For 1D impulse and momentum, we need a more integrated representational set than what Knight’s textbook gives us. They do before and after (sort of vector) diagrams and force vs time graphs for “during”.

I’m not quite ready to stray really far from what Knight supports (since I like the class to be coherent across class and text); so, although I like IF momentum charts (from modeling), I’m thinking more of cycling back to velocity vs. time graphs more strongly  and adding momentum vs. time graphs.

Something like this:

Putting together a draft for a matching task related to projectile motion. Yah!

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Revised Prompts :

Round 1: Hand out just the motion diagram, description, and list of initial values. Have students sort the cards into matches

Round 2: Add the graphs to the mix, and have students complete the matches.

Round 3: Ask students to use the graphs to determine the time of flight and horizontal distance traveled. Compare and contrast the three cases. Which one spent the most time, least time? Why? Which on traveled the most distance? Why?

Round 4:  Add equations into the mix, and have students complete the matches.

Round 5:  Ask students how they can find time of flight and horizontal distance from the equations (rather than graph). Explain what is similar / different about using graphs vs. equations.

Round 6: Take away the graphs (or flip them over), and ask students to see if they can determine the time to maximum height and the value of maximum height from the equations.  Check answers against graphs. If they get stuck, have them go back to graphs. Compare and contrast cases: Which one go the highest? Why?

Round 7: With graphs back in mix, ask to find the speed of the ball at it’s highest point. Compare and contrast. Which was moving fastest at its highest point? Why? Which one slowest why?

Round 8:  Ask students to find the final speed (just before hitting ground). Compare and contrast? How did the final speeds compare? Why?

In 2nd semester physics we started solving circuit problems. Here is one group’s whiteboard. I’ve been leaning toward having students make a new graph and new table for each reduction. In general this mix of representation helps students to make sense of what they are doing with out over reliance on equations. And solving the problem sort of feels like working on a sudoku puzzle.

Before doing circuits we did a review activity to help us retrieve information in our minds, seek our relationships, notice gaps in our understanding, and ask questions. With all new concepts, a lot of students were confusing units with algebraic symbols. We also needed to talk about difference between general cases vs point charge specific cases. Students had lots of good questions about cause of charge, electric field, and electric potential energy. We clarified a lot about connection between potential and potential energy.

In physics one we finished up our introduction to energy and cycled back to kinematics to examine free fall. I like holding off on freefall until after students have forces, impulse, and energy under their belts. Students can make sense of what we do and don’t mean by free fall, can productively grapple with why acceleration is same for all masses, and have better hooks for what we do and don’t mean by initial and final velocity.

Here is some data we collected for a bouncy ball, using a Vernier motion detector to calculate kinetic and potential energies.

Next year I’d like to design a coherent lesson around these graphs. So many cool things to notice and ask questions about.

Curriculum development has moved me in a direction of teaching momentum in following order.

First: impulsive forces 

Investigating impulsive forces–factors that effect peak force and duration. We us force sensors and change factors like mass, speed, bumper stiffness in collisions with a wall.

We then introduce and practice with impulse and change in momentum, both with sensors and logger pro and by hand. Clicker questions, ranking tasks, and a problem to determine the impulse and peak force of a baseball bat on a base ball.

Second: Collisions

Investigating elastic collisions comes first. Doing this helps conceptualize the process as momentum transfer. We start with equal masses. All the momentum is transferred. We then look at cases where some but not all of the momentum is transferred, and finally when more momentum is transferred than one had to begin with. 

After observing and discussing qualitatively, we get quantitative, but I don’t have students predict anything. We observe and analyze it in terms of momentum, for the purpose of determining how much momentum was transferred. We draw before during after diagrams.

At end, we see that the momentum of each system is constant, and I introduce concept of an isolated system We look at explosions next as another example of isolated systems that starts with zero momentum. Students analyze mock explosion data and sort them into possible and impossble explosions. A little bit of neutrino history gets sprinkled in here. 

Finally we look at Inelastic collisions, and this is the first time students use momentum conservation to make predictions. Studnets  predict final velocity, but then must also determine how much momentum was transferred. Doing so involved practice shifting perspective, from system to individual objects.  

Many times people start with Inelastic collisions, but I think that’s a mistake. While you can calculate easily, it obscures transfer. Elastic better promotes transfer idea I think.