I'm going to follow the same procedure as I used when writing a lesson for publishers based on CCSS. The first chapter I'm teaching is exponents. The textbook starts with zero and negative exponents, then standard notation (yikes), then all the multiplication properties of exponents (power of power, raising product to power, raising quotient to a power, etc.) The chapter test for the text has the usual complicated expressions with powers, negative exponents, etc. The test asks students to simplify, evaluate, and write numbers in scientific notation.

I start by finding the CCSS that seems to address exponents in Algebra 1 and find:

**Extend the properties of exponents to rational exponents.**- CCSS.Math.Content.HSN-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
*For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5*. - CCSS.Math.Content.HSN-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Next, I check the Progressions documents out of University of Arizona at http://ime.math.arizona.edu/progressions/ for an explanation of these standards. The Progressions documents seem to be the "go-to" documents for teachers and publishers alike. These are in draft form so you should continue to check back periodically for changes.

Darn, I don't see a draft for High School for Numbers but I do see something for Grades 6-8: Progression on the Number System. Then I notice the draft for Grades 6-8 also says High School: Numbers. Yay! (Lesson learned...keep looking.) Go ahead and read the paragraphs for High School Number right now. (This is the only time I will embed for you as these are changing documents. Use the link at right to get to Progressions anytime.)

The progressions document gives me an overall view of exponents as well as why the standards writers connected it with properties of rational and irrational numbers. I'm especially happy that it is noted that the distinction between rational and irrational numbers in applications of mathematics is irrelevant since we always deal with finite decimal approximations. But thinking about the distinction is good practice for mathematical reasoning. So, we've satisfied theoretical mathematicians and applications based mathematicians.

Nice overall view, but what does this mean for my lessons? Here are some education sites I've found helpful when trying to determine what concepts to cover:

And here are some places to find possible lessons:

- Oregon (references other states too...why reinvent the wheel?)
- North Carolina
- Ohio
- Arizona

And here are some places to find possible lessons:

Stay tuned...the next posting will explain what I created to teach exponents in Algebra 1.