I. The Basics of Polygons

A. Finding Perimeter

B. Finding Area

1. Recognizing an Altitude

C. Finding Circumference

D. Area of a shaded portion of a figure.

E. Use formulas to calculate volume and surface area of rectangular solids and

cylinders.

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

III. Variables and Expressions

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

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

IV. Factoring

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.

V. Linear Equations and Inequalities and Quadratic Equations

A. Evaluating linear expressions and solving linear and nonlinear equations

B. Evaluating quadratic expressions and solving quadratic equations algebraically

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.

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 using variables

** D. Systems of Equations – Algebraic Solutions ONLY

1. Linear – Linear

2. Linear – Nonlinear

** If time allows this item will be discussed in the first year, otherwise it will be covered in detailed in year two.