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

Motivational Problems on Linear Functions

**Geometry**

MP on Area

Motivational Problems on Circles

**Algebra II**

MPs on distance

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
**