Longevity — Life Expectancy — Scientists and Mathematicians — Subtraction Standard Algorithm and Addition Method

After reading 15 math challenge poems from the world’s greatest poets, the children were interested in their biographies. Some focused on each poets date of birth subtracted from date of birth (e.g., Edgar Allan Poe 40, Lear 76, Whitman 73, Frost 89, Belloc 83, Carroll 66, Dickinson 56, Farjeon 84, Milne 74, Williams 80, Hughes 65, Silverstein 69, Ciardi 70, Nash 69).  These Mathlete inquiries inspired me to create a lesson teaching two algorithms of subtraction, averages, and life expectancy. 

Those poets died at an average age of 71, below the life expectance of their era. The statistics can be argued but the current life expectancies in the United States are 78, Japan 83 (one of the highest in the world), and Swaziland 26 (lowest in the world). The pdf I gave the children was of the top 47 scientists and all famous mathematicians since before 500 AD. I chose ten random mathematicians before 500 AD and added their ages and divided by 10; the average was 61.3 years. This was double the life expectancy of the time. Of course, I took this as an opportunity to make a conjecture that mathematicians life double the life expectancy of their time. We had lively discussions in each class about why that might be the case. The children postulated that mathematicians: have larger brains, can do better problem solving, make better decisions, create medicine to prolong life, and finally, they were less likely to go to war. We also talked about the concept of life expectancy as an average so there are half as many people who die under the age of 78 in the United States and half that die older. I gave them a prescription for increasing life expectancy to the high nineties if not greater than 100: 

1. Never smoke (I have read studies that suggest that this could propel life expectance to 94)
2. Avoid drugs (exceptions are medicine proscribed by a doctor and as an adult one glass of wine per day, etc. is actually preferred to none); the children were interested in what happens if you have 3 one night; I suggested that averaging is OK but that pacing is better; OF COURSE, I MADE IT CLEAR THAT THIS IS ONLY TRUE AFTER YOU ARE AN ADULT.
3. Avoid fast food whenever possible (McDonalds, KFC, BK, D-D); a couple time a year is probably OK.
4. This was my own addition—DON’T GET HIT BY A TRUCK; this is more metaphor than actual—make good daily decisions so accidents do not happen which could make steps 1-3 above mute.

NOW FOR THE MATH: The K-1st graders I just focused on standard algorithm with no borrowing. So I highlighted 12 of the 47 scientists on the list. Their job was to put the larger number on top and subtract the smaller number using vertical subtraction. I also highlighted three pages of ancient mathematicians who would only require standard algorithm with no borrowing. See the attached pdf.

For all other children, I wanted them to learn two algorithms. Having the children put the larger number on top was not an assumption we can make. This was our first focus. The first algorithm they need to master is standard algorithm with borrowing. The pdf for showed two examples with Einstein and Newton with borrowing. I encouraged them to do this for the first page of scientists. On the subsequent pages I wanted them to practice my algorithm of adding to subtract. Essentially, if we are determining the age of a person who was born in 1875 and died in 1922, we first determine the benchmark number of 1900. First we look at 75 and ask what number do I need to reach 100, which is 25. Then, we look at the 22 and add it to 25 to get 47. For Galileo (1564-1642), we add 36 to 42 to get 78. In the board room, the accountants use computers and calculators to subtract large numbers but 90% of the math we will do in the future will be small numbers in our head with the addition algorithm. 

The older Mathletes should also look at mathematicians in any era and chose 10 random people to find their average age.  Can they see a trend in the average life expectancy of mathematicians through the ages?