1. Aim/Problem

How do I design a resistive circuit?

2. Objectives

· Design a simple electrical circuit that meets given specifications. [Content Standard 9-12 E – Technological Design]

· Algebraically predict and physically verify electrical measurements. [Content Standard 9-12 A –Scientific inquiry]

· Perform a design task as part of a structured cooperative team. [Teaching Standard E - Nurture collaboration among students]

3. Background Knowledge

Students should have already learned:

· The fundamental concepts of voltage, current, and resistance.

· Ohm’s Law: V / I = R (voltage / current = resistance).

· Characteristics and measurements of resistance series and parallel circuits.

4. Materials

[Teaching Standard D – Provide students with the time, space, and resources for learning science]

· Voltmeter (measures voltage)

· Ammeter (measures current)

· A battery

· A limited set of resistors

· A resistor color-code chart

· Wires and connectors

The instructor needs a class presentation set of these materials. Each cooperative student group needs one bench kit. The meters in the class presentation set need to be viewable by the entire class. Either large-face or projectable meters will suffice.

5. Plan

The activity is introduced by creating groups of four students. If the class size is not an exact multiple of four, divide some students into triads; some roles will be shared in these smaller groups.

Student groups are given two simple paper problems, calculating the resistance of (1) a series circuit and (2) a parallel circuit. Students solve the problems individually, then check the answers with groupmates. In both group and whole-class discussion, two concepts are elicited:

1. When resistors are combined in series, the equivalent resistance is greater than the largest component resistor. Use series circuits to increase resistance.

2. When resistors are combined in parallel, the equivalent resistance is less than the smallest component resistor. Use parallel circuits to decrease resistance.

Each group now receives a task kit. Students in each group are assigned to one of four roles: documenter, constructor, calculator, and observer. Each group is also given a list of (equivalent) resistances to construct. The objective is to design circuits on paper whose equivalent resistances match the specified goals, then construct the circuit and measure the actual resistance.

All students collaborate on design suggestions. The documenter draws the design on paper, while the constructor builds the circuit. Only available components can be used. This helps restrict the solution space. The calculator derives the equivalent resistance from the documented circuit numerically; the observer physically measures the voltage and current, and divides to determine the actual resistance. [Teaching Standard E – Display and demand respect for the diverse ideas, skills, and experiences of all students]

The group gets credit when the teacher observes the written and solved design, as well as the constructed circuit. [Assessment Standard A – Assessments must be consistent with the decisions they are designed to inform] The teacher will randomly ask group members to

· explain the written circuit diagram and how the equivalent resistance is calculated;

· identify each component in the constructed circuit with the correct numerical values;

· explain why observed results might differ from design calculations. [Teaching Standard B – Orchestrate discourse among students about scientific ideas.]

[Teaching Standard C – Engage in ongoing assessment of student learning]

[Teaching Standard E - require students to take responsibility for the learning of all members of the community]

[Assessment Standard B – Achievement and opportunity to learn science must be assessed]

[Assessment Standard C – Technical quality of the data collected is well matched to the decisions and actions taken on the basis of their interpretation]

[Content Standard 9-12 B – Understanding of conservation of energy]

Example: Construct an 83 ohm circuit from a set of 50 and 100 ohm resistors. The solution is to combine one 50 ohm and one 100 ohm resistor in parallel, then add a 50 ohm in series with the combination. The resulting resistance is 83.33 ohms. After designing this circuit on paper, the students connect the corresponding circuit and measure the voltage across and current through the circuit. They then use Ohm’s law to calculate the actual resistance, confirming their answer.

Model this example for the whole class at the beginning of the cooperative task. This ensures that students understand both the task steps and the expected results. [Teaching Standard E – Model and emphasize skills]

At the end of the activity, each group completes a PMI (pluses / minuses/ interesting questions) chart based upon the activity, including the design process that the group followed. One member of each group presents its PMI in a whole-class discussion.

If a group find itself stalled, they are free to ask another group for assistance. However, not all groups have the same problems or resistor sets! This forces intergroup assistance to focus on thinking skills, as opposed to simply giving away an answer.

6. Summary

After this exercise, each group conducts a metacognitive reflection in which each student volunteers at least one thing the group did well and one thing that could be improved next time. The teacher suggests that students focus on how group behavior contributed to (or detracted from)

· design time;

· verification time;

· individual understanding for all team members.

This reflected is written and reviewed by the teacher, but not discussed with the class. Students indicate which specific reflections are theirs by signing off on specific lines.

[Teaching Standard E – Structure and facilitate ongoing formal and informal discussion based on a shared understanding of the rules of scientific discourse]

Grateful Acknowledgment to:
Camille and Henry Dreyfus Foundation & Lucent Technologies Foundation
Dr. Samuel Silverstein and Mr. Jay Dubner, Columbia University

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