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:

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

And here are some places to find possible lessons:

• Mathematics Assessment Project 
  
• Illustrative Mathematics
  

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

Well, I'm back in the classroom! It has been 15 years since I've taught my own classes and I've been writing math curriculum for major publishers as well as doing some professional development for grades K-5. The writing has helped me ask the hard questions about mathematics and then find the answers. The PD in elementary school has given me a huge appreciation of elementary teachers! I no longer sit in my high school classroom "blaming" prior year teachers. You really can't know until you've been there. Why am I back in the classroom? Well, I've been writing to the common core standards for the last 2-3 years and I feel stuck. I don't like feel like I can write to the common core standards using the mathematical practices because I'm not actually teaching this way. I firmly believe in Richard Elmore's 6th principle for Administrators:

See Elmore's "Improving the Instructional Core" here: http://sim.abel.yorku.ca/wp-content/uploads/2013/10/Elmore-Summary.pdf

 Believe me, the publishers are having the same struggles as the classroom teachers when it comes to CCSS....how do we teach the content through the mathematical practices? Lots of good ideas are being developed and some which frankly, miss the mark. My fear is that districts will settle on curriculum that says it is "common core" without really testing it out. My advice is to be wary...see if it works for you and your students before you commit. There are so many free lessons and ideas through blogs and twitter, you can pick and choose. 

My passion has not only been about teaching math, but about how to help math teachers become better (and frankly happier) at what they do. 

Change can be a scary thing in the classroom. It can disrupt classroom dynamics, teachers must constantly adjust to new situations, and heaven forbid any administrator or other teacher drop in to your class when you are trying something new! It looks like chaos and observers often jump to wrong conclusions.

So, how does a teacher take that first step? It's scary...especially if you think you are all alone. But you aren't! Start talking within your own department to see if someone wants to join you in trying new things. No takers? Then start reading websites and blogs to find someone like-minded. Try a few activities...then comment on how they turned out. The ideal is for teachers to hold hands and jump! That might be in person or virtually. Combining forces with someone else means you'll go more than twice as fast and have more than twice the fun. Ivan Cheng from Cal State Northridge suggests this video for seeing where good ideas come from. (Thanks Ivan!)

Now, go find someone. Ask a colleague to view the video and see if they want to try. Sign up for twitter and just see what people are talking about. You don't need to post...lurking is fine. Type in "virtual file cabinet math" to a search engine and you will be amazed at your opportunities. Then give it a try...don't expect immediate success. Our goal is to create lifelong learners and to do that, we have to be that ourselves.