**Egyptian Fractions**

##### (Graham, 1964)

The first “greedy algorithm” introduced in this video is a good way to give your students practice finding common denominators, but be * very* careful which you choose. As the video shows, these can get nasty!!! If you are brave, I suggest you try solving the following greedily using the algorithm described:

2/20, 3/20, 4/20, 5/20, 6/20, 7/20… 18/20, 19/20.

What other denominators under 20 give reasonable challenges – and which are just too ugly?

Don’t even think of exploring the second algorithm 😉 Ugly!

Mathematics is the most beautiful and most powerful creation of the human spirit.

**Stefan Banach**

**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.