Factoring: The magic method

I typically teach the box method when factoring. You can find the link for the box resource here. But this year, I was introduced to what I call the magic method. First, I would like to state how peeved I am that I did not documents this method when I discovered it in high school. 

Follow this steps on the side and the scary, a does not equal 1, becomes simple again!  It is magic!  (At least that is what I tell my students).  Some still prefer the box, others prefer the gcf method using parentheses, but for most, this method stole the cake.

Geometry: Pythagorean Theorem

Always provide a leg example and a hypotenuse example. Man, did I learn from that mistake of assuming my first year as a lateral entry teacher. I need to go back and add some color, but the kids caught on pretty quickly. I do my notes and post them on my school webpage now. This totally reduces the number of questions in regards to how and where does this go for the foldable. 

By the way, the paper was part of the donorschoose package. Apparently, I must have been mentally ill when I wrote approximately as approxi"mentally". I left the mistake for the kids to see that I can make mistakes as well. In a class like my math tech 3 group they need to be assured that mistakes are okay. 

 I love the textbook for this class. It is one of the first that puts the distance formula with the Pythagorean Theorem. Thank goodness, the connection was already made!  Other than a few moans and groans about the distance formula and the requirement to draw the triangles, my class caught on relatively quickly. 

Exponent Rules and Naming Polynomials

I love teacherspayteachers. The graphic organizer from all things algebra is the bomb dot com. It was a great asset prior to playing algebra wars. I had a few errors like a missing negative sign, so that needs to be fixed prior to posting it.  I cut the foldable so the kids had their chart of squares that they need to remember on the side. If you are like my students and wonder why I skipped 14 squared, I told them I have rarely used it in higher math classes. Using this logic, I probably should have put 20 squared.

I play the video by the Ohio school of mathematical magic. Yes, that is not their name, but play one of their songs in class and BAM. Magic!  The kids are humming the tune down the hallway.

Students look like I have just taught them how to cheat when I show them how to put rational exponents in the calculator. But it gets students saying this is easy. 

I tell students that radical signs remind me of division symbols. We always divide the number "under the hat" (elementary term) by the number on the outside. This time we call it the index. The only thing I had to push hard was the square root is an exponent of 1/2. 

These types of questions pop up on the EOC every year. I see kids get overwhelmed by the equation prior to seeing that they can plug it in the calculator. Input major emphasis on these word problems. 

Colors are key to learning as visual learners. Tomorrow I will take care of my kinesthetic learners taking another example from Math = Love. 

Systems using elimination

Let me just say, wow!  The Internet is amazing!  I posted that silly donors choose video and bam I have classroom supplies coming straight to my door.  The blog had taken to the back burner, but I am back with a few posts.  I am going to do two today, the first for my Algebra class, the second for math tech 3/geometry.

I find that substitution is a difficult method to follow out of the three.  Unless you are a math nerd like I was in high school and had plenty of experience with math relays.  So finally, we come to elimination!  I think out of the three forms, minus the calculator for graphing, that this is the easiest form to solve for students.  I showed the students how to find the lcm in the calculator (a trick I didn't learn until I went back to school for my master's degree).  Go to ALPHA then over to the right to NUM and voila!  This menu can factor using the gcd, find the lcm, and plug the absolute value into your calculator.  I mean really, why did I not know about this?!

So after teaching the method, I used these worksheets from online.  There was one error on the substitution package, but the elimination seemed to be perfect.  I had students do the cut out activity as the students homework after the notes were taken.  I love this packet because it breaks the material down into steps.  The second can be used as a gallery style activity (the way I presented it) or as a matching activity.  I loved it!  The kids seems to really catch on using elimination.  I heard a few complaints from them about the number of steps needed to solve the equations.  We are playing a review game and quizzing on the three methods prior to teaching them how to just use a matrix.  Man do kids always get mad.  "Mrs. P, why did you make us do the other forms?  The matrix is soooo easy."

Note: there are limits to using the lcm or the gcd...you can only plug in two numbers and you must keep them positive.