Showing posts with label Properties of Graphs. Show all posts
Showing posts with label Properties of Graphs. Show all posts

June 1, 2014

Quadratic Functions Unit

Well, my students and I have been in quadratic functions for quite a while now! Especially since our EOC testing fell in the middle of it all. 
I also feel like I did much better job this year with letting them explore/figure out the intricacies before we formalized in their notebooks. So, for example on the "factoring" pages, we spent a day just using algebra tiles to understand what was truly happening and the relationships between the numbers. Then we formalized. 
All that to say, quadratic functions took a long time! But my students really seem to have a good understanding.

So... here are my notebook pages.

Man, as I'm uploading, most are blurry. So sorry!! Silly phone camera :(

Our Learning Goals/SBG page.
I plan to implement SBG more next year and these pages are allowing me to dabble in the idea without fully committing yet.

Investigating a quadratic function for the first time...

Focus and Directrix pages from Sarah. The kids LOVED seeing their parabolas take shape in the wax paper. I know that focus and directrix aren't technically in my algebra 1 standards, but I just couldn't resist!

The same properties of quadratic functions pages that I did last year. Still worked well and still a hit!

Angry birds and vertex form. 

Standard Form and a summary page from here. I tweaked it a little to fit my needs. 

Here's a better picture of the summary page. 
Original idea and post HERE

Then the discriminant and quadratic formula.
The students and I derived the quadratic formula (yep, that ones officially in my standards) but I haven't taped it into my notebook yet. The big orange box is where it will be taped soon. 

The factoring and completing the square pages took multiple days and I wanted to give students plenty of time to explore with algebra tiles. I gave lots and lots of problems that students built and answered with the tiles before we ever formalized and talked about procedure. 

I really liked doing it this way because students understood the factoring method. We were un-doing the distributing and pulling everything back apart. There was so magic wand waving - just some great mathematical understanding happening. 

Also with completing the square. We built lots and lots of squares, filling the missing corner and then looking at side lengths and x-values before every going through just the process. 


Well, these are most of the pages! A lot happened in class between all those pages, so sorry I can't bring you in for that! Hope something helps!

July 13, 2013

Properties of Quadratic Graphs

We talked about properties and end behavior of graphs all year long. We started with linear, transitioned to piecewise through distance-time graphs, then absolute value, then exponential, then quadratic. These are the INB pages for our properties of quadratic graphs.


Since we had talked about end behaviors, average rate of change, intercepts, vertices, positive/negative, etc. before, this was a quick extension of ideas to quadratics.

Each student got two identical graphs. Two because all the color-coding info would be jumbled on one graph. We color coded and created our flash cards all first, then taped everything into the notebook.


When students walked into the classroom on this day, our "First Things First" section of the board told them to pick up two pages. One had graphs and the other is the flashcards and envelope. They also picked up scissors and immediately got to cutting everything out. This is something I often do, give students the directions before class officially starts. I begin on day 1 telling students that they are considered tardy to my class if they haven't  begun the First Things First activity before the tardy bell rings. They learn this very quickly and don't waste time once they enter the classroom. I also promise them that I will give them a 2 minute warning at the end of class so they have time to pack up and clean up the classroom, and therefore leave when the ending bell rings.

Anyway... small tangent there. :)

As students were cutting out their flash cards they were telling each other "hey, we know what these mean!" "I know this!" "Mrs. Hester, this looks easy!" I love when they are confident with their learning!!

Once everything was cut out, I asked students where they wanted to start. They knew we had to talk about everything, but might as well let them choose the order! They would call our words that they felt confident in and provide a definition. Classmates would add to the definition and we would talk through specifics. Once I had guided the discussion to a place I was comfortable with, we wrote down the definition. We then switched to a colored pencil, marked that particular feature on a graph, and wrote the specific answer for that definition in the same color on the card.


This provided students with a general definition, as well as a specific color-coded example.
Using the flash cards in an envelope added an element of fun, as well as a way for students for study. They enjoyed pulling them out and quizzing each other.

Got any ideas about how I could make this better? What are your thoughts about this lesson?