[Unit Overview] Exponents and Radicals

Here is a brief overview of the unit I just finished on exponents and radicals.  Because of time, I did not do everything as thoroughly as I would have liked to.  However, I feel the structure is something that I can hold onto and build on for next year.

Evaluating Exponents and Radicals:

I got the idea for this structure from Sarah Hagan at mathequalslove.blogspot.com.  Here is her post on Radical Radicals.  I liked this idea so much that I decided to apply it to exponentials as well, even though my students knew more of the vocabulary that goes along with them.

Front

Back

Front

Back

We still struggled with knowing what the word evaluate means.  That is something I hope to work on a lot more at the beginning of next year:  vocabulary like evaluate, simplify, solve, expression, equation, etc.

My File

Properties of Exponents/Simplifying Exponential Expressions:

I got the structure for this lesson from Lizzy-Sensei at dontpanictheansweris42.blogspot.com.  Here is her post on Exponent Rules.  I loved the structure of it, but I didn't want to print an entire page for each student for each rule...so I changed it to a half-page structure.  I also noticed that my students would fill out the table, but then stop without answering the questions.  That was frustrating to me, and I don't know how to make it better for next time.  Also by the time we made it through all the properties the students were really bored of that structure of the lesson.

However I do know that I would plan on formatting it just a little bit better for my notebooks next year.  Also need a box around where we actually put the rule, because when I had them look back in their notes for the rule, they didn't know where it was.  I'm also thinking about reorganizing the columns in the zero and negative exponent property ones because students kept thinking that the rule should connect the first and the last column, rather that the ones that showed the zero or negative exponent.

Also students struggled to put what they had learned into practice.  It seems that they needed much more practice as they went.

My File [Reformatted as a Book]

Translating between Exponentials and Radicals:

I did an intro to try to help show WHY this is true, but I don't think it was very good.  This is something I really want to think through developing a good discovery-type lesson for my students next year.  For this learning target we put the rules into our notebooks and then I had a matching activity for them to do.  I asked them to write down their matches on the bottom of the page.

Simplifying Radical Expressions:

We added, multiplied, and simplified radicals.  We did adding multiplied, added, and then simplified to show that we could add things we didn't know we could add.

Notes

Practice

Notes

Practice

Adding Notes/Practice

Multiplying Notes/Practice

Simplify Cards

I knew that was a lot in a few short days, and I had just read Kathryn Belmonte's post on Coloring Relay, so I made my students a coloring sheet with the answers written in.  I allowed them to work individually telling them that they could color in one section once they had completed the problem that had that answer...yes some students mostly colored and didn't do a lot of math.  But it was Friday and I wasn't feeling great, so it was a compromise I was willing to make.

This is not my favorite unit.  I think it is a lot of stuff to put into one unit.  But really it is only a couple standards, so it is hard for me to balance that.  It has taken me a long time to share this because I'm not very proud of this unit.  However, I put a lot of work into it.  I created and modified everything.  It was a lot of work, but hopefully now that I have things to this point I can make it better for next year.

-Kathryn

Note:  All files must be downloaded in Microsoft Word to get correct formatting.

#MTBoS30

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