Chapter 4: Algebra and Equation Solving

#1019 Making Sparks: Where Energy Comes From—When you turn on your lights, you are plugging into a power grid which is fed by fossil fuel, nuclear and hydroelectric power plants.

Ask students to identify variables as they watch Futures Channel Movies #1019 Making Sparks: Where Energy Comes From and #1021 Making Sparks: How It Works (if you have time, show all three Making Sparks Movies in sequence, but it isn’t necessary).  In discussion, elicit or bring up the variables of “amount of energy”, “power”, and “time”, and make sure students understand the energy formula described in Movie #1021 (energy = power x time).  Explain to students that people who work with energy use algebra to describe relationships between variables and to solve problems related to their work, and that in this chapter the students are going to learn more about how algebra can help them solve such problems.

Students will work in pairs on this activity.  Prepare for the activity by collecting old light bulbs of a variety of wattages.  The light bulbs should be of two types: regular floor or table lamp bulbs in which the wattage is indicated on the bulb, and smaller bulbs that do not indicate wattage.  Create also a set of 35 index cards with various amounts of time written on them in hours (e.g., “4 hours, 7 hours, 12 hours” etc. (Use time values from 4 to 20 hours.)  Give one student in each pair one of the large bulbs of known wattage, and the other student one of the smaller bulbs of unknown wattage; give each student a “time” card. 

Tell students that when the two bulbs are used for the times indicated on their index cards, the total energy is 2500 watt-hours, and ask them to determine the wattage of the unknown bulb.  Assist pairs individual as they carry out this task, helping them to first write out the equation (total energy used = wattage of bulb 1 x time used + wattage of bulb 2 x time used), then to plug in the values they know, then to reason through the process of solving it: “How can you determine the amount of energy used by the unknown bulb?” (By subtracting the energy used by the known bulb from the total energy.)  “Write the new equation for just that bulb.”  “Solve that equation as you learned in Chapter 3.”