Monomials / Vocabulary of Polynomials
1.) How do you find the degree of a monomial? Of a polynomial?
2.) How do you determine if a polynomial is linear or quadratic?
1.7.3 Addition and Subtraction of Polynomials
1.) What kind of terms can we add?
2.) What property allows us to add those terms?
3.) How are addition of polynomials and subtraction of polynomials related?
Explain in detail.
1.7.4 Multiplication of a Polynomial by a Monomial
1.) What property do you use to multiply a polynomial by a monomial?
2.) What happens to the exponents of the variables when you multiply?
1.7.5 Multiplication of a Polynomial by a Polynomial
1.) What properties do you use to multiply a polynomial by a polynomial?
Explain how the properties are used to multiply a binomial by a binomial and
also how they’re used to multiply a binomial by a trinomial.
1.7.6 Special Products
1.) What is the FOIL method and when can you use it?
2.) What are the three special products and how can you quickly find each one?
1.7.7 Dividing a Polynomial by a Monomial
1.) How can you tell if a polynomial is divisible by a monomial? Explain in
Factoring (Off line)
1.) When you’re looking for the GCF for a pair of numbers, what do you know
about the GCF?
2.) What is the first step to factoring any sized polynomial?
3.) What has to be true before you can use difference of squares?
4.) What are the factors of D.O.S. called?
5.) How can you tell if a trinomial is a PST?
6.) What do PST’s always factor into?
7.) How do you tell the difference between a 1-step trinomial and a multi-step
8.) How do you eliminate possibilities when the first term has more that one set
9.) Once you get your problem factored, how can you check your answer?
10.) When factoring polynomials with four terms, what must be true about the
parentheses after the first step? What do you do if this is not true?
11.) What must be true before you can use the Zero Product Property?
12.) When using the ZPP, how do you check your solutions?
13.) What property do you use to solve a quadratic equation?
1.11.1 Rational and Irrational Numbers
1.) How can you tell the difference between a rational number and an irrational
1.11.2 Rational Numbers in Decimal Form
1.) What steps do you follow to convert a repeating decimal to fractional form?
1.11.5 Rational Square Roots
1.) When the directions tell you to find the square root of a number, what are they
asking you to find?
2.) What does it mean when the directions ask you for the “principal” square root
of a number?
3.) What is a perfect square?
1.11.7 Simplifying Radicals
1.) When simplifying a radical, how do you know when to use absolute value
symbols around the variable roots? Why do you have to use those absolute
2.) What 3 steps do you follow to rewrite a radical in simplest radical form?
1.11.8 Multiplying Radicals
1.) When multiplying radicals, what steps do you follow? How do you know
when you have the radical in simplest form?
1.11.9 Dividing Radicals: Monomial Divisors
1.) What do you call the method used to eliminate radicals in the denominator of
a fraction? Explain the method in detail.
1.11.10 Adding and Subtracting Radicals
1.) What must be true before you can add or subtract radicals? If that’s not true,
what do you try to do to make it true?
1.13.1 Simplifying Rational Expressions
1.) What steps do you follow to simplify a rational expression? Explain each step
and give an example.
2.) Can a binomial cancel out a monomial? Why or why not?
1.13.2 Multiplying Rational Expressions
1.) When multiplying rational expressions, the first step you should complete is
to factor the numerator and the denominator of each expression completely.
Why is it important to factor each part of the expression first? Explain
2.) Can a binomial cancel out a monomial? Why or why not?
1.13.3 Dividing Rational Expressions
1.) How are multiplying rational expressions and dividing rational expressions
related? Explain in detail.
1.13.4 Adding and Subtracting Rational Expressions
1.) What MUST be true before you can add or subtract rational expressions?
x7 3x 7
2.) How can you solve the following?