UCM: Day 2 (Getting Quantitative)
Warm-Up to Activate Prior Learning:
Start the day with some warm-ups to review what we learned about UCM in terms of a central net force and tangential velocity. A clicker question about the FBD for a car rounding a hill and one for the FBD of a cart rounding top of a roller coaster loop. Then there will be two clickers questions about the path taken once central force is removed. The first one will for horizontal UCM, but the last clicker question will for a vertical swing, released at bottom.
Reorient to our Story Line:
Then I want to return to the pendulum swing that we had talked about the previous time, where Tension Force must be greater than the Weight Force at the bottom. I’m going to take some quick force sensor data and model reasoning through how Fnet = T – W. I’m going to note that this value of Fnet must be just right amount of net force to keep the object rounding the circle. What determines how much force is necessary to keep an object going in a circle? We know from our discussion last time that too much force would cause the circle to “tighten up”, and that too little force would cause the circle to widen out. How much force was “just right”?
Elicit Ideas about How to Increase:
To answer that question I’m going to suggest we think about what could we change about the pendulum swing so that the Net Force would need to be larger in order for an object to round its circle. If needed I might suggest the following framing–think of changes we could make to the scenario that make it more likely that the string would break! The force required to make the loop would more than the string could withstand. I think this framing I’m likely to get heavier mass and faster swing. I’m less sure that students will think about size of the circle (at least in this context)… if needed, I might ask, “Is there anything else about this situation that we could change that we think won’t effect the force?” I’ll suggest we could change the length of the string.
From our list of things students are going to be asked to design and carryout an informal investigation to either answer questions like:
- Does swinging a heavier mass result in a higher net force?
- Does swinging faster through circle require a higher net force?
- Does changing the size of the string have any impact? (This one is harder to think about control of variables for speed, since we have not learned about energy yet).
Short Lab Exploration, followed up with a Data Set to Examine
I don’t want us to get bogged down in the long process carrying out each of these experiments carefully, so I’m just asking students to run two trials to see if our predictions hold up. I may even break up the groups to run tests. I do want them to think through the experiments, however, because I’m going to ask them to examine the data I took earlier in the week.
I will then show students data for Fnet vs mass, Fnet vs. Speed, Fnet vs. Radius. Students will be asked to describe which experiment we did linked to each graph, to describe the patterns they see in the graph, and to state whether the data was consistent or inconsistent with our predictions and initial findings.
Direction Instruction Lecture or Scaffolded Reading
One option will be to do some direct instruction on how these graphs relate to the textbook passages and equations, but I’m also inclined to ask students to read those passages and equations and do the work of relating the text to the experiments. They will need some scaffolding to do this well. I’ll probably then to some direct instruction to tie up loose ends, emphasize some of the points that need to be clarified etc.
Ranking Task as First Application of New Ideas (in isolation).
Then we will practice applying the quantitative ideas to a ranking tasks. If this is easy for students, we will move on. If it’s challenging, I’ll have groups present and we will discuss.
Problem-solving as Integration of New Ideas into Broader Skill Set
I didn’t want students to get too bogged down in actual lab work, because we need to turn a corner into problem solving. Even though it’s not uniform circular motion, I’m going to have students work problem about bottom of pendulum swing. My setup at the front of the room will have a photogate and a force sensor. I’m going to asks students, if I put an object on the pendulum and let it go, what information would you need to know to predict the force sensor reading? Hopefully, students will come up with mass, speed, and radius. Whether or not, I’ll be ready with questions asking them how their answer(s) relate to our learning earlier in the day (either experiments, lab data, or reading).
I’ll measure the information they say they need: mass from scale, radius from meter stick, and speed from the photogate sensor. Students will be asked to work toward a prediction.
I will either give students a list of must-haves or ask them to help me generate one:
- A pictorial representation of situation, with object of interest and boundary identified.
- A free-body diagram that shows both the individual forces (in red), the velocity (in green). Separately, they should include a vector that shows the direction of net force.
- A list of know information from our measurements.
- Mathematical work and reasoning for a solution.
Once students have a prediction, they’ll have to check out with either me or another group, and then they can check their prediction if they feel they are ready. I expect some students will calculate the net force only, and forget to reason about what value of tension is required to achieve that net force.
Additional Reinforcement (or Reflection)
I’m hoping we have time for a second round of problem-solving. This one I will use the vague question technique. I’m going to show a you tube video of a car sliding off an exit ramp, and pose the question, “If you wanted to predict how fast you could go around a curve without sliding off, what information would you need to know?”
Students I think are likely to say the mass of the car, type of car, how wide or tight the turn is, the road conditions, type of tires, and maybe even whether the road is flat. I’ll do the work of catching students contributions and connecting them to either things we could estimate or research, or connecting to assumptions we might need to make (flat road, constant speed around the turn, let’s assume the car doesn’t tip over!). If we are short on time, I’ll be ready with a list of reasonable values, but if we have time I’ll make students estimate and research values based on conditions they want to work out.
Before I let students go off, I’ll want students to do work of guessing “a number they think is probably about right”, “a number they are pretty sure is too low,” and “a number they are pretty sure to to high”… we’ll also review our list of must haves. Then students will be off to solving problem.
Too much? Maybe
Some ways to possible save time are:
- Skip warm-up questions
- Skip mini-exploration before examining lab data
- Skip examining the lab data, and just include that in my direction instruction
- Skip the part where students read the textbook passages and discuss
- Skip the “what do you need to know” discussion before solving 1st problem
- Just give them a word problem for the 2nd one.
- Or don’t do a second problem.
The draw backs of skipping each are:
- It’s really helpful to cycle back and activate prior knowledge from last class
- Doing the mini exploration is critical to students actually being able to make sense of what the lab data is even about.
- Skipping the lab data means it’s even more abstract… like, “Hey guys, someone could do careful experiments, and this is what the graphs would look like, and this is the equation you could infer” –> pretty horrible.
- Doing the explore and lab analysis, I could just do direct instruction, and not have students do the text reading stuff. This is a lot of what I normally do, but I need to work on this part of my courses.
- I don’t like skipping the part of the process where we turn a scenario into a problem. It makes the problem seem uninteresting and more likely for students to not know what they are doing or why.
- Giving them a word problem for the second problem could probably be ok… it’s more meaningful to do the work of turning the question into a problem.
- It could also just be by the end of the day we are either exhausted or out of time, and we just won’t do a second problem. I shouldn’t do a second problem, if we are rushed for time. Instead, I should have a reflection activity task ready.