Overriding Goal

  • To give students the skills, habits, knowledge, understanding and all tools needed to succeed (at the A level) in Precalulus --without being a precalculus class.
  • Students finding their own strengths and having fun.

Threads:

  • Communication, vocabulary, oral skills: students present problems to each other and explain what their goal is in performing each step within a problem
  • Whiteboard or written skills, notetaking, summarizing pertinent info in an organized manner
  • Distinguish “simplify” from “solve”; understanding what is being asked
  • Study skills and study habits for success in math,
  • Making a bridge from applications to abstraction, help with notation, perspective of algebra as a tool

Topics:

  • Functions a key topic; from here can get to many skills and motivate problem-solving Functions, notation, images, domain, range, relationships to graphs, etc. Simplifying functional expressions could include review of: Radicals (simplifying and rationalizing), removing parentheses, factoring, including fractional exponents to reduce complex fractions
  • Visualizing; graphs; recognizing shapes, using graphs to solve problems and inequalities.
  • Interconnectedness of algebra, geometry and arithmetic
  • partial fractions => leads to fractions and also systems of equations
  • Trig: understanding radian measure, reference angle (de-emphasize right < trig) as a function
  • Radicals and fractions: simplify, reduce, add, subtract, multiply, divide
  • Radicals and exponents: converting radicals to exponential form and vice versa; rules of exponents
  • Logs and log versus exponential forms and why necessary
  • Solving linear and quadratic equations and some inequalities
  • Writing equations of lines, perhaps introducing the form of a difference quotient using quadradic functions
  • Modeling and proportionality
  • Geometric ideas: circles, ideas about parallel lines and angles, 30-60 and isosceles right triangles, Pythagorean Thm., radian & degree angle measures, angles in standard position, positive and negative angle measure, reference angles;
  • Improving number sense and when an answer seems improbable, estimation and mental computation

Methodologies:

  • Should be lots of activities and hands-on explorations.
  • Applications, word problems (notthe far-fetched ones).
  • Find algebra skills weaknesses and get them in shape—use of ALEKS
  • How do students strategize and recognize what is being asked? And what has to be done to answer?
  • Problems with themes of interest to students: extreme sports, climate change issues, renewable energy, marine biology, engineering, etc.
  • Break up the 4 hours with movie clips, math jokes, playful activities with math
  • Have a big poster in the room of math mistakes, showing clearly what is wrong, and what is right

Beginning List of Specific Activities:

  • Idea: mixed bag of “problems” from Algebra, ask to verbalize as a beginning activity.
  • Every day /couple of days students produce a list of what is learned (study skills).