Absolute Value Inequalities

I opened up my teacher edition last night to review the lesson and make some notes.  I got to the rules of the absolute value inequalities and froze for a second.  The definition was terribly technical.  It took me two readings to make sure that I got it and my heart sank a little.  I started trying to figure out how I was going to get the kiddos to understand that definition.  I started looking through other resources that I had and found an explanation using two cases.  After reading that, I created the the following chart:

I got my examples from the McGraw-Hill Algebra 1 (2012 edition) textbook.

I left the case 1 and case 2 parts blank and worked them in class along with drawing the graph of the solution.  I like the idea of what I did, but I would like to redo it a bit.  I would take out the "and" and "or" part by the inequality symbols.  I don't think the kiddos got it right away.  Next time, I will have them write it by the solutions graph.  I am also not happy with the special cases part of the notes.  Oh well!  Summer is almost here and I am sure I'll find inspiration during it. 

Pythagorean Theorem

Tomorrow, I will be teaching a lesson on the Pythagorean Theorem.  I wanted to let the students actually see why it worked.  However, with the school year so close to ending and the end of the year events canceling more math classes than I can spare, I was stumped how to do it.

As you can see, I was able to put together a graphic organizer for them.  The best part of this organizer was taken from Jennie's idea at mathfoldables.blogspot.com.  She had this nifty way of showing students that the sum of the square of the legs is equal to the square of the hypotenuse.  That proof makes up the upper left hand corner.

The formula and the transposed formulas to find the length of the legs are in the upper right hand corner.  The bottom left is example problems and the bottom right is an explanation of Pythagorean Triples and two examples.

The template for Pythagorean Theorem proof can be found at http://www.teacherspayteachers.com/Product/Pythagorean-Thereom-Proof-Foldable-Template-496569.  It is a free download.  The students color each sides a different color.

Then under the hypotenuse side, the students color 16 squares the same color they did for side b and 9 squares in the same color they did for side a.  What they will see is that their are enough squares to hold all of side a and side b.

Another Foldable

I am starting to feel very good about how well my kiddos are understanding now that I have been using foldables.  I see them being used and referred to much more than their notes ever where.  It takes some thinking to put together a foldable for the lessons, but I have been doing it so far and I am pleased with the results, so it is keeping me motivated to continue with them.

I am also pleased with the data that I am getting back from the practice problems I am making them do before they start their homework.  I am thinking about mixing it up next year and putting some of the questions onto index cards and having them do a "scoot" activity in their table pods.  I have to think a little bit more about it, but I like the concept of it.  I just want to do things that are more active than filling out a worksheet.  It is my goal for this summer to find more ways to do that.

Here is another foldable that I did with my students.  I focused on making them tell me what they thought the process was after seeing the examples.  That is why the inside of the foldable is incomplete.  I just gave myself enough to get the ball rolling with the kiddos.  What I learned from this is that I haven't stepped back enough this year to listen to them and their thinking.  They weren't sure what to say and afraid of saying the wrong thing.  Talking in partners and small groups helped to open them up.  I will be working more of this in next year where I consciously make myself stop and listen.  I just learned a lot from this lesson and have found an area to improve and that is good.  It is a new direction to push myself and hopefully become a better teacher for whatever is left this year and definitely next year.

On the front of the foldable, we wrote reminders of perfect squares, prime numbers, powers of 10, and some patterns for variables.  We also wrote the answer to what a radical expression was and the product property of square roots off to the side.

The inside had 3 examples and then the steps to take to for each strategy to simplify radicals.  As I said in the post, part of the steps are missing because I only wrote enough to get the ball rolling with the students.