Intro to ThisGraphing Quadratics Foldable

I have a few favorite designs for foldables.  I love a door foldable and I love a tabbed foldable.   Both of these are just great ways to organize multiple pieces of information about one topic.   For my foldable on graphing quadratics, I used a 3-door foldable, but had the doors fold down.  I left a little area at the top for a title, so that they don't fold the paper directly in half.  By this time of the school year, my students are so used to my foldables, I don't even have to tell them what to do!  :)
 

I use this foldable in conjunction with my Frayer model for quadratics.  It usually take 2 days to cover this with my regular class of Algebra 2 but I can do it in one day with my CPAlgebra 2.   This is just the overview and then I do an additional day for graphing using the intercept/vertex methods.  Next year I want to add in a lesson on teachers.desmos.com to help support the graphing portion.  I will probably do it as a review for this year though.  If I do, I'll blog it.  :)

In the picture below, I define parabola as the shape of a quadratic but when I taught it, I didn't like it and changed it to the graph of a quadratic....which do you think is preferable? 

Intro to Quadratics - frayer style

For me, my entire notebook is becoming all about the Frayer model.  I absolutely love it!   I find it is the best way to explain what things are because you can compare them to what they aren't.  I might have a slight addiction to them but that is just because they are just so darned easy to use!

So using one to explain Quadratic equations was easy for me to do.   What a great way to show examples of equations and graphs, and non-examples.  And it even helped start the students thinking about the similarities of the quadratic equation and the absolute value function!  The minute I drew it as a non-example, they started asking questions.  Don't you love when that happens?  :)

Exponent rules Grudge Game

Exponent rules.....teaching them is another necessary evil.    I LOVE solving problems with exponent rules!  They are like a puzzle to me.  But my students hate them. They don't "get" them, they say they don't know where to start.   And now I have a structured study hall, where I help the students with their classwork...and the students in there hate them too!  Every year students come to me in Algebra 2 and they don't remember the rules.  But we use them so much in Algebra 2 that they really need to learn them.  I figure it is like learning the grammar rules for writing.  Something you need to know in order to do the next thing.   So in the spirit of "if it isn't working, change it", I decided to change up my teaching. 

So this year when I taught exponent rules to my classes, I used the Grudge game to introduce them, adapted from Nathan Kraft's Blogpost.  Click HERE to see his original post.  I did this on Day 1 and I absolutely loved it!  The kids were engaged and competitive and they did great!  They even showed they remembered some exponent rules from Algebra 1.   I usually don't like games in my classroom but this one was fantastic!   All the kids participated.  I did bribe them a bit with candy, but hey, you gotta do what works right?  End of day 1 was FANTASTIC!    This is going to be great!

Here is the PowerPoint (Dropbox) I used to play the game.  Feel free to change it.  But at least it gives you a place to start.  :)    The image to the right shows the rules I used to help me remember how to play it for future use.  I love this game so much, I can't wait to try it again.  :)




So continuing with the need for a change,  I also changed the exponent foldable I usually use to a book of exponents, modeled after Sarah Hagan's from Math = Love.   I liked the way she laid it out and hoped that it would work better than then one I used last year.  Although I love the book, and the layout, I'm not entirely sure it was better than the one I used previously.   My students still struggle with the rules and the test they took showed they still have gaps of understanding. (I gave the test before Christmas so my post is a little out of date. ;)  )






So back to the drawing board for next year and for reassessing.  But I am keeping the game.  I think that was the perfect introduction to exponent rules for Algebra 2.  However,  I need to rethink the rest of it.

Feel free to share your success with exponent rules with me and others!  :)

Factoring a >1....

Factoring a > 1......is there really any easy way to teach this???   I rank it with long division....a necessary topic to teach in Algebra 2, but no real easy way to teach it.  :)

In previous years, I taught the guess and check method.  That is the same way I was taught in high school and it works.  But teaching it is so painful.  Some students get it right away....others never get it.   In the past, once I taught factor by grouping, I would go back and reteach factoring a > 1 using factor by grouping and would seem to get a few more students factoring this way.  

This year I decided to try something different and I taught my students the box method using a factor T.   I gave this graphic organizer to them to get them started.  I provided a link to dropbox below if you would like to download it for free.

In this method students multiply the "a" and "c" parts of the trinomial, find the factors, and look for the pair that makes the "b".  Then they place the terms in the box, using this design:

They then find the GCF of each row/column and voila....they have two binomials! It is easy enough to do and most of the students understood it.   I picked this method because it works every time but as I didn't teach the guess and check method first, my students did not appreciate the efficiency of this method.   It also makes finding a prime trinomial easier as well.

Here is an example I wrote out....I tried to write it out in steps but I did not write out explanations...on a student paper you would only need a box and a factor T.

My reflection:  Next time I will teach guess and check first as it is still the method I prefer first and then teach the box method as an alternate.   I'm also not sold on whether it is better than teaching to factor using the grouping method.   Which way do you prefer?



Get the file HERE for the factor box.

Hopeful Participant of the 2016 #MTBoS Blogging Initiative

I, Suzanne Milkowich, resolve to blog in 2016 in order to open my classroom up and share my thoughts with other teachers. I hope to accomplish this goal by participating in the January Blogging Initiation hosted by Explore MTBoS.

You, too, could join in on this exciting adventure. All you have to do is dust off your blog and get ready for the first prompt to arrive January 10th!

 (Copied from Her Mathness....Wendy Menard)

This said.....writing is my weakness.   So let's just hope for the best!  :)

12 days of Goodness/Christmas

My favorite holiday is Thanksgiving.  I love the food, the family, the entire experience.  I even love prepping for Black Friday shopping.  My family loves Christmas.  The kids love the time we spend with family, singing Happy Birthday to Jesus and of course, the presents.  This year there are so many bad things happening in the world.   The news is filled with shootings, fires, and terrorism.  And let's not forget all the political name-calling and nonsense.  Frankly,  it is depressing.

I read Facebook for the fun.  I hate that it is often filled with the negative news items.  I look to the TV and news websites for that stuff but I go to Facebook for relaxation.  So what I would like to do is start a new holiday trend.  We need to bring some goodness and happiness back to the world to combat the sadness and badness.  I want to hear about the good in everyone's lives.  I want to hear about the happiness and the love. 

So I challenge everyone around the world to participate in the 12 days of Christmas.  I challenge you to post something you love every day on Facebook or your blog.  I also challenge you to do a Random Act of Kindness or an RAK.   It can be something as simple as holding the door for someone or something as thoughtful as buying coffee for someone.   Even if you don't celebrate Christmas, you can participate anyone and call it the 12 days of Goodness.  We need to bring Goodness back to this world.  We don't pray in schools anymore but maybe, just maybe, if we start to spread good will, we will start to hear about it as well.   And maybe we can change the world.

And why wait until 12/13 to start.  Do it today.  You won't regret it.  

signed, hopefully optimistic
#12daysofGoodness 

Every person is smart......

Every person is smart.  I truly believe that. What makes us unique is "how we are smart".   What makes our world go round is the fact that we are all intelligent in different ways.  Do you ever wonder how in the world your mechanic can take a car apart and put it back together?   Or why someone's cookies always taste better than yours?  It's because they have a level of intelligence that you don't possess. (Frankly, I don't either.  I'm lucky I haven't burned my house down baking.....but that is a story for another blogpost.)

Most people think I am smart because I have a degree in math.  But frankly, I'm no smarter than anyone else.  I just like numbers.  They make sense to me.  But ask me to write a paper and I am at a loss as to where to start.  The reason I blog so little is that writing my thoughts down is just too hard sometimes.   But I don't think that makes me stupid either.  It is just not my strength.   And that's ok.  

I am a firm believer in Howard Gardner’s Theory of Multiple Intelligences. I first learned of him in graduate school but I have to say he is the one Philosophy of Education that I have fully embraced.   You can see in the image above the different intelligences that he has identified and he believes there are more.   If you are curious about which one is yours, you can go HERE to take a short assessment.  I'm not sure how reliable the test is but I consider myself Logical-Mathematical and as a teacher I think I have good interpersonal skills so these results are pretty accurate for me.  My linguistic is my lowest and that may explain my aversion to writing.  :)     Try the test and see where you are smart!