This puzzle activity is designed to make the properties of the real numbers (field axioms) more explicit by having students work with them in an unfamiliar setting so that they cannot rely on memorization. The example field is a finite field with five elements. The emphasis of the activity is on the properties of identity and inverse which cause students the most conceptual errors. To a lesser extent, students will practice with the commutative and associative properties.
scratch paper (optional)
add small integers
practice the field axioms (except distributivity) conceptually with an emphasis on additive and multiplicative inverse
engage in abstract mathematics
encounter a number system other than subsets of the real numbers
practice pattern recognition