Tag: ratios and proportions

Fibonacci’s Sequence

Fibonacci, the nickname given the great medieval mathematician Leonardo of Pisa, is connected in most of our minds with the Fibonacci sequence. Spreadsheets make wonderful tools for creating such sequences. This one is amazingly simple. Just select a cell, any cell and write a formula in that cell that adds together the two cells above it. Now copy that cell down the spreadsheet and seed it with 1 in the first cell. The Fibonacci sequence is a pattern that this action shows very well. This sequence has surprising attributes, and we explore some of them as well.

Rate of Growth

We look at world population over the past 60+ years and ask whether the earth’s population is growing faster or slower today. Is it out of control and something we should all worry about or are we getting it under control? This is another problem directly related to climate change and one that students can argue with each other about. We use this opportunity to ask students about which kind of graph or chart would best convey the issue to other people. The type of graph or chart to be used to convey data is of great importance in business and industry today and one that requires students to creatively ask What if… about.

CO2 Growth

Spreadsheets offer us a nearly unlimited ability to develop and learn from case studies using real world data. We will focus mainly on climate change which is an area rich in possibilities and of great interest to students. In this case study we look at the production of carbon dioxide per person in the United States over the past 200 years. We take this opportunity to introduce students to the difference between quantity and growth, between the amount of CO2 produced and the year-to-year growth in production. We challenge students to consider whether this growth is an increasing problem.

Pennies to Heaven

Pennies to Heaven is a Fermi Problem, basically a “headmath” experiment. Fermi Problems, originally developed by Enrico Fermi, one of the greatest experimental and theoretical physicists of the 20th century, are real-world estimation problems. So we ask, “If we had a stack of pennies as tall as the Empire State Building, how big a room would we need to hold them?” Like most Fermi problems the answer to this one is a delightful surprise and requires us to think out-of-the-box. Always ask, “What do you guess?” “Would you need a whole house or something bigger, just your bedroom, or a closet, or something even smaller?”

Decimals and Percents

Ratios can be written in a wide variety of different way: as fractions, as decimals, and as percents.,with a colon, with a slash, as a fraction and even as a baseball batting average. Here we compare a decimal ratio and a percent by building decimal and percent tables in the same way and compare their patterns to the ratio patterns we are used to. Ask students what other ways of expressing ratios are there.