Unit 3
Learning Targets: Polynomials
Learning Target: I
can…

1. Evaluate and simplify polynomial
expressions and equations

2.
Recognize the connection among zeros of a polynomial function, xintercepts, factors
of polynomials, and solutions of polynomial equations

3. Graph a polynomial function and evaluate
the zeros, minimum, maximum, and end behavior; determine the domain and range
of the polynomial function

4. Factor polynomials using a variety of methods
(e.g., factor theorem, synthetic division, long division, sums and
differences of cubes, grouping)

5. Determine the number and type of zeros for a polynomial function.

6.
Find all rational zeros of a polynomial function

7.
Expand Expressions

These are my learning targets for the unit that I am just finishing up. I thought it'd be a pretty good idea to actually start reflecting on things that I did / didn't do / should do in the future for each unit.
At our mastery school, we break a child's mastery down to the Learning Target level so I like to teach by learning target. Each day, the learning target is shown on the screen and typically, I'll introduce it by asking for words that sounds familiar that they may know. Ya know, access that prior knowledge. Some of the learning targets don't have much to them so I don't do too much on the fun / practice level. Other learning targets, oh boy, do we have some fun.....
LT1  Traditional Lecture style with a nice packet (It was the first day back from spring break).
~Changes? Turn this into a fun practice day. I mean it is concepts that my kids have been doing so why not make it a full blown practice day. In previous terms, I've done this day as a bingo review day and quickly discovered that some of my kids were not where they were supposed to be.
LT2  I love chanting all these connections with the kids. They think that I am such a dork. I actually teach the LT at the same time with LT3 because we spent a lot of time with it in Algebra 2.
LT3  Graphing. Oh, graphing. I break this down into three days.
Day 1  Warm up with graphing parabolas from algebra 2 in factor form.
We then look at a picture of a polynomial and we have a discussion about all the information that they could tell me about the polynomial. It's actually a really great conversation and the things that they come up with were fabulous!
We then did some examples and I talked about how to use the calculator briefly (in terms of finding local max/min/zeros). Notice, I didn't touch on the end behavior yet. For homework, I sent them home with 8 graphs and the TI84 Graphing Window WKST which would continue to help them work through using their calculator. They actually really loved this worksheet.
The second day, we did the end behavior discovery activity by Mrs Cook. It worked really well with my kids and they really saw the connection. In fact, the average on the exit ticket was an 80%! The only issue that occured, which I hadn't foreseen was that to some, end behavior was just up/down......
On this day, I also introduced the new Graphing Polynomials Project . They had some class work time and ended with the preassessment for the Representing Polynomials Lesson.
The third, and final day, we did the Representing Polynomials Lesson and it went amazingly! It's so incredibly important to have the conversations and discussions. Many feel that the kids won't learn how to algebraically do the transformations but they can, if you facilitate the class discussion in these lessons.
After LT3, we then got to dive into factoring. Oh factoring, how my kids loathe you.
Again, this Learning Target was given three days. Prior to the first day, I had my kids do a preheat on ASSISTments where they researched and practiced sum/diff. of cubes and grouping. This allowed for these two to go rather quickly. I then got to spend the time doing synthetic and long division with my kiddos. I used my guided notes for these and I even had a kid tell me how much better this went than last term (last term, I was absent so they had to teach themselves and each other).
After a day of learning, they then had two practice days.
Day 1 of Practice actually started with a warm up where they factored three polynomials using quadratic techniques. The first was a basic quadratic and then they had the same polynomial using degree 4.... and so on.
Practice:
(2) Who Has? Grouping Edition
Day 2 also had a warm up where they were given three polynomials to find the solutions for.... many dove right into factoring and applied the knowledge wonderfully! Others, needed a bit more help. This was to help me with the lesson the following day.
Practice: (1) Factoring Tarsia
Past the halfway mark, okay! Again, fairly traditional lesson on LT5/6 where we talked about Descartes' Rule of Signs & the Rational Roots Test. We started this day off with a warm up and then analyzed the roots. I then took this polynomial and talked about Descartes' Rule of Signs. Pretty much standard lesson, though.
The last LT dealt with the binomial theorem. Last term, I had done a Jigsaw I had found on pinterest. Now, this goes well with kids who want to know more, not kids who are in the last class of the day on a Friday..... Anyways, I still really like this activity but I feel like I want to tweak it a bit.... for my Friday afternoon kiddos. This LT is also broken into two days with one day of discovery and one day of practice. On Tuesday, we will be doing the Walking in Math Land Expansion Activity. I have removed some of the cards because I felt they were too easy but I got great feedback last term from the kids!
I really love that they recognize how much practice helps! They always tell me that they feel better about the material and what's best is that they are helping one another out!
So like I said, I owe you a few posts........ mainly about this unit...... So they're coming, I promise. But this is just my break down of what all I do with my kiddos :)
How do you teach these topics?
Thank you for these great posts. I LOVE your blog. I teach 11 th grade and our standards have just changed for the 3rd time in the 51/2 years I've been teaching! I will be using lots of your ideas in my class this year! Thank you again for sharing!!!!
ReplyDeleteSo glad you like my blog Carrie! Standards will come and go but at the root of it all, the math will stay the same. That's what I always like to remember :)
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Thanks.