Algebra One Unit 7 Properties of Exponents

After our introduction day of laying the groundwork we get into all the properties. Since my students have seen this material before we can take one of two approaches. I have to gauge how strong a group I have each year. I think they will continually get stronger and I will eventually be able to do option two for everyone. Remember I have an advanced class so this will be easier to do.

Option One - work through each property

Develop each property with students. I like doing discovery work on this. But I also find that students "remember" the rules but can't justify why they work. So I may "tweak" my discovery sheet to be clearer about justifying results. After going through each property then proceed into option two.

Option Two - Students do around the room activity to gather examples for properties.

So they know the properties and now can they identify examples that illustrate each? They are given a summary of properties worksheet to find examples for and fill them in. Examples are taped around the room. They can work together. Teacher is walking around with a master key to assist students only if absolutely necessary (and be stingy with the help - ask questions of them back or say hmmm... that doesn't look like that should go there). I tell students how many examples they are finding for each. See the master key for the examples. I write them on half page sheets of paper and tape them around the room. Students have to simplify each as well.

Other useful practice for students:
A Puzzle Partners worksheet
An All Properties worksheet with lots of examples and the answer key.

And there is an ISN insert too that students put into their notebooks. my student teacher did these inserts, she did a great job, but I'll probably do some tweaking so will post my new items in 2016 as I do them.

*did I tell you what cool handwriting my student teacher has?

Powers and Negatives can be a tricky combination, so we made an ISN summary sheet for that (found it on pinterest and the blog domain page has expired but it was called somebecomepearls.com).

and it appears that I forgot to take a picture of the inside three doors - so this is from pinterst:

Other useful practice for students:
A Puzzle Partners worksheet
An All Properties worksheet with lots of examples and the answer key.

Of course after this I do give my students a summative assessment (quiz).  After the quiz they take this little handout and then we talk about radicals - squares and square roots once everyone is finished with the quiz.

We go through the first 15 perfect squares and their square roots. We also talk about other roots too and list the first 5 perfect cubes and their cube roots. All students should memorize those perfect squares and cubes - they are all good number facts to have easy mental access to. I usually do a quick memorization quiz early on for this. (yes there are some things that just need to be memorized).

To support this radical work, I want an ISN insert on radicals.  this is not in my notebook but I want to use it in the 2015-2016 school year. Thank you again Sarah Hagan from math=love  (I think I'll make the first page a "booklet" so inside students can write the perfect squares and cubes they have to memorize.)

Then we get into rational exponents - this can get kind of tricky to develop and not just "tell".  Here are some rough notes of what I do in general after the quiz on regular exponent properties and leading into rational exponents.

Then there is an ISN insert

We had students convert back and forth between radical and exponential notation.

Then we had students apply the properties of exponents to rational exponents. Here are some worksheets that I used. 

Here are my ISN masters.  I can't find the master for squaring a negative, so I will double check with my student teacher and post it once I find it OR make another one.