An "Observed" Lesson

We have a new teacher evaluation system this year.  It is a set of rubrics ... not significantly different from previous years.  The big difference is that now there are 2 formal observations - one announced, one not announced.

I volunteered for my announced visit in December.  We have been studying polynomials - and students have been working hard to pull together several concepts from graphs and factors to roots of the equations.

Previous lessons had addressed polynomial operations, division and factoring specifically.  This lesson was near the end of the unit.



Here are the three activities:

Making Connections: Polynomial Theorems
Slides from ClassKick Activity
Desmos Discussion Activity

Students did well in the unit.  The assessment results were high.  We will continue our study of polynomials in January for a few more class days.  First we will review graphs, then look at polynomial models.

Weekly Summary, continued

I'm not sure what week to call this ... and I'm taking a break from blogging!
But summarizing the week has value ...

Lessons - just 2 of them in four days because we have A/B schedules

1. Graphing polynomials are not in our standards but I'm glad we started with graphing.  We introduced polynomials by exploring the end behavior and also the behavior at the zeros.   We worked from factored polynomials.  Linear factors cross the x-axis, squared factors bounce on the axis, and cubed factors wiggle across the axis.  We created human graphs ... student volunteers represented factors of a polynomial.  The held hands showing the behavior of the graphs.  Students laughed, clapped, and graphed well!
2. We had one of those "WOW" moments when I asked students to divide 693 by 21 and then I divided 6x^2 + 9x + 3 by 2x + 1.  We laughed as we thought about the day in fourth grade when they learned long division and how that day foreshadowed the lesson we had this week.  I told them their fourth grade teacher just left out the variables so as to leave the fun for us this week.  Students liked the connection to long division ... but when I introduced synthetic division they were so sold!  Ma'am, why would anyone use long division if synthetic division works?

Coming up ... factoring polynomials.  The lesson is not cute or fun.  We'll be studying patterns, using whiteboards, I do, you do!  If all goes well I found a jeopardy game online to play ... we'll see.

I have the best students!  They returned to school ready to work, listening, taking notes, participating, and demonstrating good work!

And that's all we do with polynomials.  It's a short unit in the scheme of things.  There is so much we don't do.  But that's OK!

We will test on Wednesday/Thursday!

In the meanwhile, I've been reading a few books ... enjoying rest and relaxation!

• What Happens at Christmas by Victoria Alexander
• I Still Dream of You by Fannie Flagg
• When Crickets Cry by Charles Martin
• A Million Little Ways: Uncover the Art You Were Made to Live by Emily Freeman
• Unshaken: Ruth by Francine Rivers

Exploring Manga High!

I've been reading with interest the discussions around Khan Academy.  I don't assign the Khan videos.  I do post links to Khan videos that highlight particular skills for students who were absent or want/need more practice.  This past week I posted a set of videos (some from Khan, some from other sources) plus a practice set or two from Khan for students who failed the last test.  The idea is that students will review the skills and practice before retaking the test.  I'll let you know how it goes.  One of our math coaches recommended a training in our district on flipping a classroom.  She said I would learn why it is much better for me to create my own videos than to use Khan.  Not sure when I'll get to pause for the training but the teaser info was interesting!

The online practice site that I am exploring the most right now is Manga High.  It's a free site, with tutorials and practice.  Students earn points and medals for their practice.  The teacher can assign specific "games" as challenges and set a proficiency level. I uploaded my students' names just last week.  My A day students used Manga High in class for the first time on Friday.  So it is too early to report any significant findings.  We were starting our unit on polynomials.  Since adding and subtracting polynomials is a review of combining like terms from the fall I wanted students to engage in something other than our routine practice.  All of my ninth graders were just issued laptops 2 weeks ago ... so almost every student could practice online.  It was amazingly quiet in the room ... the talking was about math ... and students were celebrating the high scorers.  Naturally I was pleased with that for sure!  But will students practice on their own time?  Will they go to that program when they feel like they are missing a key piece of instruction?  I don't know yet!

X Marks the Spot!

This past week I had the opportunity to attend our district's just in time math workshop.  The focus of the day was quadratics ... primarily factoring.  The goal was to introduce teachers to multiple ways to present factoring.  Since I have been out of the classroom a while, I found the presentation refreshing!

In the next few weeks, we will teach polynomials, and then attributes of quadratics.  I plan to introduce factoring using those attributes ... as we examine the x-intercepts ... demonstrating how those roots are solutions to the equations.  Obviously this limits us to very specific graphs ... ones that integer roots that are easy to see on a graph.

Then as we begin to pursue factoring in earnest, we will use "flashback" to illustrate the inverse relationships between multiplying and factoring.

1. We will use x puzzles to build number sense ... numbers that multiply to equal one number while adding to equal another number.  I found these puzzles online (Sum and Product Pre-Factoring Puzzles) ... I plan to use the x puzzles even before we get to multiplying polynomials ... just as puzzles!  I hope that just exploring them as puzzles before we get to factoring will reduce anxiety in factoring.
2. Algebra Tiles will help to demonstrate the area model of multiplication.  We'll use the tiles for factoring as well.  I plan to use the ones at Illuminations for online practice.
3. From there we will use the "box method" (an array) to multiply and then to work backwards to factor.

One method I don't plan to use that was presented at the workshop is the "Kick It" or "Kick Back" method. It seemed contrived - a bit of math magic.  If you want to read more about it, check out this blog post!

I noticed that Julie at I Speak Math has a template for X-Box Factoring ... I plan to borrow it to slip into our dry-erase sleeves as we practice!

I'm looking forward to our new unit ... first a few Laws of Exponents, and then ... polynomials!