Ms. Z

I was so inspired by Ilana Horn's (@tchmathculture) guest post by her own teenager, Faking Excellence: The Art of Milking Mediocrity For All it's Worth, that I have to tell you how.

The writing is my favorite kind of prose: creative non-fiction, self-reflective, witty, smart. Having a Senior in high school, we, (my daughter and I) can totally relate. As I read, my heart went thunk, as I fall into every teacher trap she laid, "Greet your teacher upon entrance, have book and supplies with you at all times..." My daughter carries a certain book with her at ALL times, how long could it possibly take to read one novel? Now I know it is just for show, as is her overflowing pencil case. I must admit, I do love the oversupplied student...

"Live life like an overworked student..." Oh so my daughter...though she ALWAYS has time to respond to friends, go to movie nights, and fit in a fantasy shopping spree online. "Do you want me to be sad and lonely? Aren't you the one who told me to spend more time with people?" Though I must wonder if this makes me a flakey teacher because I feel for students and let them slip things to me late (with explanation.) I so don't want to the one who gives the students busy work. I try to pick and choose assignments wisely, does this make for lazy students?

To linger over the greatness of the writing and try to make peace with my gullibility, I gave my students the opportunity to read the blog as extra credit. I wrote a Google Form,

And feel so excited to make more response sheets like this one to check for not only content understanding and mastery, but to hear my student's voices. We are not a 1-1 school so I am not sure I can REQUIRE a response.

How do you use Google Forms and response sheets to assess students and inform instruction?

It is important for Newbies, Oldbies, and Inbetweenbies to look for resilience in ourselves. How do we handle a dismal result from a well-planned lesson?

Blame and negative talk to ourselves are not useful or productive. So acknowledge it didn't go so well, and tweet out to your PLC, share with a trusted colleague, sleep on it, check the MTBoS Search Engine, take a run or a bath, or both!

I wanted my students to discover which triangle congruence shortcuts worked and which didn't. Last year I had good success with lesson inspired by the original CPM Math 2 curriculum, where the students cut out various triangles, we put them up on the board and decided which were the same and which were not. Problem was, not enough accuracy with protractors and notion that vertices had to be the endpoints of the triangles, so sometimes non-congruent triangles ended up in the SSS category for example.

So this year I started with a lesson inspired by one I found on James Rahn's website: Discovering Ways Triangles are Congruent. I wanted to use Patty Paper to try to get a grip on accuracy. The idea was to create triangles from all the permutations of six parts of a triangle, each of three vertices and each of three lengths. Problem was there were too many triangles (9). The students didn't like making a triangle out of one single angle, or just an angle and a side.

Most students used the arrows at the end of the rays as endpoints and closed the triangle, so many of the triangles looked the same and plus, each student had about a zillion pieces of patty paper to try to keep organized and categorized. There wasn't enough time to debrief and I wasn't prepared to store the bazillions of pieces of patty paper for the students.

After reaching out to MTBoS community and reading a January 2015 post by Kate Nowak on the same topic, I re-organized thanks to Kate's helpful recording sheet and tried again the next day. I focused on what I wanted the students to specifically see, and decided to concentrate on the triangles given three pieces of information.

This time, instead of every student doing every iteration of a triangle with the six pieces from James' lesson, I gave the groups of 4 and 5 students the same 6 pieces of information as they saw previously, and using Kate's recording sheet, specifically asked the students to use the patty paper to create one each per group of very specific triangles in specific orders. For example, create a triangle using side AC, then, CB, then, side BA. ENDPOINTS MUST BE VERTICES AND ANGLE VERTICES MUST LINE UP WITH SEGMENT ENDPOINTS!

I told the students they could divide the work up anyway they wanted...each take a triangle to create, work all as a team, as long as when they were finished they had 5 triangles, on 5 separate pieces of patty paper, labelled for the corresponding letter with the directions for the triangle. You have 20 minutes, GO!

I put 5 pieces of colored paper on the board and had a member tape up their triangles with the ones that were built the same way.

My husband teaches Multi-Media studies at the Santa Rosa Junior College. He started as a K-8 music teacher, including band, chorus, classroom music, and drama. He did musicals with all the grades.

What does this have to do with Math, and in particular, graphing? Well my husband can tie his careers together too, because in the end, he is really a storyteller. This is his mantra. Does your photo tell a story? Does your website tell a story? Does your logo, animation, digital portfolio, tell a story? If not, go back and make it tell one.

So when I was about to teach Polynomial Functions, it dawned on me, equations are little stories. They tell us about their shape, their domain, their range, their limits, their relative extrema, their x-intercepts, their y-intercepts, etc... They also tell us what family they belong to and how they are different from their parents. Each is unique and this became really clear when the students got to building a polynomial function.

For this lesson I wanted the students to tell the story of the equation through its graph.

The students had to understand:

→What role the degree played in the graph’s end behavior.

→What role the multiplicity of the zeros played.

→What was the effect of the leading coefficient have on the graph.

First we used Amy’s Polynomial card sort (thanks Amy) to make sense of these equations. I loved Amy’s script and pretty much followed it.

After we got used to the shape of the graphs, we explored methods of finding the roots. We used all the typical methods: factoring, rational root test, quadratic formula, long division and synthetic division. Along the way, we found out that some of the roots were imaginary, that they came in these conjugate pairs (we giggled, bc someone said, “oh like “Orange is the New Black.” Now I can’t think of these pairs of numbers without immediately translating it into “conjugal.”)

It was fun to watch them discuss and grapple with zeros vs. intercepts, (more on that later) and found out that their factoring skills stink. (How do we involve CCSS with the mundane task of factoring, I want my Pre-Calc kids to be able to have TOOLS to factor nearly anything.) Then they got this gift:

Find the equation of a third degree polynomial the following roots such that f(1) = -60.

2, 3 + 4i

Most students got this far: f(x)=x^3-8x^2+37x-50 but couldn’t figure out what to do with the

f(1) = -60.

So we talked about what story does f(x)=x^2-x-6 have? How many different graphs have zeros at 3 and -2? What does f(1) = when a is 2, 3, -5, 6, -1, 1, etc…

The students understood from this exploration that there are infinitely many equations with roots 2 and 3 + 4i. Next time I will use the slider function in Desmos to help the students find “a” before we do it by hand. (Why I didn’t think of it this year is beyond me.)

I wish I had done this first: (I am a tad intimidated by sliders)

In the end, the students did get that the leading coefficient makes f(x) have a unique story.

It was then way more fun to move on to rational expressions. The students were now curious to see what an analysis of f(x)=N(x)/D(x) would produce.

Dear MTBoS,

I stole and embellished, and added (hopefully). And I caught your sense of humor.

Meg at Insert Clever Math Pun Here so inspired this post. I could not figure out why with her post on Polynomial Functions she had a clip of John Travolta and Saturday Night Fever. What? Then the light bulb went off and I made this:

Here is link. Maybe the students should make their own? I was going to make it matching, but thought the conversation would be richer if they had to make them up. Thoughts?

Happy Blogaugust <3

Dear Math Bloggers,

This one is for you. You have given me so much, I have been racking my brain trying to figure out what worthy goodness I could share with you. Well, nearly every morning, I treat myself and family to a reminder of our two years spent at the American School of India, New Delhi. Chai tea.
Here is a a coveted recipe I hope will sweeten your day and take you on a quick retreat.

Chait tea for 2

For 2 cups of water add:

5-6 pods caradamom smashed
5-6 whole cloves
1 inch fresh ginger smashed
A 2-3 inch stick cinnamon
sprinkle of nutmeg

Boil spices in water until water is color of spices:

Then add 2 cups of milk, at least 2%
and 1 rounded tablesppon of sugar

Bring to a boil and then turn off heat and add three bag of black tea: You can use Lipton's, Lyon's, PG Tips, or any Irish Breakfast or English Breakfast (I use Trader Joe's Irish Breakfast).

Let steep 5 minutes. Pour out through a tea strainer after 5 minutes. Pour into a to-go cup or mason and jar and make your journey to work a mini vacation!
Save it for at work, for a pick up at break.
Be a tea wallah, and double the recipe and deliver it by thermos to unsuspecting teachers and watch them smile!
Enjoy!

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