This activity is intended to allow students the opportunity to explore and hypothesize about the rules of divisibility without being told. There are two sheets for each rule for 2, 3, 4, 5, 6, 9, and 10. One sheet is printed without clues, and the other sheet is printed with clues. You can use these to differentiate the activity based on the level of your learners. You may want to model completing one of the sheets for your students so they can see your expectations. Students are required to use evidence from the two lists of numbers to support the rules they develop. In addition, there is a quick reference sheet (sheet of 4) for students to put in their math notebooks once you have gone over the students’ discoveries about all of the divisibility rules. Finally, you can allow your students the chance to apply their new rules by assigning the worksheet, or use the task cards (which are the same numbers that are published on the worksheet) and recording sheet in a mix-freeze-pair type activity or at a center.
20 Task Cards with Recording Sheet
Quick Reference Guide
2 Differentiated Discovery Sheets (one with clues; one without) for Rules 2, 3, 4, 5, 6, 9, & 10