In this article, the authors first present the Hands Together! task. The mathematics in this problem concerns the relationship of hour and minute durations as reflected in the oft-overlooked proportional movements of the two hands of an analog clock. The authors go on to discuss the importance of problem solving in general. They then consider…

Early in their study of one-dimensional kinematics, my students build an algebraic model that describes the effects of a rolling ball's (perpendicular) collision with a wall. The goal is for the model to predict the ball's velocity when it returns to a fixed point approximately 50-100 cm from the wall as a function of its velocity as it passes…

We present a nontrigonometric graphical method for predicting the trajectory of a projectile when the angle and initial velocity are known. Students enrolled in a general education conceptual physics course typically have weak backgrounds in trigonometry, making inaccessible the standard analytical calculation of projectile range. Furthermore,…

This paper describes my attempts to look deeper into the so-called "shoot for your grade" labs, started in the '90s, when I began applying my teaching experience in Russia to introductory physics labs at the College of Charleston and other higher education institutions in South Carolina. The term "shoot for your grade" became popular among…

This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the…