Algebra 2 INB - Complex Numbers

Complex Numbers

I love teaching Quadratic Equations.  I think it may be my most favorite unit to teach all year.  I'm not sure the kids always enjoy it but I sure do.  :)  I am a terrible blogger.  I do lots of things in my classes that I'd like to write about but never seem to take the time.  (Kids are taking a test right now!)

I teach both a college prep (honors) class and a regular class.  I sometimes do things differently with the regular as I've had time to "tweak" my lesson before I get there with them.

This is the foldable I created to help me teach Complex Numbers to my regular Algebra classes.  I use ALOT of frayer models in my class.  I've found it is a great way to show students what something is or isn't....HOWEVER....A frayer model isn't just for vocab anymore!   This was the way I decided to have my students organize their notes for Complex Numbers. So far, I'm liking the way it is going. 

I made this on a full piece of paper and we will fold it to make it fit in our book.  You can fold it in half, or in quarters to have it open up.  

If you like it and can see a use for it in your class....go HERE to download it for free.

Trigonometry INB

So it has been A LONG time since I posted on this blog.  Almost every day I think of things I would love to write about but just don't have the time to sit down and do it.  

Today though, I thought I would start my posts about my Trigonometry INB.  I don't know that I do an INB in the way in which it is fully theorized to be, but I LOVE the way I do it and it works for me and my classes. :)

Today I was teaching an application of radian measure - Length of a chord, to my trigonometry class.  When I drew in the central angle for the chord, one of my students loudly asked, "WHY does EVERYTHING come back to triangles??"  Another student replied, "Because a triangle is the perfect shape. "  In the true manner of a teachable moment, I felt the need to explain why I agree that a triangle is a perfect, useful, shape......but in a fun, hands on way!

I pulled out a pipe cleaner and a straw from my closet (I realize most math classrooms don't have these items hanging around, but I am called the "mathbooker" here are school so I have LOTS of craft items in my closet. :)  )

You cut the straw into three pieces that would form a triangle, (this is a great time to remind students that not all three lengths will necessary make a triangle either). 

Put the pieces of the straw on the pipe cleaner. 

Form the triangle. Twist the pipe cleaner ends together and cut off the excess.

I also do this again, but I cut the straw into 4 pieces to make a quadrilateral. 

We then compared the strength of the shapes.  It took a lot of pressure to get the triangle to bend.  And it didn't bend at the vertices, it bent on a side b/c the straw gave way. 

Since this was a trig class and not geometry, we had a GREAT discussion about the uses of triangles, and why they are used for support on bridges, etc.

Going back to my INB....I have a student who is a little crafty (she loves the INB), and proceeded to use her triangle to form the angle in her arc for her lesson on chords.  How creative was she?  Of course, I took a picture, and I now know that this is going into my own personal INB for next year and maybe I can lead the discussion to get the students to ask these questions again. :)

 Just thought I'd share! :)  I'll try to get more pics of my INB's up soon. 

I know it has been a while since I have written and I was really hoping to catch up on my posts over Christmas break but that didn't happen either!  Just too busy with family.  And that is a good thing!

But since I did bring my books home I am taking the opportunity to upload one picture quickly that I did.  It is on PEMDAS.  I can't take credit for the organzier but it was so long ago I can't remember who I "stole" the idea from.  Feel free to claim credit if it was you!  I am uploading it in response to this picture that is circulating on Facebook.  I CANNOT believe the number of people getting it wrong?  The tag with it says that 9 out of 10 people do not answer this correctly!  I am really hoping this is not true but I was astounded at the number of incorrect answers that were listed below it! 

I think next  year when I teach it I will definitely point out all the "facebook" problems that circulate. :)

Algebra 2 INB pages

I don't have a ton of "great" pages for this book yet but here are a couple that I really like......

I LOVE this foldable!  I used it as a review of slope with my Algebra 2 class.  I got it from I Speak Math.  She had a download on her website so make sure to visit it and look around.  Again...she is another FANTASTIC blogger to follow!  My students really loved this foldable as a review.  It is so organized and we were literally able to go through the entire topic in about 15 minutes in class.  Which was great because going over the homework always takes so long that having a short lesson was great!

This was my "output" page that went with the slope lesson above.  As we were going through the foldable, the discussion of horizontal and vertical lines came up.  However, I did not cover them thoroughly, so I posed this question to my students and asked them to provide a mathematical explanation as to why these are true.  Not one student was able to put the reason into words.  I had one student get vertical correct and a different one got horizontal.  I was disappointed in the results but realized that THIS is why we need to start having our students write more in their math classes.  In PA, students perform poorly on the state tests as a result of this.  I am hoping that my INB will help change this for my students! 

Having come off the success of the slope foldable, I decided to try and create my own for reviewing the ways to graph a linear equation.  I adapted this from a foldable I had seen online somewhere and thought it fit this topic.  I really liked it and will definitely use it again!

This is the inside of the foldable.  Since I had already reviewed the x/y table in a previous lesson I decided to show horizontal and vertical lines for the x/y table part.  My students were surprised to see what the tables looked like but seemed to get it quickly. 

I wrote the wrong topic at the top of my page!  I was so mad but realized that the topic was on my foldable so it didn't really matter. If you want to know how to create this foldable, check out my Algebra 1 INB pages post.  I explained it there.  It worked really well for this topic.

Algebra 1 INB Pictures

Ok...so here are some of my Algebra 1 INB pages.  Many of the ideas have been taken from Math = Love Blogger, aka Sarah.  If you have time, check out her blog. She is amazingly creative!

My coworker Mary Horvat taught me this song to sing to my classes for adding signed numbers.  It is catchy and the kids love to hear my awful singing!  LOL!

Nora Oswald, of Simplifying Radicals, showed me this foldable she found on the internet. I  used it and loved it!  It is so simple to make too!  You take three sheets of paper, and you can use less or more as needed, and offset the size of a tab.  My tabs are 3/4 inch for this one (I think).    You can find the foldable in a book by Dinah Zinke as well.  I've used it for several different topics as well.  You can make it with lined paper if you want to have the students write regular "notes" on it too.

 I found this book in an online book by Dinah Zinke that was a downloadable PDF. Click HERE to view it. She has a lot of amazing ideas in it.  It is well organized too.

I get to take full credit for this lesson!  The foldable is pretty easy, just a trifold.  It made sense b/c this concept is usually taught in a table format anyway.

I need to change this problem for next year.  I meant to put one of the numbers in percent form but forgot in my rush.  But overall I liked the problem structure.

Sarah, of Math = Love, mentioned using combo meals to explain the distributive properties to her students.  I really liked the idea and used it a bit in the class.  Not quite to the same extent she did but the kids really liked the analogy.  I had my students define terms in the glossary portion of their notebook.  They are also supposed to transfer all definitions from the Frayer Models to their glossaries as well.  My classes are pretty lazy about doing it, but I'm thinking their first notebook check will cure that!

This page went with my lesson on like terms.  I wanted to see if they could apply the abstract to a different type of problem without instruction.  They did great!

I found this Frayer Model on a website created by Lincoln County Math Teachers.  It is a great resource for some foldables/organizer. 

This was the output side to my lesson on square roots.  I adapted the fold from one I had seen on Sarah's Math = Love's blog.  She did it with exponents but it worked well here.  I am introducing simplifying radicals with it.

I tried to give appropriate credit for all of the pages above.  If I missed you for some reason please feel free to comment and leave your website!

Interactive Notebooks

Mathematician's Notebook.....these were magic words to me last April when I heard them at NCTM in Philadelphia. They are also the reason I started this blog. 

I have always required my students to keep a notebook in my classes.  All classes regardless of subject.  When I returned to teaching 4 years ago after taking several years off with my children, all I could think about was how boring they were.  I knew they were better than nothing but I knew they weren't as effective as they could be, or wanted them to be. I figured if I didn't like them...why would my students.  The only thing they liked about them was the "easy" grade.

So when I went to NCTM last year, I saw the title: Creating STEM Experiences for Middle School Students with the Mathematician's Notebook.  The presenter was Tammy Jones and I was entralled from the first moment she showed her notebook!  Here was EXACTLY what I was looking for!  The coolest part for me was that she used a graphing composition notebook.  When I was in high school, I LOVED writing notes to my friends on graph paper!  So how cool would it be to create an entire notebook out of the graph paper? 

Pretty cool as I'm finding out!  I am LOVING my interactive notebooks!  I am using it in my Algebra 1 and my Algebra 2 classes.  I did not use them in my business math class but am seriously considering it for next year!   I am keeping one for me for each class as well.  I find that I am reflecting more on my lessons at the end of each day and the notebook gives me a place to put notes for next year.  It is helping me to stay organized as well.  So far, I am much better with the interative part for Algebra 1 then Algebra 2 but I am working hard to get them both to be better. 

I couldn't do this without the many blogs that I read daily and steal ideas from.  These teachers are amazing!  I will try to credit them all as I post pictures of the ideas I stole from them!

The best compliment I have received the other day was from the football coach...he said one of his players loved my class because it didn't feel like math, it felt like scrapbooking!  LOL!  I laughed because that student's class also told me they felt like they were in kindergarten...with all of the cutting, glueing, and coloring they are doing.  If this translates to better understanding, then I am okay with teaching kindergarten to high schoolers!

Is a Gumball Machine a Function???

I started talking about this last week when I was reviewing functions with my Algebra 2 class and it took on a life of its own in my mind.  When we were discussing input and output it made me think of a gumball machine.  I'm not sure why, but if I had to guess it's because my three rugrats at home cannot pass a gumball machine without hitting me up for a quarter!  And since you have to put IN a quarter to get OUT a gumball....that's where my mind went.  Because I used it as an example in my classroom, I couldn't very well assign it as a homework assignment or even an exit ticket type question. However, next year, I plan to use it as my output question in my INB.  Here is my formal question:

Is a gumball machine a function or not?  Why or why not?  Please explain/support your answer using mathematical reasoning. 

With all the changes that the Common Core is bringing to our curriculum, the one I am trying the hardest to incorporate into my classes is the writing.  I am trying to get my students to write more, explain more, and hopefully, understand better. We are working on proper vocabulary as well.  In my opinion, I think my INB will help me do this more in my classroom.  It certainly is making me reflect more on my lessons at the end of each day.  And now I have somewhere to keep those reflections for next year.