Introduction to Algebra TopicsLast Update: May 23, 2011

There may be other topics that we will run across, but these are the ones that I came up with for now.

    Warm Up Topics
  1. exponents: problems from Exponents and Radicals Handout #1-8, 10, 16, 20, 22, 25, 50-52
  2. GCF, LCM of numbers (handouts from Holt book) and factored algebraic expressions (come back to this)
  3. complex fractions
  4. addition of numeric and algebraic simple fractions (no factoring of polynomials needed).
Unit 1
  1. types of numbers: natural, whole, rational, irrational, and real
  2. repeating decimals and other arithmetic topics as needed (check chapter 0 and 1 of Algebra book)
  3. interval notation and solve simple inequalities including some with absolute value and others with negative coefficients on variable
  4. order of operations: plug values into an expression and simplify
  5. solve linear equations
  6. sets: unions, intersections, set builder notation, interval notation
  7. linear inequalities
  8. absolute value and absolute value as a distance
  9. absolute value inequalities
  10. solve simple linear equations and more inequalitiy problems
  11. Compound Inequalities
Unit 2
  1. polynomial expressions and terminology: add, subtract and multiply
  2. divide polynomials
  3. polynomial expressions: factor
  4. introduction to graphing
  5. lines: slope intercept, parallel, perpendicular, graphs
  6. Solve factorable polynomial equations.
  7. graphs of factored polynomial expressions
Unit 3
  1. Roots of numbers, square root, cube root etc.. Rationalize denominators including denominators like: √(2)+3.
  2. complex fractions: add and subtract numeric expressions
  3. complex fractions and add and subtract algebraic fractions
  4. Roots of algebraic expressions.
  5. rational expressions: factor and
  6. revisit complex fractions with things that can be factored and simplified
Unit 4
  1. function notation: domain and range, evaluate at values, read info from a graph as well as from a given equation
  2. solve polynomial equations, and rational equations
  3. solve polynomial and rational inequalities at least graphically
  4. work with linear functions
  5. quadratic functions
  6. polynomial and rational functions and graphs
  7. study systems of equations
  8. application problems:
Unit 5 and beyond
  1. extention of ratio problems to right triangle trig
  2. counting problems
  3. transformations of functions
  4. linear models
  5. quadratic functions in terms of transformations
  6. complex number arithmetic and plots
  7. algebra of functions
  8. inverse functions
  9. piecewise defined functions
  10. Sequences: Recursively and Explicitly defined, Arithmetic, and Geometric