SWBAT explain the mathematical relationship between energy and power.

Students meld math and science in their pursuit of making sense of energy and power.

You open this lesson by having students run and walk up stairs, measure height of stairs and time their ascent. Next, help them to define energy and define power. Give the units and their relations. Work an example or two. Turn them loose on some practice problems.The lesson closes by bringing the class back together to discuss their staircase race results. Who was most powerful in the class?

**Note: **The concepts covered here are similar to another lesson in this unit titled Human Power Lab. If you taught that lab, consider this lesson an extension.

**Materials:**

- pencil, paper, brain. If you do the staircase race, you’ll need tape measures/meter sticks and stop watches.

**Technology Tools Used**: none

**Useful Vocabulary:** energy, power, joule, watt, newton

15 minutes

To begin this lesson, engage your students in a friendly competition. Tell them we are going to determine a measure of who is the most "powerful" eighth-grader. To do this they will walk and run up a flight of stairs. They will need to calculate the total height that they ascended, the time it took them to walk and to run up the stairs, and they will need to record their weight.

Provide each student with the Staircase Race handout and read through the directions with the class. This might be a good time to set/discuss behavior expectations - what it "sounds" like, "looks like, and "feels" like.

You will need a tape measure or meters sticks for measuring the height of the stairs and stopwatches to time the students.

Determine the best way to manage this activity. I send my students off in groups of four or five to different stairwells in our building. Since they are eighth-graders I trust them to work responsibly without my direct supervision. Of course I give them a strong warning about the consequences of misbehavior. If you are unable to do this, then make a reasonable adjustment on how to manage this activity.

I give the students 15 minutes to complete this and return to class.

30 minutes

As the students return from the staircase race, they are going to be very jubilant and excited about their results. Now students calculate energy and power and work. The first part of the Power, Energy, and Manipulation of Units worksheet covers some of the basics of the mathematics behind these formulas.

You may choose to manage this a little differently than I have outlined in the lesson. For instance you might go over these mathematical formulas in sections one and two first as your opening activity then have the students engage in the staircase race and then go back to section 3 where they calculate work and power from the data of the staircase race.

Either way make sure that they have a clear understanding of the meaning of these formulas.

In the video below two my students share their thoughts on how this lesson helped them make meaning.

10 minutes

Who was the "most powerful"? Bring students back together at the end to discuss their staircase race results.

*Did you use more energy walking or running? How do you know? Remember, time is not a function of energy.**Did you use more power walking or running? How do you know?**Who was most powerful in the class?**Do they agree with the results?**What other ways could we measure power?**Did strength have anything to do with it?*

30 minutes

You can extend the math of this lesson with some conversion practice. I use a bulletproof method of converting units. I write down what I have and what I want to get. I chain together conversions in the form of fractions, according to a simple law. I change the units one at a time until I have what I want. If there is a unit I don’t want on the bottom (top), I put it on the top (bottom) of the next fraction in the chain and on the bottom (top) goes the equivalent in a unit that is closer to the one I want.

Check the worksheet for examples. It’s important to demonstrate the process step by step, and to enforce that while circulating and observing. If kids ask questions like, “oh, do I multiply or divide here?”, that’s a sure sign they are not using or grasping the method, for the units themselves are your guide; they tell you whether to multiply or divide. One strategy is to place the units first, then fill in the numbers.

** **Circulate while they practice. They typically tear through the easy stuff, often skipping steps or not using the method. If they are floundering on the more difficult problems, do force them to use the method and write it out. Positive framing is important in this lesson, because many students will find it challenging at first. Overall, I got great feedback on this despite the difficulty.