Visions of Exploration STEM Lessons

Contents

Thank you for visiting AFA’s Visions of Exploration program page. If you aren’t a participating teacher, feel free to use these free lessons and learn more about what we’re doing in schools across the country.

If you’d like to participate in this program, contact your local AFA chapter.

### Mathematics:

Exercise converted to electricity

#### Introduction

While most of today’s discussion around green energy production only includes the harnessing of macro environmental

sources (wind, solar), there has begun to emerge a new breed of entrepreneur whose more micro approach to the issue

is making a difference to society in general and to one’s bottom line in particular. Such is the case with producing real,

usable electricity by the retrofitting of thousands of exercise bikes and elliptical machines found in health clubs and

businesses around the country.

What are the large-scale implications for such a creative venture, and just how valid are claims made by the two retrofit company

spokespeople quoted in the “Exercise Converted to Electricity” article? What is the rate of those bike and

elliptical conversions, and how much electricity can actually be produced in this way? In the exercises below, you will

perform scale conversions and related computations to access the information necessary to address some questions

regarding economy and ecology.

Materials needed:

Paper and pencil

Calculator (for checking purposes only)

#### Economy (45 minutes)

Speaking on behalf of The Green Revolution, a Connecticut-based retrofitting company, was Jay Whelan, Chief Economic

Officer.

1. Mr. Whelan quoted retrofit-sales numbers for his company since April 2009. Assuming continuous sales up

to and including the month this article appeared in USA TODAY (August 2010), how many months of retrofit

sales are being measured?

2. If The Green Revolution has retrofitted 1,000 bikes at 60 gyms, what is the average number of bikes retrofitted

per gym (rounded to the nearest whole number)?

– To the nearest whole number, what is the average number of bikes The Green Revolution has retrofitted

per month?

– To the nearest hundredth, what is the average number of bikes The Green Revolution has retrofitted

per gym per month?

The other retrofitting company cited in the article was the Florida-based firm ReRev, whose spokesperson is Beth Bennion,

Marketing Director.

3. Ms. Bennion quoted retrofit-sales numbers for her company since June 2008. Assuming continuous sales up

to and including the month this article appeared in USAToday (August 2010), how many months of retrofit

sales are being measured?

4. If ReRev has retrofitted 300 bikes at 23 gyms, what is the average number of bikes retrofitted per gym

(rounded to the nearest whole number)?

– To the nearest whole number, what is the average number of bikes ReRev has retrofitted per month?

– To the nearest hundredth, what is the average number of bikes ReRev has retrofitted per gym per

month?

5. To the nearest whole number, what is the per-gym-per-month ratio of The Green Revolution’s sales to ReRev’s

sales? Explain how you arrived at your answer.

#### Ecology (45 minutes)

A watt is a measure of the rate in which energy is converted and is equal to 1 joule of energy transferred per second.

When 1,000 watts of electricity are used in one hour (= 1,000 watt-hours), it is more common to call it a 1 kilowatthour

(= 1 kWh).

1. If the average house uses roughly 10 million watt-hours per year, how many kWh would that be?

– If the average house uses 28 kWh per day, how many watt-hours would that be?

2. “(Mr.) Whelan estimates a spinning class of 20 people over a year could light 72 homes for a month.” If a

20-person cycling class can generate anywhere from 2.5 to 3 kWh, is Mr. Whelan’s statement accurate?

Explain your reasoning.

3. “ReRev says a 30-minute workout on one of its ellipticals generates about 50 watts, enough to run a laptop

for an hour…” At that rate of generating electricity, if 4 retrofitted ellipticals are pedaled for 45 minutes

each, how long could 3 laptops stay charged?

4. Suppose we own a health club and retrofit one of our ellipticals from ReRev at a cost of $1,000.

– If the national average price of electricity is $0.15 per kWh, how many 30-minute workouts would

there need to be before we recoup our $1,000 investment?

– Pedaling non-stop (24 hrs./day, 7 days/wk.), about how many years would that take?

5. During one particularly hot week in the summer, we leave our air conditioner on 24/7. It takes roughly 3

kWh to run our air conditioner. For the amount of energy used by the air conditioner for a

week, how many days (at 28kWh per day) would we have been able to supply electricity to

our house with the air conditioner turned off?

### Exercise converted to electricity – Teacher’s guide

Concepts:

Numbers, operations, rounding, fractions, decimals, scale conversion, dimensional analysis, scientific notation, ratio,

proportion, equations, real-world problem solving

Objectives:

Students will:

– Solve problems involving the multiplication & division of whole numbers

– Round whole numbers & decimals to a predetermined place value

– Multiply & divide both fractions and decimals to solve problems

– Convert between any two number representations (fraction, decimal, percent) without using a calculator

– Interpret & use ratios to show the relative sizes of two quantities

– Understand proportions and use them to solve problems

– Write & solve one-step linear equations with one variable

– Read, write, compare, & solve whole-number notation problems

Prerequisite skills:

Of the three prerequisites, two are mathematical and can be troublesome for some students- scale conversion and dimensional

analysis. The third, reading for information, is a specialized skill that requires practice and support across

all grade levels.

#### Standards

Numbers & Operations – Base Ten

– Perform operations with multi-digit whole numbers and with decimals to hundredths.

Numbers & Operations- Fractions:

– Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Measurement & Data:

– Convert like measurement units within a given measurement system.

Ratios & Proportional Relationships:

– Understand ratio concepts and use ratio reasoning to solve problems.

– Analyze proportional relationships and use them to solve real-world and mathematical problems.

The Number System:

– Compute fluently with multi-digit numbers and find common factors and multiples.

– Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide

rational numbers.

Expressions & Equations:

– Work with radicals, integers and exponents.

Time to complete

1 block period or 2 traditional (45-minute) periods

Teaching suggestions

The first 45-minute segment (Economy) might best be accomplished by pairing students and walking them through

each of the five questions. The second 45-minute segment (Ecology) is tailor-made for group work, and time for these

five problems could be expanded to accommodate presentations of the various solution strategies used.

#### Answer key: Economy

1. 17

2. 17, 59, 0.98

3. 27

4. 13, 11, 0.48

5. about 2:1

#### Answer key: Ecology

1. 10,000 kWh/year, 28,000 watt-hours/day

2. inaccurate

3. 2 hours

4. 133,333 workouts, about 7.6 years

5. 18 days

Visions of Exploration lessons are designed to enhance students reading, writing and comprehension skills, while introducing them to topics in science, technology, engineering and math. Each contains a recent article found in USA TODAY along with discussion questions and an activity. The lessons prepare students for the world beyond the classroom and inspire them to become explorers.

-Paul Wojcik, math teacher Millennium Middle School Sanford, Florida