## 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
Shipwreck problem solution
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.
Teacher Guide–Outline and Inquiry Logic Line
Student Handout
Best Paycheck Deal (supplement support problem)–exponential function creation
Teacher Guide–Solutions, Part I Inquiry # 1
Teacher Guide–Solution for Population Brain Twister problem
Teacher Guide–Problem solutions for remainder of packet
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

Sustainability Context Background Resources:

2. Sustainability overview slide show pdf
4. Climate change tutorial slide show
5. “State of the World” 2020
6. Sustainability and Climate curriculum and information portal link
https://scottbeall.com/climate-and-sustainability-course/
This link contains a wealth of resources from a climate and sustainability course I’ve taught over many years and implemented in classrooms. Most recently it was used in a MHTC course. Some of the materials require PD course support for meaning and usefulness, however much of it is stand alone and useful without any PD support.

## 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

## Integrated Music and Mathematics

This link brings you to resource portal for a set of activities from my book Functional Melodies–Finding Mathematical Relationships In Music. The activities are primarily designed to be used as supplemental enrichment in a mathematics class, to make math concepts accessible for students through various musical contexts. The curriculum is highly adaptable however to flip this emphasis and use mathematics as a vehicle to teach music. Most of the book is available here as pdf downloads, along with a link to 89 audio tracks. Implementing this material is best accomplished with a PD course, however the materials have detailed teacher plans that, with some prep time, can allow implementation without any PD support.

## Student Interest Based Original Projects

This option allows students to reflect on their values, interests, curiosity and aptitudes, and research or create a math application or connection around an interest area of their choice. Provided below is an interest survey and a planning document to use for such a project. The planning document contains a sample list of actual student generated topics from an 8th grade classroom at. H.H. Wells Middle School in Brewster, NY.
Student Interest Reflection
Planning guide

## 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…

Multi Step Inquiry Problems

1. Checkerboard Squares
Checkerboard for working
2. Corey the Camel
Corey solution-max number
3. 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
Koch Snowflake Elementary Version
4. Best Paycheck Deal (supplement support problem)–exponential function creation
5. See “Sustainability and Climate” problems above

Stand-alone Single Problems

Support Activities and Resources