# Investigating Work and Forces - Day 1

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## Objective

Students will manipulate elastic materials (rubber bands, plastic spoons, and springs) to generate force and distance data, then develop a model for estimating the work done.

#### Big Idea

Macroscopic scale objects (springs, for example) can serve as substitutes for microscopic scale objects like charges.

## Warmup

15 minutes

Today I wish to transition from paper-and-pencil activities to some lab work. Before doing so, I want to ensure that the recent thinking about work and area is thoroughly understood. To that end, the first half of class is dedicated to work and area ideas, including a one-question quiz.

To get the day started, I provide my students another geometric warmup. As this is the third question of this type they have seen, I set an additional challenge of completing the problem within 10 minutes. My purpose is to set an expectation that with familiarity should come facility and success. This is in addition to the more general purpose of the warmup exercise - to allow students to mentally transition from one class to another at their individual pace. As usual, students may collaborate, particularly if they can't seem to get started.

After the 10 minutes are up, I provide a solution for students to consider. I take a few minutes to show the connection between this force function and the generic linear relationship of y = mx + b. My students often don't immediately see physical functions like this one as being the same form as the generic mathematics form - I think reinforcing the connection to a very familiar math idea is important and helpful.

## Student Presentation

20 minutes

We pause our study of electrostatics to have the next 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.

Here's a set of slides from today's student-team presentation. It spurred a rich conversation about the level of confidence in a conclusion one can draw when the data is scant.

## One-question Quiz

25 minutes

I provide students with a one-question quiz focused on work as area. This is a single question that is presented as a quiz immediately after (typically, though not in this case) a practice session. Unlike a quiz, however, students can indicate the lowest score they'd like to accept! For example, a student can indicate a "16/20" and, should I score the quiz as a 15 or lower, I don't count it. Only a score of 16 or better will be recorded. Finally, I allow students to use their notes, as this is truly meant to be a formative assessment. I do, however, ask each student to work individually. Here, students are creating private space by using their binders. A solution is provided for convenience.

My goal here is to reduce anxiety about the grade while simultaneously providing myself with some formative feedback. If the majority of students achieve their score (or better), I know that the concept is well-developed.  If not, my next lesson's warmup problem can be targeted to the issue at hand.

Today's quiz does not follow a practice session, which occurred in the previous class. In deference to this, I provide a 5-minute window for review of those practice problems with an opportunity for students to check for understanding before proceeding.

## Prompt for Investigation

5 minutes

As I want my students to be acting like scientists as often as possible, I present them with the challenge of collecting a valid set of data from which they are to determine the amount of work done to an object. The lab goal is to take at least one material that resists movement (elastic materials like springs, magnets, and plastic forks and spoons) and gather data that will allow them to establish how much work they did. To be successful, they will need to create the kind of graph that we've been analyzing - a force versus distance graph. Though students are not dealing with charges, with this activity I promote the idea of doing work by overcoming some resistant force. For me, the trade-off is worthwhile - charges are hard to gather, contain, and measure, while the elastic materials we use are much simpler to manage.

I distribute the Work and Area Investigation prompt and address any quick questions.

## Lab Work

15 minutes

Students move to the back of the room and I distribute materials for each team. Students begin to investigate the elastic material at their station (rubber bands, springs, elastic therapy bands, plastic flatware, and magnets). We use Vernier Dual-Range Force Sensors to collect force information and standard rulers for distance measurements. if successful, students will collect a wide range of forces and distances which can be turned into a graph. At that point, students can employ the techniques we've been working on - approximating the area under a force versus distance graphs to determine the total amount of work done.

There isn't a lot of time left in the period by this point, so it is unreasonable to expect teams to get too far in their investigations. On the other hand, the time available (roughly 15 to 20 minutes) is sufficient for familiarization and some first steps towards collecting valid data through systemization. For example, teams that are measuring the force it takes to extend a spring will have to recognize that manually stretching the spring will produce erratic data - one's hands can only be so steady! That team will need some time to create a more satisfying method for stretching the spring with minimal variation.

Here is a reasonable first step for one team. Notice how the student is simply holding the spring at an extended distance. Soon, he will recognize the inherent flaws in this approach.

Students continue with this work until there are just a few minutes to go in class. At that time, I ask them to return material to the back bench. We continue with this investigation in the next class.