Course Topics: Algebra 1: 2008-09

KEY: Level 1: Black Font (CP/Honors Need to know)

Level 2: Green Font (CP Nice to know/Honors Need to know)

Level 3: Red Font (Honors Nice to know)

Unit 1Preparing for Algebra: Review and Readiness6/7 wk total

REVIEW - things you should know, either formally or intuitively

  • Definitions (.5/1 week)
  • What is Algebra?
  • Commonly used terms: sum, product, quotient, difference, distributive, associative, commutative, evaluate, solve, simplify, expression, terms, like terms, degree, coefficient, equation, prime, composite, perfect square, inverse (opposite vs. reciprocal)
  • Sets of numbers we commonly refer to: integer, real, natural, whole,rational (we will not use imaginary)
  • Situations mathematicians dislike: division by zero and square root of negatives
  • Review of required skills(1/2 weeks)
  • Order of Operations (GEORGE)
  • Plugging-in and evaluating algebraic expressions
  • Distributive Property (can be done only to operation one level lower based on GEORGE (OLL))
  • Combining Like Terms
  • Solving equations using a flow chart and backtracking

* Test on REVIEW topics at this point *

READINESS - filling in some potential gaps before we really begin

  • Rules of Integer Exponents(2/1 weeks)
  • Zero Power, first power, product of powers, quotient of powers, power to a power, power of a product, power of a quotient(OLL), negative exponents, negative exponents in the denominator, fractions raised to a negative power
  • Function Basics(1.5/2 weeks)
  • Simple representation: function machines
  • Structure & vocab: input/output/rule, and domain/range
  • IS vs. IS NOT: machines that "don't work correctly" (ie, one input can give two outputs)
  • Formalization: function notation (can use whole words)
  • Alternate representations of Functions
  • Describing in words, table, graph (vertical line test), equation
  • Graphing Calculator Basics (1 week throughout Unit 1)
  • Different screens, quitting, ENTER, toggle keys, 2nd ENTER, insert, STO, difference between negative and minus, clear memory
  • Additional tips/tricks: Graphing calculator presentations (replay key, substituting for a variable, ANS, etc.)

* Test on READINESS topics *

Unit 2A Balanced Approach to Algebra:

working with equations4/3 wk total

  • Intro to the Balancing Method(1/1 week)
  • preferable when the variable is on both sides
  • ax + b = cx + d - backtracking does not work
  • Special cases in the balancing method(1/1 week)
  • Equations with no solutions and identities/number of solutions
  • Graphing one variable inequalities on a number line (new)
  • Solving one-variable inequalities
  • Multiply/divide by a negative
  • Chunking
  • clearing out fractions
  • Other types of one variable equations (2/1 weeks)
  • Rate problems
  • Absolute value
  • Squared quantities
  • Word Problems
  • Literal Equations(ie. solve for length in terms of width and area)

* Test on BALANCED APPROACH TO ALGEBRA topics *

GOAL: END OF 1st Quarter

Unit 3Graphing different Families of Functions10/10 wk total

Theme: multiple representations – table/ sequenced table/graph/equation for

each family/function

  • The First Family of Functions: Linear(5/6 weeks)
  • Real world meaning of slope and intercept

y = b + mx. Focus on Start, constant addition/subtraction

  • Graphing linear equations and graphing lines from tables
  • Constant first difference insequenced table
  • "A picture is worth a thousand words" and "A line is worth infinite points": how a graph is a picture of the solution set - all the values that "work"
  • Direct Variation
  • Finding the equation of a line given a graph/given two points/point and slope, vertical and horizontal lines
  • Checking your graph with graphing calculator: Table, plotting points, graphing equations, setting the window
  • Slope of perpendicular/parallel lines
  • Word Problems:

* Test on LINEAR FUNCTIONS topics *

  • Graphing other families: Exponential (5/4 weeks)
  • Exponential – relate to linear y = b * gx
  • start with real world global application, table, look for patterns
  • Exponential Growth/Decay Equations (clearly stated rate)
  • Percentage increase, decrease
  • Graph (identify growth/decay)
  • Table: Constant Multiplier & Differences same as original function
  • Graphing parabolas, or "quadratics"
  • Equation contains x²
  • Graphing equation using tables - always a good place to start
  • Table: Second Difference Constant
  • Cubic functions - start with a table and look for patterns
  • 4th Degree Functions - start w/ table, look for patterns
  • Odd vs. even power function in general - patterns?
  • What happens between zero and one and after one
  • Inverse - start with table, look for patterns
  • Examples of Inverse Relationships
  • Balance: distance from center
  • Rectangle example

* Test on GRAPHING OTHER FAMILIES topics *

GOAL: End of 2nd QTR

4: Revisiting Lines (6/6 weeks)

  • Revisiting Slope Intercept Form
  • Standard or General Linear Form, Ax + By = C (useful for quickly finding both intercepts and graphing, helpful when slope is undefined)
  • Transforming General Linear Form into Slope-intercept form for use on graphing calculator
  • Point-slope Form (useful for writing an equation given a point and the slope, or two points)
  • Transforming Point-slope Form into Slope-intercept form for use on a graphing calculator
  • Word Problems: One variable
  • Systems of Equations
  • What is a system of equations?
  • Writing Simple Linear Combination/Standard Form
  • Number of Solutions
  • Solving Systems using a student selected method
  • Solving by Graphing
  • Solving by Substitution
  • Solving by Elimination
  • Using Calculator
  • Real world examples/word problems (Coin/Mixture/Rate)
  • Solving a system of equations with 3 or more variables
  • Two variable inequalities
  • Graphing on a coordinate plane
  • Dotted/Solid boundary
  • Shading
  • Systems of Inequalities
  • Solve by hand
  • Solve using the calculator
  • Linear Programming

* Test on REVISITING LINEAR FUNCTIONS topics *

5: Playing with Polynomials (4/4 weeks)

  • What are they? (vocabulary): term, coefficient, constant, standard form
  • Classifying polynomials: types, degree, Rational Exponents
  • Addition/Subtraction
  • Multiplying monomials
  • Multiplying polynomials/repeated distributive property/FOIL
  • Factors/GCMF
  • Factoring (Patterns/Difference of Squares)
  • Factoring by grouping (chunking)
  • Arithmetic with radicals (tie into rules of exponents)

* Test on PLAYING WITH POLYNOMIALS topics *

6: Revisiting Quadratic Functions - Finding Zeros (4/4 weeks)

  • Vocabulary: vertex, open up, open down, maximum/minimum
  • Graphing on a graphing calculator
  • Standard Form, Vertex Form
  • Real World Application(projectile)/ Why are quadratics the “cool” polynomial?
  • What is a zero? Real world meaning, extraneous roots
  • Solving Quadratics using student selected method
  • Solving by Balancing/Backtracking
  • Solving by Calculator
  • Solving by Factoring
  • Quadratic Formula
  • Discriminant (leading to number of roots, factorability)
  • Completing the Square
  • Solving Radical Equations

* Test on REVISITNG QUADRATIC FUNATIONS*