**Session Author: **Penny Dunham

The divisibility rules are often “accepted without proof” by both teachers and students. The problem explored in this session involves a rich, novel way of looking at “amazing numbers,” to authentically develop notions around patterns of divisibility as a solution strategy.

“This session offered opportunities for the group to use a wide range of strategies, depending on which approach a person chose in solving it. Some gravitated toward abstraction, which perhaps tilted their work toward MP7 and 8 in an algebraic sense. Others did more with modeling. All of us were involved in arguing, sense making, reasoning abstractly, and precision. All of us looked for structure and tried to apply repeated reasoning, but (as noted) some did so verbally and others with algebra. Tool-use depended on whether you used an organized list, table, visual model, or algebra.”

#### Resources

#### Categories

**Strategies:**

Try a smaller problem, Problem posing, Multiple representations**Topics:**

Algebra / Arithmetic, Number theory**Styles:**

Illustrates a concept, One rich problem**Mathematical Practices:**MP1, MP2, MP3, MP4, MP5, MP6, MP7, MP8