Exploring Intermediate Algebra
Tuesdays and Thursdays at 4:30 pm Eastern for 16 weeks
Instructor: Lisa Fontaine-Rainen
In Exploring Intermediate Algebra we will dive into the end of a traditional Algebra course and the beginning of a traditional Algebra II course, with a focus more on deep understanding, seeing connections, posing problems, exploration of student ideas, and applications in problem solving. Our spine for the course will be material from Art of Problem Solving Introduction to Algebra, using material that starts at chapter 10, though not in book’s order. This material will be supplemented heavily with other problem solving and project work.
This class will be held over 16 weeks, with two meetings per week. Students will be expected to engage in the material outside of class through homework assignments that will provide options for different levels of challenge. Quizzes and tests will be given, but the purpose of these is two-fold – to help students prepare for such testing in the future and to guide our learning. They will only be formally graded on request – otherwise, they will receive comments only.
To be prepared for this class, students should feel comfortable with working with variables in linear equations and systems of linear equations.
Syllabus is subject to change – the class will emphasize student exploration and support their approaches to thinking through ideas. Questioning and exploration will take center stage more often, so specific topics may take more or less time depending on these explorations. Should we find we are not going to get through everything listed in the syllabus, we will make decisions together with families about what to keep and what to either drop or move to another class.
Week 1: Functions, graphing functions
Week 2: Functions, composition and inverse
Week 3: Absolute value - equations, inequalities, and functions
Week 4: Piece-wise functions exploration – taxicab distance
Week 5: Polynomials, radicals, and complex numbers
Week 6: Introduction to Quadratic Equations and Factoring
Week 7: Advanced factoring techniques and graphing quadratics
Week 8: Completing the Square and the Quadratic Formula, Vertex Formula
Week 9: Quadratic Inequalities, geometric definition of parabola
Week 10: Quadratic problem solving, explorations
Week 11: Exponential Functions, logarithms
Week 12: Logarithmic functions, radical functions, rational functions
Week 13: Sequences and Series: Arithmetic and finite geometric
Week 14: Sequences and Series: Infinite geometric and telescoping
Week 15: From pattern to equation
Week 16: Student led explorations and problem solving
Flexibility is key, and student learning needs are the guiding force.
Please note that class will not meet on Thursday, November 28th, due to US Thanksgiving.