The best task!

In my few years of teaching, I've shown a number of 3Act tasks or similar and I have gotten mixed results.  But there is one task that I've always had a lot of success with.

Tell students that they are getting a contract of employment.  The contract is going to last 30 days, 5 days a week.  On the first day of their contract, they get $0.01. That's right, 1 cent.  On the second day, it doubles. Now they get $0.02.  On the third day, it doubles again and so on and so on.

Goodbye, Canadian penny

How much money do you think that you will make after 30 days?

I usually start off by handing out the contract, having kids fill it in and then asking them to write down their best guess.  Answers usually range from $10 to $1000, but not much over.  Then I ask them to fill out a chart with how much they are getting paid per day and how much they're getting paid all together.  They start to get to work because they all have calculators and it just seems like easy button pushing.

Then the  magic happens.

At some point some murmuring begins to happen in the classroom.

"Is this what you  have?"  "This can't be right" "Oh my god" "This is crazy!"  "I want this job"

Not a single student isn't frantically trying to figure out how much money they're going to make.  Every single one of my students is engaged in the task.  Everyone wants to know the answer.  How much money are you going to make?  On the last day you make about $5 million.  Altogether, about $10 million.

I do this task every year and I always get great results.  I attribute it to a couple of things:

1. Low risk.  No one knows what the answer is so everyone's guess is equally valid.

2. Simple calculations.  Not everyone can calculate terms in a geometric sequence or series, but everyone can type *2 on their calculator and hit enter.

3. Interest.  The task is genuinely interesting, students get invested in the idea of getting paid this way.  Some even propose that they're going to suggest it to their boss.

This is an extremely powerful task for introducing geometric sequences or series.  The follow-up question is: Is there an easier way to figure out how much you can get for the 30th day without having to write out all the previous days?

It's fantastic, I love this task.