Students knowing the exponent properties is essential, more importantly, however, is knowing how they came to be. This task uses what students know about the definition of exponents as repeated multiplication and supports them in making generalizations from many example problems. Students are supported in connecting their understanding of the definition of an exponent to the properties that can be used to streamline the process. With an emphasis on finding patterns, using repeated reasoning, justifying reasoning and generalizing results, students will quickly learn the 6 most common exponent properties and be able to explain why they work!
Exponents Exploration:Exponent Explorations Task
Download: Exponents Exploration
This is a Level 3 task in that students are making connections between the exponent definition and the exponent properties. They are learning a procedure for simplifying which makes this a “Procedures with Connections” task. We are suggesting a method and supporting with a structure for how to determine these procedures, but we do not suggest a solution or a conjecture for each of the six suggested properties. Many aspects of this task maintain high cognitive demand because students will need to justify their work to generalize procedures.