Math mind hacks: start with answers, ask for problems

Math Mind Hacks is a series of mini-posters about quick, smart activities that grow mathematical minds. Today’s hack is inspired by a story Gregorio Morales told in response to my interview 5-Year-Olds Can Learn Calculus:

I work with children 12-16 years old. My idea is to incorporate creativity in their mathematical works. For example, one of the activities I use is to show a number (for example, 9) as the answer of a problem, and then I ask them for the problem. At first the problems are rather weak: “I have 4 apples and Peter gives me 5 more, how many apples do I have now?” But as the class goes on, some very beautiful problems arise. Maybe another day the number is 259 and they find it harder to come with a nice problem. And another day I go to class with the number 1278513. It’s incredible how many mathematical concepts they are able to invent in order to find a beautiful problem whose answer is my given number.