*“The publication in 1687 of Newton’s Principia Mathematica established mathematics as the methodological paradigm of theoretical science. Newton perceived patterns in the accumulated astronomical data of his time; he abstracted from these patterns certain general principles (whence Principia); then he used these principles to deduce patterns both known and unknown in the behavior of planetary bodies. His was a science of patterns rooted in data, supported by deduction, confirmed by observation.” Lynn Arthur Steen, 1988*

Choose an Experiment. If you are new to spreadsheets or to Excel, we suggest you start with Basics: Ins and Outs introducing spreadsheets, and then Basics: Times in 2 Steps to learn to use copy and paste and relative vs. absolute addressing, a critical spreadsheet concept. You will quickly become a spreadsheet maven. Then choose any Experiment that interests you. We have more coming so keep coming back. Enjoy and let us hear from you.

**Submit your Spreadsheet Math Experiments on our Experiments Template**

## Lights Out: Pulling Chains

One of the most interesting mathematical puzzles has a long corridor with lights in the ceiling, each with a chain to turn it off and turning on those lights that are off. If there are 100 lights and persons, which of the lights will be on when everyone has had their turn. The first person walks through the hallway and pulls every chain turning all of the lights on. The second person pulls every other chain turning every other light off. The third person pulls every third chain turning off those lights that are on and on those that are off. After the last person has gone down the hall, which lights are still on? This puzzle has a tremendous amount of math in it.

**Art Bardige, Sustainablearning with the help of Chuck Olson from a Puzzler on Car Talk**

## Napoleon’s Pyramid

Napoleon’s Pyramid Spreadsheet

Was Napoleon right? In 1798 Napoleon conquered Egypt and brought his officers to the Great Pyramid of Giza. While his young officers climbed to the top, he sat in the shade and figured out that there was enough stone in the pyramid to build a 3 meter by 1/3 meter wall around the whole of France.

*Credits: Art Bardige, Sustainablearning, based on a lesson by Professor Len Vacher, University of South Florida*

## Basics: Ins and Outs

Basics: Ins and Outs Spreadsheet

We introduce Excel to students through getting them to model a business. Ins and Outs directs students to think of models having Inputs and Outputs, the essential ingredients for thinking about spreadsheets as function machines. Students learn the basic vocabulary and actions of the spreadsheet, to use and construct formulas, and to build tables. We emphasize proper table etiquette which includes heading for columns and rows, as well as units. And we emphasize beauty, making tables look good and easy to read.

Credits: Larry Reeves, Sustainablearning; Art Bardige, Sustainablearning

## Basics: Times in 2 Steps

Basics: Times in 2 Steps Experiment

Spreadsheets give us two ways to address cells, relative and absolute. These are powerful ideas that make spreadsheet math very efficient enabling us to build even complicated spreadsheets rapidly and with fewer errors. Here we introduce these two forms of addressing by seeing if you can make a multiplication table in just two simple steps. This is part of the Excel Basics series.

*Credits: Art Bardige, Sustainablearning*

## Good Times

Times tables can be magical places. Make a times table with your spreadsheet. Now draw a clear rectangle on it, any size or shape around any of the products. Now, multiply the top right number in the rectangle by the bottom left number. Then, multiply the other two corners together. You will find these corner products equal to each other no matter what the shape of the rectangle. Is that true for every rectangle you draw on a times table? Why?

*Credits: Art Bardige, Sustainablearning*

## Odd Times

Everybody from 2^{nd} grade on has learned the multiplication facts, the 12 by 12 multiplication table. Yet no one that I have talked with has ever been asked this simple question about it. “How many of the facts in the 12 by 12 multiplication table are odd numbers?” Now you may think this a silly question or one that has little value. It is, as you will find, not trivial or silly. Now tell me what you think.

*Credits: Art Bardige, Sustainablearning*

## Repo Man: The Loan

Part of the Financial Literacy series, Repo Man deals with getting a car and taking out an auto loan. We approach the problem from its very basic definitions of principal, interest, and time or term to setting up a spreadsheet to determine how much the car of your dreams will cost you. You will learn the difference between a Simple Interest Loan and an Amortized loan, and how to keep the Repo Man away from you.

*Credits: Art Bardige, Larry Reeves, Peter Mili, Corri Taylor, Sustainablearning*

## The Chessboard

Chess was invented in India about the same time as our Arabic number system. We retell the folktale about the Ruler and the inventor of chess who asks, in return for his invention, for only the amount of rice a chessboard would have if the number of grains were doubled in each square. We ask you to figure out who would be happy with that prize, and we ask you the What if question. What prize would they ask for?

*Credits: Art Bardige, Peter Mili, Sustainablearning*