My colleague extraordinare over at The Mathy Murk, asked our Geometry team how we wanted to introduce the notion of midpoint. She was inspired by Dan Meyer's 3 Acts. I wasn't sure what the parameters were and was a little stuck by own notion of midpoint having to be something collinear. And thus the "notion of where is the best midpoint" was born. Please, oh, please comment on how you would make this lesson BETTER!

Students walk in and are handed a blank half sheet of paper:

Teacher: Draw two houses. (Check some of these beauties out)

 After 90 seconds: Teacher again: Put a dot on the midpoint between the houses.

Teacher: Come tape yours up on the whiteboard.
Teacher: Discuss with your table, which midpoint is the best.

 The odd thing was, that 99% of the students floated the midpoint.

Would you call this midpoint a floated midpoint or a foundational midpoint?

Only a very small handful of students put the midpoint on the ground lined up with foundation of the houses.
(One of the team came in at break, "Ack! no student (out of 30) put the point on the ground! But at least someone suggested it, thank goodness.")

Next we made a list of criteria and had a debate about the assertion:

The best midpoint is inline with ground and foundation.

Lots of pro and cons.

Phew. We talked about congruent segments, definition of between, what does middle mean, and finally, definition of midpoint. It was all a worthy discussion, AND, how could have it been better? Oh, and the best house of them all:

The Smurf house!

Why is it that Regular M and M's are 1.69 ounces per package, but Peanut Butter M and M's are 1.63 ounces per package?
(The M and M Anomaly, Planet Money, June 6, 2014)

How do All You Can Eat restaurants make money?  (How Do Restaurants Set Their Buffet Prices, Marketplace, June 9, 2014)

What does one do when his child has a rare disease and you find out that no pharmaceutical company wants to invest in research because it isn't profitable? (ie, virility drugs sell more than FIVE Billion dollars annually) "For Sufferers of Rare Diseases, Options are Rare Too, Marketplace, June 9, 2014"

Why will it take at least 10 years for the number of US women CEOs to be on parity with the number of male CEOs when women make up nearly 60% of the work force? (Women make up about 3-4% of CEOs in the US currently) (Will Women CEOs Still Standout in 2024? Marketplace, May 21, 2014)

I have been collecting these juicy morsels of audio files for months and days, knowing how they inspire me, and wondering how I can use them in my classroom to inspire my students. I was listening to this line from Marketplace when my students were just finishing exponential growth and parent graphs:

“[This] kind of social change isn’t a line. It's a curve. It's slow to begin with, like the adoption of a new technology, and then it ratchets up. And it has all these spillover effects. Talented women mentor other women. They mentor other women. The curve gets very steep very quickly.”

I was so excited because I knew my students could visualize and draw out reasonable graphs to describe what this professor from Harvard was saying.

These stories light me up. They make me curious. I know somewhere in these stories there are opportunities for low entry, high ceiling questions that can lead to meaningful mathematics:

Compare and Contrast
Academic Vocabulary
Crafting Meaningful Arguments
Modeling Mathematics


      As far back as I can remember, my family has played cards. Random memories include:
  • Playing Black Jack with my dad at age 4 or 5 in my grandmother's apartment in San Francisco (1967 or 1968)
  • Mother's bridge parties (1969 to 1975)
  • Playing Casino with my Nana while Merv Griffin hummed in the background
  • Winking, biting my lip, and raising my eyebrows to signal my Mus partner that I had something good
  • Spite and Malice with my sister anytime, anywhere. 
  • Flying and being given a deck of cards
  • Again at 4 or 5 crawling over to my Aunt Polly's sleeping bag to see if she was awake enough to play Cribbage at the first sign of summer light
We played other games too, Parcheesi, Chinese Checkers, Dominoes. My dad taught me Pinocle and Poker too. Don't you think this is where I began my love affair with math? And my parents were always in disbelief...I am not.

During our Probability unit in Algebra 2 I am amazed at how few students have experience with a standard deck of playing cards. They don't know about the four suits, the number of cards in the deck, how many of each suit there are, or even how to multiply by 13's. It seems such a part of my cultural literacy.

How have you translated "a standard deck of playing cards" with today's students? Is there some hip video game I am clueless about? Is there some new board game that is all the rage?
James Altucher is a quirky business guru, podcaster, diy learner. If he were a math teacher, he definitely would be in on the MTBoS. He wants you to be better. (Yeah, he wants you to buy his books, but he also wants you to learn from his mistakes and he wants your path to be easier because he learned a lot of it the hard way.)

Why am I bringing up a business dude? BECAUSE, he recently had Austin Kleon on his show. Their conversation was powerful and resonates strongly with the MTBoS philosophy. Some of what they discussed was about how to have creative success. You have to put your work out there. Even if it isn't perfect, those you trust will help you make it better. (So MTBoS!) He talks about how most of us have been influenced by others. Cool. Talk about who inspires you, what articles, blog posts, activities are piquing your interest and making you feel empowered. Acknowledge your heroes and whose floating your boat at the moment and how they have inspired your work.

We have all known the teacher who thinks they are the expert. They must be the keepers of the knowledge and want their students and colleagues to hang on their strategically parceled wisdom. What James points out is that this kind of teacher/speaker/boss/worker/human misses out on a valuable part of the equation: LEARNING. Wow! My self-esteem regarding my quirky, risk-taking, growth mind-set teaching style got a little less feeble, I think I grew an inch. What a relief to know that even though I have been teaching a long, long time, it is not only okay, but actually enlightened to acknowledge that I am NOT the solitary expert on ALL of Geometry!

Perfect timing to meet the challenge of the last two teaching weeks of the year.

I hope you all have a wonderful year end and an invigorating summer.

It has been about 100,000 years since I have posted. Call it survival. Call it a CCSS learning curve.

I did want to mention my amazing colleague's blog, Mathy Murk, especially if you care about mathematical modeling, alternative assessment, and constructing viable arguments. Jessica Murk is a constant inspiration to me.

Mrs. Murk always says to her students, "I want you to be critical consumers of information." And if you are one of Murk's Geometry students, you are getting plenty of practice!

Go check it out!