Full Glass – multiplying fractions

(MathPickle, 2013)

In a bar I once overheard the proverbial argument “glass-half-full” versus “glass-half-empty.” A second later my own beer arrived and the waiter inexpertly poured it with the beer glass at the wrong angle so the foam over-brimmed the top of the glass. The waitress was apologetic, but I waved her away – my lips desperately sipping the overflow.

It got me thinking about the speed and angle of beer delivery, but by the end of the evening my friends were faking enthusiasm for this new puzzle.

They made me promise not to call it the “beer-half-full-glass puzzle” and I decided to take their advice.

The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

Bertrand Russell

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!

This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP6 Be precise!

This is where our 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!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.


Please use MathPickle in your classrooms. If you have improvements to make, please contact us. We'll give you credit 😉

Gordon Hamilton

(MMath, PhD)


Lora Saarnio