In 1999, the State of California adopted and mandated standards that affect all public high school students and their teachers.  The Standards set forth the concepts, skills and topics appropriate for students going on to the study of Geometry and Algebra II and are required for high school graduation. 

Originally, the state expected that each student graduating in 2004 or later would pass the California High School Exit Examination in mathematics and complete Algebra I  in order to qualify for graduation. In the past year, these expectations have been "modified" so that the High School Exit Examination requirement does not take effect until 2006 and the Algebra completion requirement does not take effect until 2005.  

My intent is that our class conforms to the Standards: that it is taught in such a way as to adhere to both the spirit and the letter of those Standards.

The following is a summary of the Algebra Standards portion of the Mathematics Framework for California Public Schools.  The following items will be color coded according to which module they are taught in Module A , Module B , Module C, or Module D, or not explicitly taught. Those items not explicitly taught according to the Mastery Mathematics model are included as time allows under current circumstances (see my Commentary on Algebra I at Chaffey High School).

1. Know and use the basic properties (including closure) of the real numbers (including the subsets of integers, rational numbers, and irrational numbers).
2. Understand and know how to take the opposite, find the reciprocal, take a square root, and raise to a fractional power.  Understand and know how to use the rules of exponents.
3. Understand absolute value and how to solve absolute values equations and inequalities.
4. Simplify and solve linear equations and inequalities in one variable.
5. Know how to solve multi-step problems (including word problems), involving linear equations and linear inequalities in one variable. Be able to explain each step.
6. Graph linear equations and find their x-and y-intercepts.  Graph linear inequalities.
7. Be able to tell if a point lies on a line, given the equation of the line.  Find linear equations by using the point-slope formula.
8. Understand how slopes relate in parallel and perpendicular lines.  Find the equation of a line parallel to and perpendicular to a given line through a given point.
9. Solve a system of two linear equations in two variables (by substitution, elimination, and graphing).  Solve a system of inequalities by drawing its graph.
10. Add, subtract, multiply, and divide monomials and polynomials.  Solve problems (including word problems) by using these skills.
11. Be able to factor second- and simple third-degree polynomials using GCF, difference of squares, perfect squares, and grouping methods.
12. Simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to lowest terms.
13. Add, subtract, multiply, and divide rational expressions.  Solve challenging problems using these methods.
14. Be able to solve a quadratic equation by factoring or by completing the square.
15. Be able to solve word problems (including rate problems, percent mixture problems, etc).
16. Know what a relation and a function are, and be able to tell if a given relation is a function.
17. Be able to find the domain and the range of a function (by graph, by set of ordered pairs, or from an equation).
18. Be able to explain why a relation (defined by a graph, by a set of ordered pairs, or by an equation) is a function or not.
19. Know how to use the quadratic formula, and how it comes from "completing the square."
20. Be able to use the quadratic formula to find the roots of quadratic equations.
21. Be able to graph quadratic equations and identify their roots as the x-intercepts of the graph.
22. Be able to tell using the discriminant whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.
23. Solve physical problems (such as motion under gravitational force) using quadratic equations.
24. Use and know simple aspects of logical argument such as the difference between deductive and inductive reasoning, hypothesis and conclusion, and use of counterexamples in proofs.
25. Use properties of the number system to judge the validity of results, to justify procedural steps, and to prove/disprove statements.

Extremely Important: If a student has difficulty with any of the items listed above, it is imperative that they immediately arrange tutoring sessions with Mr. James or another person who is competent with algebra and acquainted with these standards.

You may obtain more information from the California Department of Education's web site for K-12 mathematics standards.

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