ALGEBRA I - Semester 1
(Integrated Algebra - Part I Revised August 2008)
I. Variables and Expressions (5 weeks)
A. Basic Operations with Monomials and Polynomials
1. Evaluate monomial and polynomial expressions given a value or values for the variable(s)
2. Multiply and divide monomial expressions with a common base, using the properties of exponents
3. Add, subtract, and multiply monomials and polynomials
4. Divide a polynomial by a monomial
5. Find values of variables for which an algebraic fraction is undefined
6. Multiplying Binomials – FOIL
7. Use formulas to calculate volume and surface area of rectangular solids and cylinders.
8. Percent error calculations.
B. Exponents
1. Rules of Exponents
2. Zero Exponent
3. Negative Exponent
4. Scientific Notation
a. Converting to and from scientific notation
b. Products and quotients using scientific notation
(The Variables and Expressions unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.A12-A.A.15, A.N.4, A.G.1,, A.A.3, A.G.2, A.CM.5, A.RP.6, A.RP.5)
II. Factoring (3 weeks)
A. Factors
1. GCF
2. Trinomials with a leading coefficient of one (after GCF is factored out)
3. Trinomials with a leading coefficient other than 1
4. Difference of Perfect Squares
B. Algebraic Fractions
1. Finding a value(s) for which an algebraic expression is undefined
2. Simplify fractions with polynomials in the numerator and denominator
3. Add and subtract fractional expressions with monomial or like binomial denominators
4. Multiply and divide algebraic fractions, expressing the result in simplest form
Note: Item 3 will be taught but whether or not it will be tested will be at the discretion of the individual teacher. This item is not listed in the NYS Integrated Algebra curriculum, however we feel by teaching both types of factoring problems together, our students will have a better understanding of the material.
(The Factoring unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.A15-A.A.20)
III. Linear Equations and Inequalities and Quadratic Equations (5 weeks)
A. Evaluating linear expressions and solving linear and nonlinear equations
1. Translating from verbal phrasing into mathematical expressions, equations, and inequalities
2. Distinguish the difference between expressions and equations
3. Write algebraic equations/inequalities that represent a situation
4. Analyze and solve linear equations and/or linear inequalities in one variable
5. Determine whether a given value is a solution to a given linear equation or inequality
6. Solve all types of linear equations in one variable
7. Solve literal equations for a given variable
8. Solve linear inequalities in one variable
9. Solve equations involving fractional expressions (resulting in linear equations in one variable)
10. Solve algebraic proportions in one variable (resulting in linear equations in one variable)
11. Solve absolute value equations
B. Evaluating Quadratic Expressions and Solving Quadratic Equations Algebraically
1. Solving Quadratic Equations by applying the zero product property.
2 . Solve algebraic proportions in one variable which result in a quadratic equation.
3. Understand the relationship between the roots of a quadratic equation and the factors of a quadratic expression.
Note: The introduction of the quadratic formula in this unit of study is optional.
Note: The individual teacher may chose to test multiple times within this unit. Whenever possible, the instructor should stress to students the importance of being able to evaluate all expressions, identify and distinguish between the different types of equations, and know the appropriate/best method for solving the linear or quadratic equation.
(The Linear Equations and Inequalities and Quadratic Equations unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.A.1-A.A.6, A.A.21-A.A. 26, A.N.5, A.CM.11, A.A.8, A.A.26, A.A.27, A.A.41, A.A.28, A.R.8, A.G.4, A.G.5, A.G.8-A.G.10, A.A.11, A.G.1)
IV. Applications and Word Problems (3 weeks)
A. Applications of linear equations using word problems (coin, perimeter, consecutive integer, age, motion, etc)
B. Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation.
C. Area Problems
** D. Systems of Equations – Algebraic Solutions ONLY
1. Linear – Linear
2. Linear – Nonlinear
** If time allows this item will be discussed in the first semester, otherwise it will be covered in detailed in semester two.
(The Applications and Word Problems unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 -
Embedded with the semester through the use of warm-up problems, applications of the above material, and review sheets are the topics listed below.
V. Mathematical Representations
A. Set Notation and Venn Diagrams
1. Use set-builder/interval notation to illustrate the elements of a set, given the elements in roster form
2. Finding the complement of a set
3. Finding the Intersection and Union of Sets (no more than three sets)
4. Finite Sets and Infinite Sets – use set-builder/interval notation to illustrate the elements of a set, given the elements in roster form - including graphic representation using inequality graphs
5. Empty Set
6. Subsets
7. Overlapping/Intersecting Sets – graphical and algebraic
8. Disjoint Sets
9. Use Venn diagrams to support a logical argument
B. Properties
1. Identify and apply the properties of real numbers
a. Closure
b. Commutative
c. Associative
d. Distributive
e. Identity
f. Inverse
2. Emphasis on examples and counterexamples
3. Absolute Value
a. Definition
b. Using absolute value to evaluate expressions
(The Mathematical Representations unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.A.29-A.A.31, A.RP.11, A.RP.12, A.CM.2, A.CM.3, A.N.1, A.G.4, A.N.6)
