When the first grade math students came to class today, I told them that I was going to hire them for a special kind of job lasting 7 weeks. The only thing the job requires is that you calculate your salary. What a deal! Even better, the kids get to choose their own salary from two options.
Option 1: You get $100 the first day, $200 the second day, $300 the third day, and so on. Each day you are paid $100 more than the day before.
Option 2: You get 1 cent the first day, 2 cents the second day, 4 cents the third day, and so on. Each day you are paid double what you were paid the day before.
The kids selected an option and circled it on their worksheet. All but two students chose Option 1 (lest you think those two had some special insight, they both claimed to have selected Option 2 “because it’s easier.”).
I ALLOWED THE STUDENTS TO USE CALCULATORS FOR THIS ASSIGNMENT. PLEASE let them use calculators at home! Please force them to use a calculator if necessary! For their sake, your sake, and mine.
Using our calculators, we started figuring out the salaries. We worked out the daily pay for week one for both Options, and then calculated the weekly total for both Options ($2,800 for Option 1; $1.27 for Option 2. The kids who picked Option 1 were feeling pretty smug).
I let the kids loose to work on their own. Most kids stuck with calculating daily pay and weekly totals for Option 1. A handful worked on daily pay and weekly totals for Option 2.
I told the students in class that once they get to about week 5 on Option 2, they may start to feel like banging their head against the table. THIS IS THE SIGN THAT IT’S TIME TO STOP. Please don’t force your child to finish if the numbers are unwieldy and your child is not enjoying the work. By week 5 or so of Option 2, they get the point — Option 2 yields waaaaaaay more money than Option 1.
I just want them to get a general understanding of how quickly doubling yields huge numbers. It doesn’t seem possible that starting with one cent would be the more lucrative option, but it sure is. With Option 1, the grand total is $122,500. With Option 2, a student would be making more than that per day by Wednesday of Week 4. On Sunday of Week 5, a student would be earning $171,798,656.00 per day.
The students were disappointed to learn that I would not actually be paying them this money. I only wish I could!