This is a flow chart of courses at the Illinois Mathematics and Science Academy (IMSA). Here are brief course descriptions of the Mathematical Investigations sequence (most students begin in MI II).

Mathematical Investigations III, Rational Functions Unit (M. Kammrath)


• Learning targets for the Rational Functions unit. Introductory comments on the unit.


• Day 1: Group activity on rational functions using Winplot. Homework based on this exploration.


• Day 2: Exploration on rational functions. Use of sliders in Winplot has students actively engaged. Complete for homework.


• Day 3: Class discussion on the exploration. Homework for more practice; selected answers are provided. There are also Winplot files to download for homework problems five, six, seven and eight, and nine.


• Day 4: Further exploration on rational functions; expectations set previously. Students self-direct. Separate homework with selected answers.


• Day 5: Group activity on rational functions (with selected answers projected on screen). Separate homework. Answer key to the homework problems.


• Day 6: Worksheet on writing rational functions (with selected answers projected on screen). Separate homework.


• Day 7: Critical thinking with error analysis. Review sheet for homework.


• Day 8: Worksheet on rational inequalities.


• Day 9: Rational functions unit exam.

BC Calculus I, Sample Assessments (V. Matsko)

Here is a copy of my assessment philosophy distributed to the mathematics team at the beginning of the semester. Below are sample assessments and copies of student work.


• Critical reading assignment; this was not so successful.


• Original Problems 1 assignment.


• Original Problems 3 assignment.


• Sample of student work on writing original problems.


• Sample of student work on writing original problems.


• Sample of student work on writing original problems.


• Sample of an Oral Quiz.


• Sample of an exam on derivative concepts.

Topic areas for sample problems:


• Sample pentomino problems. A set of pentominoes can be created using attempted using this pentomino template. (Note: Templates should be copied onto cardstock, which is a paper with weight 135 g/m² or greater.) For the doubling problems, use these double pentomino templates.


• Sample problems involving the floor function.


• Sample problems involving geometric dissections.

Solutions to selected problems:


• Partial solutions to the pentomino doubling problem.


• Solutions to some of the floor function problems.


• Solutions to the geometrical dissection probelms.