On other websites:
[ A fixable percents-error in emission cuts by 2030 and by 2050; also qualitative feel for students: peak.exports.html]
Under on-going construction and revision.
Enhancements and new additions to come! Corrections, typos, suggestions and requests welcome!
Environmental Mathematics
for
Quantitative Literacy (QL)

Activities for students/groups of students, and resources for teachers, by Dr. Harel Barzilai

  • New! Overheads (PDF) by Dr. Troy Banks from a talk-and-workshop he gave at Trinity College, with problems, he indicated to me, being based on materials I developed, many (not all) of which appear on this website.

  • Jan 2009 Joint Mathematics Meetings Overheads Part I and Part II by Harel Barzilai.
  • To be added: some type of Creative Commons CopyLeft; some protection from students seeing solutions.

  • Wk1 HW: Introduction to Google Calculator (useful tool for rest of course for HW, for Final Project..)
  • Wk1 HW:Paper Recycling (Back-of-envelope Estimation, comfort with large numbers)     [Solution here ]

  • Visualizing Large Numbers: Oil and Surface Area and Solution here
  • Wk2 HW:Visualizing Size and Scale ; Wk3: Time & Large Numbers
  • Interpreting news articles on sea level rise (units conversion, inter-article comparisons, gen. QL)

    Introduction to CO2 and Global Warming

    In-class (multi-day) activities for groupwork, discussion, and finishing for HW:
    1. CO2 levels: Using Lines and Slopes Finding slopes numerically (y2-y1 ÷s; x2-x1); estimating visually by using ruler to connect two points ; advantages/disadvantages of numerical vs. graphical data; and related quantitative/graphical literacy.
      Partial **Solutions** (in red font in link)
      Partial explanation (see also here) for why rate of increase for CO2 temporarily slowed around 1990.

    2. Worth 1000 Words? Graphs and the Environment will update image IA (and text) to reach 2014
      Background information: After additional research expanded data from 400k to 650k to 800k years.

    3. For class discussion/HW, graphical literacy question: in this image (backup here) why does the "Red" portion look big in one graph and small in the other?? Why does the graph where red is smaller have the "black part" larger??

    4. For class discussion or HW: "How many times faster is CO2 increasing now, than the fastest it has ever increased in the last 800,000 years, according to the BBC story in link C under "Optional Supplemental Reading" in Worth 1000 Words? activity HW followup? How much faster is CO2 currently increasing than the fastest previous increase in the 800,000 year record given that:
      The "scary thing", he added, was the rate of change now occurring in CO2 concentrations. In the core, the fastest increase seen was of the order of 30 parts per million (ppm) by volume over a period of roughly 1,000 years. "The last 30 ppm of increase has occurred in just 17 years. We really are in the situation where we don't have an analogue in our records [[BBC]

    5. Overhead CO2 not only at peak levels, but rate-of-increase is at peak.
           Rates of change: they matter overhead: why it's often important to look at not only the Quantity you care about, but also to look at the rate of change of that quantity (see also rates of change of Acidification)

    Percents

  • General Background:

  • Mastering Percents: A Quantitative Literacy Exploration (For HW or part done in groupwork in class, then continued for HW, and finalized in followup class/discussion)     [Solution here ]
  • Non-enviro practice: Percent Increase/Decrease     [Solution here ] (Housing Prices)

  • Percents and the Environment:

  • Efficiency and Waste Heat: Waste heat     [Solution here]

  • What Percent Savings? (with hints)     [Solution as can be outlined for students here ]

  • HW: How can a 20% 'cut' equal a 2% increase?!?     [Solution here ]

    Proportions

  • What's Your Consumption Factor?     [Solution here ]
        [A second Solution proving the "doubling" and using more standard proportions; is in pencil and will be uploaded here!] Another example cited in JMM presentation

  • Hypothetical "Project Section" as Homework: Annual Tons of CO2 HW plus, "scaffolding" which helps students get started on how their final course Project might look like.     [Solution here ]    [More Comments]

  • ADD: SECTION WITH GENERAL-QL NON-ENV .AND LINK TO "TIEM SCALES" AND LINKS TO TO PDF'S (ALREADY IN THIS DIRECOTORY, *time-sca*)

  • Warmup: Calculating MPG
  • HW: Surprisingly many ways to Graph Your Driving     [Partial Solutions here ] [comments] New Solution: [PDF solutions part III and IV] [ COMMENTS HERE ON DISCUSSING 'DIMINISHING RETURNS' WITH CLASS] **Hints and Tips***

  • Coming: A great MPG problem/class discussion modified from Mother Earth News.

    Exponential Functions

  • Generating the Generations: Modeling Exponential Growth a sometimes surprising new twist on the traditional "what will Earth's population be in N years?" problems.
  • China's Growth

    Introduction to Peak Oil

  • "Rock Oil, Rock Oil, everywhere"     [Solution here ] Was not used in Enviro-QL course due to lack of time; was authored as (and used in an SU environmental history class) part of local QL-Across-the-Curriculum grant

    →Resource for instructors: Peak Oil is less well-known that Climate Destabilization ("climate change") but of critical importance. Primer: What is Peak Oil?

    Other Materials

  • Screening Mammography (QL and Mathematical Modeling)

        [Partial Solution (don't peek until you try to solve, good to experience students' view!) to Mammography Screening is here ]

  • HW: How high would your annual household energy usage lift the Statue of Liberty?     [Solution here ]

    Other Misc. Materials
    (Used in other courses, but no time to use them in this course, during Spr 08 semester)

  • Save the Pups! There's more to max/min problems than "minimize fencing" or "maximize profits"!! (Featured on RadicalMath.org)     [Solutions here using algebra (if vertex form of parabolas is known) [Also solutions using calculus and, if you insist, using Calc III]]


    See also:
  • Archive of Reform Calculus Resources (indexed by the Math Archives since the 1990s)
  • College Algebra / General Lib. Arts math .

  • Math and social issues (justice, democracy, etc) (coming soon)

  • Tribute to Black Mathematicians (Created in 1999 for Black History Month)



  • Notes to self 1) quantitative economic environmental analysis: "uneconomic growth" see index of Herman Daly
  • Arctic ice: Look at not just area but volume, which incorporates ice getting thinner not just less coverage, and the graph is more drastic than the area graphs that the media (if they show any graphs at all) generally include.