Mathematics: Curricular Overview
Concept  Example #1  Example #2  Example #3 

Geometry: power of deductive reasoning  Thales and pyramid of Giza  Eratosthenes and circumference of earth  Chinese proof of Pythagorean theorem 
Statistics: chance  Birthday Problem  Odds of rolling a 3 versus a 7  Simpson’s Paradox
Bayes Rule Base Rate Problem 
Exponential Growth  The rice on the chess board  Paper folding  Inflation 
Calculus: optimization  The optimal size of a can  The camel problem,
Dido’s problem 
The pipeline problem 
Magic Numbers  Pi – what is so special?  The mystery of e

Can you visualize i? 
Scaling  First power lengths  Second power–areas  Third power
volumes 
Counting  Taxes + virtues +
Income + 
Cooking ingredients  Good deeds per day; smiles; kind words 
Calculating  Ratios: santa/Grinch
Real versus reported earnings 
Real versus nominal returns, pre tax versus after tax returns  Discounted versus non discounted cash flows or reported debt
And real debt 
Ethics of mathematics  Is economic inequality a measure of injustice?  How to distinguish between factors behind ethnic disparities?  How to measure factors behind gender disparities?
What is a fair interest rate to charge a sibling? 
What is the biggest hole you can cut into an 8 by 11 piece of paper?
How many piano tuners in Chicago?
How does Social Security work?
How does the welfare system work? (EITC, minimum wage, TANF, Medicaid)
What is the difference between the Federal budget deficit, the Federal debt, and the real debt of the federal government?
What is the difference between real and nominal interest rates and return?
What is bracket creep? Why are benefit payments inflationadjusted and tax brackets are not?
Which numbers are highlighted and which ignored by proponents of a flat tax?