Picasso’s Cuboids (MathPickle, 2016)
This puzzle sequence gives practice in volume calculations. Here is a classroom presentation.
After looking at the presentation above, you may choose instead to use an area variant of the puzzle. In this case, for an integer n, you would be searching for four variables
a ≧ b ≧ c ≧ d
a*b + c*d = n
and c*d is as large as possible.
You may also wish to experiment with a hybrid of volume and area… a ≧ b ≧ c ≧ d ≧ e such that a*b*c + d*e = n or a*b + c*d*e = n
Please be the first to email me about how this puzzle worked in your classroom: gord at mathpickle dot com
Standards for Mathematical Practice
MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:
MP1 Toughen up!
Students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.
MP2 Think abstractly!
Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.
MP3 Work together!
Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.
MP4 Model reality!
Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.
MP5 Know the tools.
Students master the tools at their fingertips - whether it's a pencil or an online app.
MP6 Be precise!
Students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.
MP7 Be observant!
Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist 😉
MP8 Be lazy!?!
Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?