Problem solving with exponents



A related, and more generic, question is:



Open-ended problem solving: Make the largest possible number

Use the numbers 2 and 3 only once (but any combination of mathematical symbols you know), make the largest possible number you can. Make the smallest possible number you can. Make a number as close to zero as you can.

Bonus, use any numbers you like, and then look for patterns between the numbers. In general, which collection of operations will produce the largest number for any two given initial numbers?

Thanks to Michael Pershan for the idea.

Open-ended problem solving: Fermi problems


Some examples of Fermi problems are:

How many phone books are delivered in NYC?
How many piano tuners are there in the United States?
How many different civilizations like ours exist in our galaxy?



Open ended project: Investigate facial recognition algorithms


  1. Investigation phase:


  2. Problem posing:


  3. Experiment
  4. Share results


Open-ended problem: How likely is it a quadratic equation will factor?

This question comes from Professor Wright via Twitter:

When Professor Wright means factor, he means, be written in the form (dx + e)(fx + g) with d, e, f, and g all being rational numbers.

Here are some questions to extend this investigation:

How often does ax2+bx+c factor with rational values of a, b, and c? Does the range of numbers we choose to look at matter? What if we allow d, e, f, and g to be irrational numbers? How often does this factor if a is 1? What if a is 2? Is there a relationship between the value of a, and the likelihood the quadratic function factors? Can you write a computer program to test out your hypothesis?

Open ended: Creating Arrays








Open-ended: Perfect Numbers

A number is called perfect if the sum of the proper divisors is equal to the number. 8 is not a perfect number because the proper divisors of 8 are 1, 2, and 4, and 1 + 2 + 4 = 7, which is not 8.

Can you find a perfect number? Can you find all of the perfect numbers less than 1000? Could you write a program to find all of the perfect numbers smaller than a million? Is there a largest possible perfect number?