# Electric Energy: Calculating the Cost

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## Objective

Given the local generation service charge for electricity, students calculate the cost of operating various appliances and electronic devices.

#### Big Idea

The cost of using electric energy (in dollars) can be found by multiplying the electricity service charge (in \$ per kW hour) by the power rating of the device (in kilowatts) and the time in use (in hours).

## Context and Supplies

This lesson, students calculate the cost of operating various electrical appliances and devices. In the previous lesson, Circuit Power, they learned how to apply the concept of power to a circuit. With that knowledge, students calculate the cost of electrical energy based on the power rating of the electrical devise, the time it is in use and the rate the electric company charges. The formula is cost = rate*power*time. Students practice the calculations with numbers I provide and then apply the calculation to a device they chose and use during their everyday lives.

Several NGSS science practices are used as students not only perform the calculations, Science Practice 5: Using mathematics and computational thinking, but also determine which appliances cost the most to operate and justify their reasoning with evidence, which is an application of Science Practice 4: Analyzing and interpreting data, Science Practice 6: Constructing explanations, Science Practice 7: Engaging in argument from evidence and Science Practice 8: Obtaining, evaluating, and communicating information. Since voltage is an electric potential due to electric fields, the performance standards HS-PS3-5: Develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction. This lesson also employs CCSS Math Practice 2: Reason abstractly and quantitatively, Math Practice 3: Construct viable arguments and critique the reasoning of others and Math Practice 4: Model with mathematics.

## Calculating the Cost of Electrical Energy

10 minutes

I inform students of today's objectives, given the local generation service charge for electricity, they are to calculate the cost of operating various appliances and electronic devices. I let them know that they are to also calculate the cost of the device they choose last night for homework, as assigned during the lesson Circuit Power.

Students are to take the following notes in their notebooks as I go through the short Calculating the Cost Power Point. This slide show explains step-by-step how to calculate the cost of electricity using the formula Cost = Rate*Power*Time. It is a simple formula, but it is  essential that the units are correct.

• Cost has units of \$
• Rate has units \$ per kilowatt-hour
• Power must have units kilowatt
• Time must be in hours

The slide show has a sample problem that models how to do the calculation and how the units cancel out to leave only dollars. After the slide presentation, students apply the formula to a series of problems they get in the next section.

## Calculating the Cost of Electrical Energy - Practice Problems

35 minutes

Students spend the next 15-20 minutes on the calculations on the Cost of Energy worksheet. Every student gets a sheet and they work on it on their own. This practice fortifies the formula and prepares the students for doing these calculations on future problems where they not only calculate the cost but also evaluate the appliances used.

While students are engaged in the activity, I walk around the room and monitor their progress. I also employ the Colored Cups which is an efficient way to inform me of when students are in need of support.

As students finish the front of the worksheet, I display Cost of Energy - Solutions so that students can evaluate their own calculations and understanding on those problems. If a student has problems on the front side of the sheet, I prefer that they figure out on their own where they went wrong. I find that this struggle is where the best learning happens. If students continue to struggle, then I help them through the process.

## Solar Power Cost - Homework

5 minutes

With 5 minutes left in the period, I gain the attention of the class. For homework last night, everyone chose an electronic appliance or device and estimate the hours used per month. During this activity, they were to calculate the cost to opperate their appliance. Now I have each table of four students determine who had the cheapest and most expensive device and they share out with the rest of the class. This gives students an idea of the ranges of cost involved and how they contribute to the cost of electric energy in their homes.

Among the less expensive items to use are the charger for their mobile devices: usually less than \$2/month. Among some of the more expensive items students chose to analyze are an Xbox or Play Station. Used for a few hours a day, cost around \$10/month. Not surprisingly, no students analyzes the truly expensive hot water heater or other such device. Surprisingly, daily use of a hair drier or toaster oven, though they have the highest power ratings of all the items that students chose, cost only \$1.50 per month. Students concluded that this is because they are in use for 5-10 minutes at a time.

For homework tonight, students are to listen to a 15 minute podcast on why solar energy has become so affordable just recently.  The link, Solar Energy, is placed on my google classroom site along with the following instructions:

• Listen to episode #616 of NPR's Planet Money.
• What are the three reasons why solar panels have dropped in price?
• What questions would you ask a company before installing solar panels on your house?