Saturday, September 26, 2015

Story Time in Mathland

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.

Wednesday, August 26, 2015

Riffing, Because That's What We Do

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

Sunday, August 23, 2015

The Best Recipe I Can Give

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!

Saturday, August 15, 2015

Blogaugust #4--First Days--The Myth of "I am Bad at Math"

Thanks to John Mahlstedt @jdmahlstedt, I am motivated to blog about one of the first activities we do in Geometry, school-wide. (Not sure if article came from Danielle Buckman or Jessica Balli, both amazing teachers I am privileged to call colleagues).

We all share and read this article with our students: The Myth of I am Bad at Math, from the Atlantic Magazine. We all teach/share it our own way. 
(One teacher, whose baby boy was due in two weeks, came in the first two days of school, just because she thought the lesson was so important, she didn't want to trust it to a substitute teacher!)

Here is my approach: 

The exit ticket for the day was to agree or disagree with the statement, 
       "Math ability is mostly genetic." 
After the students wrote their reflection, I gave them time to move to an AGREE and DISAGREE side of the room and explain their thinking. 

I sent the article home with each student and gave them the following assignment:
Read the article and highlight 3 new vocabulary words (if you know them all, highlight three interesting words), determine and write the definition from the context, write down 2 big ideas in your own words, and 1 question you have. 

The next day, we discussed the vocabulary, then we broke up into groups of 4 and practiced active listening using "Collaborative Conversation Notes" I learned about at an EduImpact Conference held at our county office of education ( (here is an article about how to use the template). I had the students summarize one or two big ideas they could agree on in the center.  Our group conversation after was touching. All of the students moved to the DISAGREE side. Here is one group's change of heart, "We disagree because if you understand it well, you do good, but if you don't, you have to try harder and get better."

This year, I will ask the students to come up with some "myth" statements. When I have enough, I will give each group one to rewrite as a "growth mindset" statement perhaps taking something from what they learned reading the article. I wrote in Blogaugust #1 that I was inspired by Sarah Hagan and her post on a growth mindset bulletin board that she made from inspiration from @druinok So this is how I will approach crafting the statements to create the bulletin board of Growth Mindset statements.

Moving from I can't to ...yet.

Thursday, August 13, 2015

Got Me Some VNPS

Student size whiteboards. Check. Now we need verticalness, and my DH is outta town. Not that I mind swinging a drill, it is just going through the shower board and not sure what to do if it shatters. (Also, who knows if I am allowed to screw things into the wall, I just did it and figure I will ask forgiveness, but wait, this is why I am so sure I have little to worry about...)
Mirror holders! Yay! I am so happy and the boards are so secure. There is a plastic bit that expands as you screw it in.
(Sorry about the ugly brown walls and the funky picture)

After a full last day before the kiddos also occupied the school, I did collected these in my backyard:
And made a peach, rhubard, raspberry, apple crisp (sorry no pic).

Happy First Days of School ya' all. More on that next post.

Wednesday, August 5, 2015

Day 2 #MTBoSblaugust

So two things are running around my head today.

First, is all the growth mindset stuff inspired by Jo Boaler from Stanford and Carol Dweck who wrote the book Mindset. I love it! I love the message. Productive struggle makes positive change. I was inspired by Sarah Hagan and her post on this bulletin board that she made from inspiration from @druinok

Gorgy, right? But then I started thinking about the students owning the space and the words. So now I am thinking, I will ask the students to write their negative thoughts about math and learning and then have them work as a group with one card at a time to change the words to growth mindset statements (we will do first one together), then I will make a bulletin board! I promise I will take pictures and share them. The Dollar Store has gold starts for, yup, $1.00. Hah.

The second thing is Christopher Danielson said at TMC 15, "Find what you love (about math) and do more of that in your classroom," (see my previous post). Well, I do love listening to NPR and I do love Freakonomics, and I just love this very, very special episode:
How to Create Suspense
See the graph paper in the background, math, right?

Everything is in there, a movie producer, sports, a crime novelist and the question, what makes something suspenseful? What is the most suspenseful sport? What could you do to make a sport that is more suspenseful? (silly economists didn't know the rules to Quidditch).

We can appreciate this episode, or we can try to bring into our math lives. #WCYDWT

What/whom do you listen to that makes your math heart go pitterpat?

Monday, August 3, 2015

Joining #MTBoSblaugust Day 1

Got a new Chromebook (Thanks Tech Guy and District) and I am having fun keeping track of all my Mathy Friends from TMC15 and those I have followed for a while now.

I love sayings and being inspired and inspirational. (Do more of what you love, Christopher Danielson) Here are some of my favorites old and new that decorate my room.

New: Hannah, 17, a rising Senior, shared this one with me from her Twitter Feed:
The next one I have on my wall and also on the cover of my daily binder where I can see it.

The next one needs no explanation and has a prominent place in my room:

This one is front and center:

My favorite and well worn poster is this one because I have worked most of 29 years in two high schools in the heart of Sonoma County wine country and it is the heart of the growth mindset.

And this one:

Ummm...this too:

I do have the 8 math practices and "Welcome to Mathland" so you don't think I am a complete hippie. Women, where are you? I want the 4 Claims too.

I would like to add this one but maybe I just need it personal-size:
My teenager and her friend think I should add this one:

What's on your walls?