I speak a great deal about the “PBL continuum” from low to high – how much problem-based work you are able to do in your classroom (see blog entry). Below are the sets of “Motivational Problems” or MPs I call them, that allow you to assign problems for discussion while also covering topics listed in a traditional syllabus in order to stay with a set of colleagues. You do need to make sure you explain to the students that they are considered “Motivational” in nature because as homework problems the students are not necessarily supposed to know how to complete the problems in total. They might only have an idea of how to start or how to connect it to what they learned the previous day. Be sure to tell the students that they are only to grapple with them for about 20 minutes or so, perhaps you have assigned 6 or 7. The next day in class, the class will discuss all of the problems and be sure to formalize any new material that was learned. You can then assign “practice problems” from the textbook.
Here are some that I have put together over the years. If you choose to use them please give credit to all of the contributing authors who include Phillips Exeter Academy faculty, Emma Willard Faculty and myself. As I continue transitioning to a new curriculum in my Algebra II course this year, I will probably be writing more, so keep checking in.
Algebra
MP on Slope and Equations of Lines
Completing the Square Thread
Geometry
MP on Area
Motivational Problems on CirclesMore Motivational Problems on Circles
Trig Thread
MPs on distance
Algebra II
MP on quadratic equations and graphs
Motivational Problems on Optimization (max/min with functions on calculator)
MPs on Rational Exponents
MPs on Polynomial Functions
Understanding Asymptotes
MPs on Exponential and Logarithmic Functions
Trigonometry
MP on Sum and Difference/Double angle Identitites
MPs on Trig Ratios on Axes
MP Graphs of Trig Functions
Precalculus
MPs Advanced Functions
MP combinatorics and sets
MPs on Counting
MP Sequences
MP Series
Calculus
BC Calculus PBL Problems