##
* *Reflection: Staircase of Complexity
Forces and Work Revisited - Section 4: Shape of and Key Questions about Coulomb's Law

*Student Responses to Area Dilemma*

*Staircase of Complexity: Student Responses to Area Dilemma*

# Forces and Work Revisited

Lesson 3 of 15

## Objective: Students will continue to consider the area under force versus distance graphs, particularly those that result from two charges being moved with respect to one another.

*80 minutes*

#### Warmup

*20 min*

The overall goal for today's lesson is to have students develop a geometric model for estimating work done when charges are pushed together (or pulled apart). This consideration of work/energy provides my students with an opportunity to demonstrate their understanding of the change of energy in an electric field (NGSS HS-PS3-5). Furthermore, to do this, students must use Coulomb's Law to predict electric forces between charged objects (NGSS HS-PS2-4). Finally, student teams will begin to share their findings from the "Hot Rocks" investigation, an activity that showcases students as scientists and achieving the Science and Engineering practices of arguing with evidence, analyzing data, using mathematical reasoning, and communicating scientific information.

The warmup problem revisits the geometric approach developed in the previous class. There are several parts to it as I hope to ensure a deep understanding of the ideas we've developed so far.

The first three parts of the warmup ensure that students are recognizing the linear nature of the function. The final three parts are more geometric in nature and revisit the idea of finding areas in order to calculate work done. I want to reinforce this idea with a non-constant force; this is where we left off in the previous lesson. Furthermore, by the end of this lesson, I want my students to wrestle with a function that is simultaneously non-constant **and** non-linear: Coulomb's Law is an inverse-square function that defies a single, geometric solution.

Students work alone or collaboratively, recording their answers in their notebooks, for about ten minutes as I circulate to assist students and assess overall comfort with the problem. Then I take the time to show solutions (both the first few, algebraic solutions and the latter, geometric solutions) on the board and reinforce the ideas of area and work. This sets up the latter segment of class when we'll consider the area under the non-linear Coulomb's Law function.

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#### Student Presentation

*20 min*

We pause our study of electrostatics to have the first of several student presentations from the "Hot Rocks" investigation of the previous unit. Students generated interesting secondary questions while exploring calorimetry experiments that featured heated rocks and cool water baths and pursued those questions by designing their own procedures. I use this kind of culminating activity - as opposed to the more traditional lab report - because the challenge of facing a live audience increases the authenticity of the learning; I ask our students to be more like scientists and, by submitting to this "peer review" we can approximate that.

These presentations provide opportunities for students to report conclusions to their peers, based on the distinct evidence they collected on their chosen question. As a result, the entire project allows each team to engage in many of the NGSS Science and Engineering Practices including Asking Questions, Planning and Carrying Out Investigations, Analyzing and Interpreting Data, Constructing Explanations, Engaging in Argument from Evidence, and Obtaining, Evaluating, and Communicating Information.

In addition to a presentation score, students receive an "audience score." Above and beyond the obvious expected level of attention, I challenge each student to ask at least four questions over the course of the four presentations they'll see in the next week or so. At first, the questions seem a bit contrived but the spirit of honest inquiry inevitably takes over and the questions become more authentic over time. For example, an early question might be "How much water did you use in your trials?" which would count as a question but leads to little, if any, depth of understanding. Later, however, the questions become more thought-provoking like "What did you expect to find by altering the experiment the way you did?" I use a blank roster sheet to record questions and comments along with a scoring sheet for the presenters that focuses on several of our school's learning expectations.

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One aspect of culture I wish to foster in class is a sense of student-ownership. To that end, I now introduce a long-term project: Electrostatics Student Demonstrations. The idea is to have students find an interesting demonstration, typically on the web, and to either show it and explain the process in class, or replicate the demonstration on their own. I have a small set of helpful materials (rods, furs, etc.) for certain kinds of demos but make no promise that I can provide all materials. This, naturally, influences which demos are chosen.

The demos are meant to be simple, fun, and short, and should that capture key ideas about electrostatics while simultaneously generating enthusiasm, interest, and "ownership" of the classroom. Today, I hand out the project description, allow some time for students to read it, address questions, and generally elaborate on the nature of the project. Students may work solo or in pairs and need to choose a demo within the next week. Later on during the week students commit to a time frame for delivering the demo later, as I want only 1-2 demos on any given day.

#### Resources

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In this section of class, I want my students to apply their geometric model of "area as work" to electric charges which, naturally, are governed by Coulomb's Law. As this is an inverse square law, the shape is very non-linear and does not lend itself immediately to being modeled perfectly by geometric shapes. I have two goals here: first, to have students truly recognize how their current approaches will be insufficient and, second, to have students suggest some creative ways to amend their approaches.

I break up this segment of class into two sections. To start, I ask students to sketch the force versus distance graph for electric forces as expressed by Coulomb's Law. This is done as a turn & talk exercise to promote mathematical thinking and talking. After discussing the shape, I check in about the graph and ask a series of questions to consider: Where are the charges? What does d mean? What does d = 5 mean? How would we determine the work done when the separation changes from A meters to B meters? These questions are meant to ensure that the shape of the function is deeply understood and to reinforce the idea that the area under the curve will be equal to work.

Once we've re-stated the area idea, we confront the dilemma - the shape under the curve is NOT a simple geometric shape, nor any combination of shapes, so we must estimate. (See sample force graph for a template to use with students.) Once again, I have students turn & talk to imagine strategies for estimating the area. After a few minutes, I collect student ideas - like this combined triangle and rectangle -at the board and facilitate a discussion about their best estimates.

As we continue to consider this idea, we will adopt a common preliminary estimation method, then work to improve upon that. We end the lesson with some preliminary evaluations of these student ideas and the promise to return to this conversation in the next lesson.

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- LESSON 1: Introduction to Electrostatics
- LESSON 2: Introduction to Forces and Work
- LESSON 3: Forces and Work Revisited
- LESSON 4: Enhancing Our Model of Work
- LESSON 5: Enhancing Our Model of Work - Revisited
- LESSON 6: Investigating Work and Forces - Day 1
- LESSON 7: Investigating Work and Forces - Day 2
- LESSON 8: Multiple Charges, Multiple Forces
- LESSON 9: Self-Directed Day
- LESSON 10: Charges and Forces at Right Angles
- LESSON 11: Redefining Work - An Introduction
- LESSON 12: Redefining Work - Day 2
- LESSON 13: Electric Potential Energy - Introduction
- LESSON 14: Electric Potential Energy - Day 2
- LESSON 15: Reflection on Electrostatics