SWBAT compare multiply and divide measures of energy through scientific notation and the laws of exponents

Operations with exponents and scientific notation can help us make sense of the energy we use in today's society.

5 minutes

I start this lesson with a "cold open," where I launch immediately into the lesson. The theme is built around the movie **Back to the Future** and the idea of generating 1.21 gigawatts of energy. Many of the students have never seen the movie, but I play the theme music and show the movie poster with a countdown until the lesson begins (about 1 minute, which is the time it tends to take for them to enter the room.) As students enter the room, I stand by the door and say something like, "We are going back to the future!"

The cold open is more thematic than mathematical. The goal is to get students *excited* about the adventure in the lesson. It is an approach I like to use every week or so. It can happen on any day and be modeled around any theme. I like to use the element of surprise to add some flavor to the lesson.

After a minute or so, I give a brief synopsis of the movie and play the clip. Then we talk about number used in the clip, the gigawatt. (I display Lightning Storm Texas in the background.) To give students some context, I discuss the meaning of a watt (a measure of power). Our reference point is the lightbulb, something they might all know (around 60 watts). We work our way up to the gigawatt (and beyond). My basic approach is to list out the names and their meanings. I use different colors for prefixes and let students know that they are common and used for all types of measurements (kilo means thousand, so kilowatt is one thousand watts, kilometer is one thousand meters, etc). When I introduce each new name, I write the name and number and ask them to tell what the prefix means. The idea is that a student will see 1 kilowatt = 1000 watts, therefore kilo means 1000.

Here are some common names I show:

Femtowatt = 10^-15 watts

Picowatt = 10^-12 watts

Nanowatt = 10^-9 watts

Microwatt = 10^-6 watts

Milliwatt = 10^-3 watts

watt = 10^0 watts

Kilowatt = 10^3 watts

Megawatt = 10^6 watts

Gigawatt = 10^9 watts

Terawatt = 10^12 watts

Petawatt = 10^15 watts

I love showing this list because each of these amazing numbers has an application and we have a opportunity to show some of those. For example, the intro clip already shows that a Gigawatt is a useful measurement for lightning. Students naturally wonder what the other measurements might be used for and I get to tap into that. I also use this opportunity to spiral back and review the meaning of each number. I ask students to write each value in standard form. We take the time to review each and I ask them to explain how they know they are write. If they are stuck I remind them of the basic intuition behind each conversion, for example 10^3 = 10 x 10 x 10 = 1 x 1000 = 1000.

30 minutes

I let students know that we are going way beyond lightning and looking at something both groundbreaking and unbelievable: lasers! I like to show a fun clip of a laser, so I use the Death Star Clip. I show students some of the photos of the world's strongest laser which produces 411 trillion watts of power over 23 billionths of a second. I like to show them some of the photos of the facility that houses the laser NIF sky view. I let them know that they are going to compare power levels between this laser, the 1.21 Gigawatts, and common appliances of their choice. Mathematically the goal is to use the division and multiplication of numbers in scientific notation in a meaningful context.

**Here we ask to use following guidelines:**

-Make all comparisons in watts

-Finish this statement: " __________ 100 watt light bulbs would equal the power generated by the laser"

-How many times stronger is the power level of the laser than the 1.21 Gigawatt lightning bolt?

Then I ask them to create some division questions (although I might not name them as such):

-Answer three questions like, "how many high efficiency light bulbs would it take to equal the same power (watts) as the laser?"

**And finally multiplication:**

-Make at least one statement about energy (watt hours), "if the laser ran for x hours, the energy would be y."

I tend to explain the last one and give a simple example (going back to the lightbulbs). If a lightbulb uses 100 watts of power and is on for two hours, then we have used 200 watt hours (energy).

I have a variety of appliance-watts, but tend to give out only 1 and let them choose how to compare. If I find that they are struggling, I help them with an example and remind them of the division algorithms that reviewed the day before.

The expectation is for students to present their findings at the end. The challenge is in they compare. For example, if I know students can challenge themselves, I ask them to look at the wattages over a span days or weeks. If I know they are struggling, I will tap into their number sense and ask them to find the wattage for something like 46 billionths of a second (twice the length in time of the original experiment). The fun is then to ask them why this is easier than a number like 1,000,000 seconds.

25 minutes

The goal here is for students to share their comparisons and ask the class to validate their calculations. I sometimes start with a basic calculation, but if a group created an interesting and challenging comparison, I start with that to launch the conversation. Students are typically interested in these types of summaries because every group had a slightly different investigation. This means that they have some background and can give feedback, but they are still seeing something new. Sometimes we regurgitate the same problems too much in math.

I don't review the statement about the lightbulbs or 1.21 Gigawatts, since I used that in my circulation to check how groups were doing. I only review that question if many students struggled with the material.

I also only review comparisons from students if I know that their is something they could learn or someone they could help in the conversation. Otherwise we make up a comparison of our own on the spot. I really want this summary to be unexpected and interesting for the class.

The questions I ask are always based on the content they create, but I like to ask questions like, "how could we estimate that division in our head?" For example, if you have (6.4 x 10^6/3 x 10^3) we could round our coefficients to 6 and 3 and then use the laws of exponents to our advantage. This is a moment for solving a problem in class but also spiraling back to the laws of exponents a necessary step in dividing and multiplying with scientific notation.