Sustainability and Climate

1. The End of Oil— When will all the oil reserves of planet earth be consumed?  How important is it for society to transition to renewable fuels?  How are projections made? What is the value of math as a source of truth?  Math topics:  Geometric series and sum formula, scientific notation, exponential functions and equations, solving multi-step equations.
Student handout
Student Analysis and Reflection
Critical thinking reference
Teacher guide
Oil Consumption Growth Rate Change–Historical
Problem solution (notes)
Practice Problem–Shipwreck
Sum formula intro activity–Gummy bears
2. Electricity Consumption/cost Calculation–How can any facility, a home, business, school, etc. reduce its energy consumption, lower its footprint and reduce cost of operation?.  Math topics:  Unit conversions, units of energy, rates, setting up equations, solving multi-step equations.
Student HO
Problem solutions
Appliance wattage chart
3. Global Population and Ecological Footprints–What is an ecological footprint and when will humanity reach carrying capacity on Earth?  What can be done to reduce per capita ecological footprints?  What is the relationship between standard of living, population, land area, and a nation’s ecological footprint?  Math topics:  Proportions and ratios, scientific notation, creating function models, solving multi-step equations.
Student Handout
Best Paycheck Deal–exponential function creation
Teacher Guide Part I Problem 1
Problem solutions for remainder of packet
Solution-Part I Problem – Population Brain Twister (one person per square foot of earth)
4. Ocean Fisheries–What dynamics and parameters are in play for sustainable ocean fisheries?  What economic decisions and geopolitical implications are inherent in managing ocean fisheries?  What does civilization need to pay most attention to in order to preserve the future of ocean fisheries?  Math topics:  Solving multi-step equations, creating math models, estimation.
Student Handout
Problem solutions

5. Concentrated Solar Energy Technology–What are the physical principles in play in solar thermal electricity generation and how can a collector be designed?  (In this problem the student will create the mathematics to design a solar thermal collector).  Math topics:  Analytic geometry, distance formula, locus definition of a parabola, solving quadratic equations.
Student Handout
Student Handout with strategy
problem solutions

Physics and Engineering

1. Golden Gate Bridge Cables–How are the lengths of suspension cables on a suspension bridge calculated?  How long are the cables of the Golden Gate Bridge in San Francisco, CA? (In this inquiry the actual plans of the Golden Gate Bridge are used as a resource to perform the calculations). Math topics: Equations for parabolic graphs and circles, manipulating algebraic formulas, calculation.
Student Handout
Solution
2. Time Dilation and Pendulum Wave Machine–What are some of the discoveries that made Albert Einstein famous?  What is the theory of relativity?  What is the relationship between time, mass and velocity for any object?  Can that be measured and calculated?  How do we know it is true? Math topics: transforming algebraic formulas, evaluating expressions, solving algebraic equations. A problem for designing a pendulum wave machine is attached to this post as an “extra” item.
Student Handout

Special Problems

This category emphasizes logic, creative problem solving, ingenuity, and perseverance in an assortment of open ended problems. This type of classroom work has often taken the for of “problems of the week”. TheseMath topics: creative problem solving, calculation, multiple representations, strategy development, and much more…

1. Teacher support–rationale and strategies for open ended problems
2. Checkerboard Squares
3. Commuter Train
4. Commuter Train help
5. Corey the Camel
6. Its All Gone
7. Who’s Who
8. Bobo and the Train
9. Tangent Circles
Tangent Circles Solution
10. Problem Report Write-up guide
11. Fractal Geometry-The Koch Snowflake:  What are fractals and why are they useful?  How does one create a generalized formula from a pattern?  How can an infinite series equal a finite number? Math topics: perimeter, area, iteration, generalizing pattens in sequences
12. Special Problem Answers and strategy notes

Context Setting Materials