I was motivated during my flight today to come up with physics problems that have multiple right answers, have a low barrier to entry and a high ceiling. Here’s my go at it, along with thoughts.
The idea behind these is students are supposed to come up with as many ways as possible.
1. Draw as many velocity vs time graphs that show an object moving +45m from where it started.
Extend 1: Describe each in words.
Extend 2: Pick one and draw its corresponding position vs time graph.
2. Draw pictures depicting situations where a normal force exerted on an object is different than the objects weight.
Extend 1: Pick one to draw a free-body diagram that will help you to explain your reasoning.
Extend 2: Categorize them by Fn > mg and Fn > mg.
3. Draw a picture of a situation where the initial and final states consist entirely of potential energy.
Extend 1: Draw energy pie charts for the initial and final state and at least two in between.
4. Identify the mass and initial velocities for two objects objects that when they collide, they stick together and remain motionless.
5. Draw free body diagrams for an object that will accelerate at 1 m/s/s.
6. Draw a velocity vs time graphs and categorize them into those that involve an object turning around and those that do not .
Extend 1: Come up with a rule.
Extend 2: Do the same for position vs time.
7. Draw a force that acts on an extended object such that the Torque due to that force is CCW.
Extensions: multiple forces where net torque is…
Brian’s Development Rules of Thumb:
– Situations should involve relationships with wiggle room. For example, consider a = Fnet / m. Not only can Fnet and m vary but the same Fnet can be accomplished in different ways. Torque similarly has wiggle room in location, angle, choice of pivot qualitatively and force, distance, angle quantitatively.
– Design around tasks that get close to known difficulties, but don’t over constrain things to make it narrowly about the difficulty. For example, don’t do, “Negative acceleration and speeding up”. Just do speeding up velocity graphs and see what happens. Or if you are going to go right at difficulties, don’t make it a trick or you being clever. My normal force situation I think tackles a difficulty in a straight forward manner and it may work, because there are do many ways to do this.
– I like processes where initial and end states are constrained but not the process in between. (Energy example above). This provides a large variety.
– I think you want choose representations very deliberately. Perhaps, ask students to start with or move to representations that support semi-quantification, or ask them to extend to multiple representations. I think it’s OK to start with picture, but it’s important to bridge to a representation (Normal and Energy are examples)
– When using in class, I would want to think carefully about the sequence of individual work leading to group work leading to whole class sharing and discussion.
– If I designed the task with a particular issue to come up and it didn’t spontaneously, I would just introduce it and ask students to consider it.
– I think these tasks are very amenable to the Five Practices for Orchestrating Productive Discussions framework. (Link to come on an edit)
Anyway, what do you think? I’m interested in what others would come up with.