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

Sunday, February 21, 2010


Don't be surprised when students ask why learn exponents? When will they use exponents? and so on...
At the beginning of each unit topic, students should have a good overview of at least three things:
- Starting point: what they already know about the topic (assessing experiential knowledge) ... Where am I?
- Destination: how is the knowledge useful (applying new knowledge, connecting to real-life experiences) ... Where am I heading? 
- Journey: what will they be learning (exploring knowledge content, examples, archiving knowledge) ... How do I get there? 
This overview will help students to become aware of their learning goals, interests, and questions related to the topic. 
- The examples used (for teaching and explaining concepts) should be challenging, intellectually stimulating and interesting to students.
- Help students to become familiar with applications of knowledge in contexts outside of mathematics.  

Saturday, February 20, 2010

Student Misconceptions

Common mistakes that students make ...
Multiplying base and exponent
Applying distributive law on exponents
Anything to the power of "zero" is 0
Scientific Notation! A negative on an exponent and a negative on a number (are they the same?)
Equating a negative on an exponent and a negative on a number are equal
Don't make these mistakes ...


Commonly asked questions ... 
  1. What is exponents? 
  2. How to read an? 
  3. What is x½
  4. Which models facilitate understanding of the concept [of exponent multiplication]?
  5. How is exponents useful?
  6. How is exponents useful in everyday or real life? Give some examples...
  7. What are some real world applications of exponents?
  8. How is exponents connected to other topics in high school Math? 

Friday, February 19, 2010

Understanding Multiplication of Exponents

There are at least three ways of explaining multiplication of exponents. We present these ways (as instances) using the repeated multiplication model. Using this model, we can derive and explain the multiplication law of exponents. 

Instance 1:Area of a 2D shape – SQUARE
Instance 2:Volume of a 3D object – CUBE

But what if the bases of the exponents being multiplied are different?
Instance 3:Different Bases

Instance 3a: Different bases; Bases with a LCF (lowest common factor)
Instance 3b: Different bases; Bases with a LCF (lowest common factor) and a coefficient
Find out more ...