First Period: Well, what do you think? Anybody, anybody? I can wait you out...OY VEY!

By second and third (we are on block schedule, so we are now from 10am to 2pm) Things are oh, so much better!

Mostly I learn from try, try, try again. My favorite question go to is: How are they alike? How are they different?

Some examples:

Similar Triangles vs. Congruent Triangles
Similar Triangles vs. Dilated Triangles
Solving Equaliites vs. Solving Inequalities
atrigb(x-c) +d vs afcnb-c) + d

Other favorite questions are:
Harold says, Emilia says, who's correct? Are they both correct?

What is another way?

How do you know your solution makes sense?

How do you know?

When did you know you were on the correct path to a solution?

Where did you fall off the ramp? When did you stop understanding?

What was so and so thinking when they took the next step?

I am determined to start writing more of my questions ahead of time, and write them HUGE so I will remember to ask. I would also like to be in the habit of answering more questions with another question, even if it is only, "What do you think?"

As I have been thinking about this prompt, I am reminded about how much you learn when ask students super straight forward questions.

When you write SinA/a what does it mean exactly?
What does proportional mean?
If the scale factor is 5/4 is the image bigger or smaller?
Is the answer going to be more than or less than?

My favorite new technique is inspired by Kate Nowak, simply, "What is the Question?"

29 years and so much room for improvement...Thanks MTBoS



%math %blog %education %learn %cool
Week 2
My Favorite Things:

Favorite Geometry Activities: Too Much Trash. Guess I am a proportional reasoning kick. "If everyone in Windsor lined up their recycled papers for a year it would reach 249, 289 miles! That is 4,000 miles shy of the Earth to the Moon!" Says Casey M. a ninth grader in my Geometry class that took the amount of paper his family uses in a day, and extrapolated the data based on Windsor, California. *Just found out cannot link to document on Blogger, so just message me for copy of project and Rubric. 

Off the Quadrilateral Island: This is a simple little sort we did with Quadrilaterals. I gave groups of 3-4 students one line of this hand-out: (Not mine, got it from Google, can't find my original source, does anyone recognize it?
%math %blog %education %learn %cool


The directions are for students to use the proper marks to show your assumptions about each figure in their row. Then decide which quadrilateral doesn't belong and explain why. The product is a poster that explains the attributes of the survivors and why the quadrilateral they choose was kicked off the island. We did a gallery walk. The students only got 20 minutes to decide, plan and make the poster. 


Favorite Ice Breakers:
From Dinner Party Download Podcast: The hosts, Chuck and Josh, ask all their guests two questions: What question are you tired of being asked and what is something that we don't know about you. 
Another is: Uncommon Commonalities. In a group of 3-4 (preferably 4), one student, say the oldest, draws a pair of concentric circles. 
Have students divide up outer ring with the number of students in group. Each person has to find something unique about him/herself to put in outer ring. In the center ring, they have to find something they have in common, can't be about school, the town they live in, or gender. Some pretty interesting facts come up. My favorite was a group of two boys and two girls, where all had at least two pierces in their ears. You get unique allergies, folks who play instruments, black belts, people who were born in other countries, all kinds of cool people tricks. 

Favorite Places to Get Insight:
Twitter: #MTBoS
Desmos
Geogebra
Wolfram Alpha

Favorite New Source for Mathematical Thinking:
If you teach any kind of proportional thinking, you have to check this site out! 
Example:
%math %blog %education %learn %cool

Love! 



Happy #MTBoS Challenge Numero Uno!

One, two, three good things! Woot! My daughter Sarah, studying in London (LSE) for Junior year abroad, decided if she was going into marketing, she better be good at what she does, and what better way than to start with her dear mother's old blog.

S: I wanted your blog to look clean, not with that dumb starfish and the yellow writing.

Mom: Have at it, just make sure I have my MTBoS buttons...







That was Sunday. Monday, I found out David Bowie died while I was driving to school. The students walked into a room blasting "Changes" and I changed my Facebook profile to this:
(Thanks Fintan in Ireland) (When I got home the Hubs and I danced around the kitchen in tribute)

But the good thing on Monday was that I was given a huge compliment by a student who always pushes back, as in "Can't you just show us ONE way to write it?" He said, "Zimmer, I hope I get you on my Senior project panel, you embrace diverse ways of approaching things."

And today, Tuesday, I gave "My Favorites" presentation to my students from TMC 15 (found on the wiki) about where trig sum and difference formulas come from. It went especially well 2nd block. We used my special Neon paper, and no paper airplanes afterwards. Just gotta say, I am not sure of the pedagogical need for the sum and difference formulas in the average person's life, yet it sure forces the students to get their Algebra trip together before entering college!

Earth to Major Tom...

Why do I have to learn this? I am so lucky that 29 years in, I still have Aha's (or Alzheimer's).

sin75⁰ for example. My calculator does this Sh*t, so why should I? I know why, in one of those moments of clarity, because...if I never made you look at the sin75⁰ as the sin(30⁰ + 45⁰) and only let you use your calculator, you would never get to discover that the trig functions are not distributive. Mind blown, KaPow. I have TOLD the students over the years that the functions aren't distributive, but I have never delivered a reasonable reason for why they should care until now.

Another important reason I discovered for WHY Precalculus and Trigonometry students should find the exact value of sin75⁰ is because...I uncovered SO many misconceptions about adding radicals, I felt like a complete idiot that I had assumed a skill level that just wasn't there. 

E.D. a student with a 95% average: (✓6 + ✓2)/4 = ✓8/4

V.C. a student with a 90% average: "I have no idea how to add ✓6/4 + ✓2/4

And on and on it went. I felt so lucky to have tripped on this little secret from students with A's and B's in Algebra 2. Phew.

For another time, why do so many students struggle with adding fractions? Anyone? Anyone? 

We had a new seating chart in Geometry. I like to use ice breakers to warm the kids up, especially after a break. I sneakily chose this one: Think about your favorite destination in the United States. Share that destination with your "elbow" partner. But I had bigger, more devious designs for their answers. 

I needed a lesson idea for unit analysis. I liked this one http://betterlesson.com/lesson/614611/dimensional-analysis from Betterlesson.com that I tweaked. 

I asked a student who usually has ants in their pants to come up front and another pair of wigglers to come up also. I gave the antsy one the job of jumper and the wigglers as spotters. The idea was to have wigglers measure a vertical jump. Then I picked a volunteer to tell me their favorite destination, her house. Great. Go on Google Maps and tell me the exact distance in miles from our campus to your house.  The question was "How many Ian jumps to Katie's house?" Going from centimeters per jump to miles. I was lucky that a smarty pants student wasn't as smarty pants as he could have been, because he asked Siri how many centimeters in a foot, not the entire distance. Phew. For the next part I let the students design a jumping activity--vertically or horizontally, to one of their destinations, had to go from centimeters to miles. For their partner's destination they had to use "strides in one trip across the room." As in there are how many Susie trips across the classroom to get to Imagination Island? Again from centimeters to miles. As it was raining, this was a great activity. The one stipulation was that they had to use the centimeter to foot conversion that smarty pants came up with. 

The next morning I showed them this picture:



And asked what questions did they have?
Then I said to look over with their partners what questions could be answered knowing that the ball used 840,000 rubber bands and 1/4 bag of 3" rubber bands contains 460 rubber bands. Our calculations were way off, but we had a lot of fun and asked what could have led us astray. 

Their homework was from a blog post I found on the MTBoS search engine Ms Z Teaches in Mathland
(Hey, that is my own blog post from 3 years ago, almost to the day!). Their job was to take something that they threw away, and measure it by length, area, or volume, determine how much it would be if every person in Windsor used the same amount, and make that amount TELL A STORY. So what if it is 1,000 miles long. Give us an exact location. Can the amount fit in our classroom, in the gym, fill Lake Tahoe? Students were exited to show me how far pieces of paper used lined up in a year (4,000 miles shy of the moon lined up end to end). Can't wait to see their illustrations!

Does this count as modeling?

About how kids are cheating these days next time.

Hope you have good times with your kiddos this year!

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?