Our Goal

"Understanding Multiplication of Exponents"
To create an instructional sequence (a.k.a. lesson plan) featuring:
- different models to present the concept
- select problems to facilitate student understanding
- explanations to bring about student understanding
- common student misconceptions
- ways to address misconceptions
- connections to real world experiences
- connections among mathematical ideas

Lesson Plan for Junior-High School Exponents

Lesson Plan for Junior-High School Exponents
A concept-map of multiplication of exponents

Instances and Non-instances

What's in and what's out? What is the scope of our explanation and illustrations in this blog?

Instances are what (examples, concepts) we consider to be in the scope, and non-instances are those outside the scope of our discourse. 
Our goal is to develop deep conceptual understanding and procedural fluency at exponents and multiplication of exponents. The table below provides examples of various exponential forms (powers of) in the instances and non-instances.
Scope: Multiplication of exponents


Power (an expression of): Xy
pronounced as:
“X to the power of y,” or
“X to the y,” or
“yth power of X”

Examples: 23, 42, 165, 1031                                                                                                                                                                                                                                                                                                                                                                              
Model (for explaining instances): repeated multiplication 
Base: positive integers (e.g., 1, 2, 3, 4, 5)
Exponent: positive integers


Examples: 05, -24, 6-3, 00, -e1.8, (-8/9)1/3 , 0.56-1/3
Model (for explaining non-instances): 
repeated division, ...

Base: variables, real numbers (e.g., -1, -22, -1/2, -5/9, 73/4, 3.142, p, 0.7, e, √2)
Exponent: negative integers, fractional, decimals