How many different ways are there to make change for a dollar? As mathematicians we often search for patterns in a problem. However, for this problem, there is no simple, predictable pattern to build to an answer, encouraging participants to reach outside their comfort zones and ponder alternative strategies in order to make progress. This monetary problem is engaging, and classroom adaptable with multiple entry points.

Combinatorics
Number Theory
Problem Solving / General

Manipulatives
Multiple Representations
Problem Posing
Problem Sets
Try a Smaller Problem

MP1 - Make sense of problems and persevere in solving them.
MP2 - Reason abstractly and quantitatively.
MP3 - Construct viable arguments and critique others' reasoning.
MP4 - Model with mathematics.
MP7 - Look for and make use of structure.
MP8 - Look for and express regularity in repeated reasoning.