Camden Hills Regional High School

Home of the Windjammers

Honors Algebra I
Math
 
Description:

This is a class for students who have not done much work with variables and variable expressions in the 8th grade but are motivated and interested in beginning as 9th graders.  This is a fast paced course which will cover topics including: simplifying expressions, solving equations and inequalities, solving linear systems by multiple methods, a complete study of exponents and exponential functions, polynomial, radiacals, basic trigonometry and quadratics, factoring, and solving quadratics.  Steady work will be required.

 
 
Outcomes:

CCSS Standards Assessed  (***Graduation Requirement)

***A.SSE.1.a      Interpret parts of an expression, such as terms, factors, and coefficients.

  1. Variables and Expressions

Vocabulary

Writing Expressions with multiple operations from phrases

Writing Phrases from Expressions

Writing a Rule to describe a pattern

N.RN.3             Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and irrational number is irrational…

  1.  Order of Operations and Evaluating Expressions

Exponents

Order of Operations

Evaluating/Interpreting Expressions

  1. Real Numbers and the Number Line

Analyze/Simplify radicals

Classify, compare, and graph real numbers

  1. Properties of Real Numbers

Identify and Use properties of real numbers

Operations with Real Numbers

Distributive Property

A.CED.1  Create equations…in one variable and use them to solve problems.  Include equations arising from linear…functions.

  1. Solving equations

Solving one-step equations

Solving two-step equations

Solving multi-step equations 

A.CED.4   Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations…

A.REI.3  Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 

  1. Literal Equations and Formulas

Rewriting and Using literal equations and formulas

  1. Solving Proportions

Proportions and Similar Figures

Percents as Proportions

  1. Solving Inequalities

Write, graph, and identify solutions to inequalities

Sets and Set Theory 

 F.IF.1  Understand that a function from one set…to another set…assigns to each element of the domain exactly one element of the range…

  1. Relations Vs. Functions

Identifying Functions in their Varying Forms

Linear and Non Linear Functions 

F.IF.5  Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes…

  1. Graphing and Interpreting Functions

Graphing a Function Rule (Linear and Non-linear)

Continuous Vs. Discreet          

 F.LE.1  Recognize situations in which on e quantity changes at a constant rate per unit interval relative to another.

  1. Finding rate of change/slope of a linear relationship

Finding/interpreting slope of line

Finding slope from chart

Finding slope from coordinates

A.CED.2  Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate plane… 

  1. Direct and Inverse Variation

Interpreting, solving and graphing direct and inverse relationships. 

F.IF.7 (Introduction (non mastery)) Graph linear…functions and show intercepts….

F.LE.2  Construct linear…function…given a graph, a description of a relationship, or two input-output pairs…

  1. Writing/Graphing Forms of Linear Equations

Slope Intercept Form

Point-Slope Form

Standard Form

A.REI.6  Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

  1. Solving Systems of Equations

Solving by Graphing

Solving by Substitution

Solving by Elimination

  1. Applications of Systems of Equations 

A.REI.12  Graph the solutions to linear inequalities in two variables as a half-plane and graph the solution set to a system of inequalities, showing the intersection of the corresponding half-planes.

  1. Graphing and Solving Systems of Inequalities

N.RN.1  Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values…

  1. Properties of Exponents

Product of Powers

Quotient of Powers

Power-to-a Power

Zero/Negative Powers

Rational Exponents/Radicals

F.IF.7.e  Graph exponential…functions, showing intercepts and end behavior…

  1. Exponential Functions

Graphing Exponential Functions

Solving Simple Exponential Functions

A.APR.1  Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 

  1. Operations on polynomials

Vocabulary

Adding/Subtracting Polynomials

Multiplying Polynomials (Distribution, FOIL, special cases)

Factoring Polynomials

GCF

Factoring Quadratics a=1

Factoring Quadratics a>1

            Special Cases

            Diff of Squares

            Sum/Diff of Cubes

F.IF.7.a  (Final(mastery)) Graph…quadratic functions and show intercepts, maxima, and minima.

             1.  Quadratic Graphs and Properties

Maxima/minima/vertex/intercepts/Axis of Symmetry

A.APR.3  Identify zeros of polynomials (quadratic) when suitable factorization is available, and use the zeros to construct a rough graph of the function. 

            1.  Zero-Product Property w/vertex formula 

A.REI.4.b  Solve quadratic equations by inspection…by factoring…

A.REI.4.a  Use the method of completing the square to transform any quadratic equation in x into and equation in the form

            1.  Solving using Radicals

            2.  Completing the Square Method

            3.  Using the Quadratic Formula