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The Desmos/Mathalicious happy hour in New Orleans on Friday was a great end to a long week of conferencing with math teachers, math ed professors, and the occasional vendor. My unofficial crowd estimate puts it at something like 50x the size of their 2014 event in Denver, CO.

The Desmos team and I wrote up some happy hour questions which were fun enough that several people requested the complete list. You should feel free to use them also. Please address complaints, quibbles, or corrections to Bill McCallum c/o Illustrative Math.

1. Math Homophones

All of the answers in this round are well-known mathematical words or phrases. (Example: "It lies under the mantle and belongs to use all" is also known as the "Common Core.")

  1. Bad news at the dentist for Salman. (A: concavity.)
  2. A ski run you feel really good about. (A: positive slope.)
  3. A lady’s partner who’s gotten some sun. (A: tangent.)
  4. Messages you send in the same direction. (A: parallelograms.)
  5. Treads on the Red October. (A: subtraction.)
  6. Mickey’s British mother-in-law. (A: minimum.)
  7. It said, “please come aboard two by two”. (A: arcsine.)
  8. A change to a military banner. (A: standard deviation.)
  9. Louisiana Governor Huey drawn and quartered. (A: long division.)
  10. An airplane bathroom that is not vacant. (A: hypotenuse.)


  • Answer to the question, “Have you seen a letter jacket belonging to one of the protagonists from Monsters University?” (A: isosceles.)
  • A condition in which you become a better dancer after having a organic beer. (A: natural logarithm.)
  • A matching outfit you’d wear in freezing cold weather. (A: polar coordinates.)

2. Kids Say The Darnedest Things

We asked four hundred 3-5th graders some questions about math. You're going to tell us what they said. We asked them …

  1. … who invented the Cartesian plane, a) Albert Einstein, b) Carter Von Ludvig, c) Rene Descartes, d) Eric Cartman, e) none of the above? What percent said the correct answer? (A: 9%.)
  2. … to name any mathematician. Name the top four answers for one point each. (A: In order of descending popularity, Albert Einstein, my teacher, Eric Cartman, Carter Von Ludvig.)
  3. … which is there more of, a) feet in a mile or b) pounds in a ton? What percent said the correct answer? (A: 57%.)
  4. … what their favorite number was. Name the top four favorite numbers of elementary students? (A: In order of descending popularity, 7, 10, 8, 11.)
  5. … which would you rather have: $100 or a stack of quarters from the floor to the top of your head? Which was the winner? (A: $100. That got 67% of the vote. Did they choose well?)
  6. … which was heavier, a) a ton of bricks, b) a ton of feathers, or c) a ton of kittens. What percent said “kittens?” (A: 5% The winner was a ton of bricks at 93%. Good job, kids.)
  7. … what was faster, a) the speed of light, b) the speed of sound, c) the speed of wind, or d) the speed of kittens. What percent said “sound”? (A: 25%.)
  8. … if zero was a) even, b) odd, or c) neither. What was the most popular answer? (A: In order of descending popularity, Even [46%], Odd [10%], neither [44%].)
  9. … what the biggest number is. Name the top four most popular answers for one point each. (A: In order of descending popularity, infinity, one hundred million, one billion, googleplex.)
  10. … to name the shape of a stop sign. Name any of the top four most popular answers for one point each. (A: In order of descending popularity, octagon, hexagon, pentagon, hectogon.)

3. Common Critters

Even though your students may struggle to meet the Common Core State Standards, some members of the animal kingdom are doing just fine. We're going to match a standard to an animal. You tell us if the statement is backed up by a scientific study or if we just made it up.

  1. Salamanders can "identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies." (A: True.)
  2. Ants can measure lengths indirectly and by iterating length units. (A: True.)
  3. Goats can prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. (A: False.)
  4. Chickens can fluently add and subtract within 5. (A: True.)
  5. Octopuses can tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. (A: False.)
  6. Dolphins can construct viable arguments and critique the reasoning of others. (A: False.)
  7. Crows can use appropriate tools strategically.(A: True.)
  8. Owls can count out a number of objects from 1-20. (A: False.)
  9. Parrots can correctly name shapes regardless of their orientations or overall size. (A: True.)
  10. Spiders can apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (A: False.)

4. Music Round

We're going to play 10-second clips of famous songs. You need to name the number that features prominently in the song.

  1. "99 Problems," Jay Z. (A: 99.)
  2. "22," Taylor Swift. (A: 22.)
  3. "Jenny," Tommy Tutone. (A: 8,675,309.)
  4. "Take Five," Dave Brubeck. (A: 5.)
  5. "Summer of '69," Bryan Adams. (A: 69.)
  6. "Seasons of Love," Cast of Rent. (A: 525,600.)
  7. "A Thousand Miles," Vanessa Carlton. (A: 1,000.)
  8. "Sixteen Candles," The Crests. (A: 16.)
  9. "100 Years," Five for Fighting. (A: 100.)
  10. "American Pie," Don McLean. (A: π.)

I spent some time recently with the Leadership, Curriculum and Instruction department of Oakland Unified School District and I think they're doing some of the most thoughtful work around. They nurture their talent, celebrate successes, promote good ideas from within, and sustain what seems (to this outsider) to be a very health professional community.

Their Instructional Toolkit for Mathematics [pdf] deserves your attention. It describes their defining "strategies and experiences," including:

  • Number talks
  • 3-reads
  • Participation quizzes

I particularly like their "Evidence-Gathering Card," which grounds a lot of abstract ideas (like "A growth mindset matters") into "student vital actions."


From our friends at the Shell Centre:

The aim of Shell Centre Publications has always been to ensure that a number of seminal works in the field of mathematical education remained available. We have now reached the point where our most popular items are out of stock, and have come to the decision that it is time to stop storing and selling physical books. Digital distribution is the best way to keep these works available, so in the coming months, we will be making many of the publications on our list available, for free, as PDF downloads.

These books are just great. The Language of Functions and Graphs, in particular, has a couple of career's worth of great activities, lesson plans, and essays on teaching functions. Highly recommended.

[via Michael Pershan]

Why Joe Schwartz Blogs

Joe Schwartz:

I’ve been teaching for over 25 years and this is the best way to document what it is that happens in classrooms. A friend looked at my blog and then said to me, “Now I get what it is you really do.” Of course we can never actually capture all the moments, both large, small and in between, but I think all of our blogs together can do that. And in the climate we find ourselves in today I think that is very important.

Joe's blog is one of my favorite recent subscriptions. You should subscribe.

It's really hard to find dedicated elementary math teacher bloggers for a lot of really good reasons. In particular, they generally teach everything so why would they specialize their blogging. All of this makes Joe's blog invaluable.

Two good starters:

I'm reposting Michael Fenton's question here, less because I'm interested in you seeing my answers and more because I'm interested in seeing yours. Ignore his five-year qualification. If your motivations for blogging have changed over any stretch of time at all, let us know why.

In 2009, I blogged because:

  • I wanted a record of what I taught and believed about teaching that I could reflect on and laugh at later in my career.
  • I needed a community. I taught in a rural district with five other math teachers (two of them married). Fine educators, but they were in different stages of their career and had answered a lot of questions I was just starting to ask. I needed people.

In 2014, I blog because:

  • I want more interesting questions. In 2009, I was asking questions about worksheet design, PowerPoint slides, and classroom management. By articulating my questions and noticing which of them created vibrant discussions and which of them fell with a thud on the bottom of an empty comments page, over five years I have moved on to some questions that make my work a joy to wake up to every day. eg. What do computers buy us in curriculum design? What does good online professional development look like? What does it mean for students to think like mathematicians and how do we scaffold that development? What is the "real world" anyway and what does it buy us in math class?
  • I need to stay connected to classroom teachers. I'm fast approaching the date where I'll have been out of the classroom for longer than I was in it. Which scares the hell out of me and keeps me asking for advice from real life classroom teachers on this blog and reading, like, five hundred thousand teacher blogs every day.

A readership is more essential to my goals now than it was then. If you guys aren't tuning in and pushing back at my ideas and offering your own, those ideas get a lot dumber. (In 2009, by contrast, I had 120 students to let me know when my ideas were dumb.)

So a lot of what I do in my blogging lately is try to send you signals that I read and value and act on your responses. (See: the recent confabs; featured comments; putting the word out on Twitter that there's an interesting conversation brewing, etc.)

Perfect encapsulation of all of the above: this week's circle-square confab, which featured 62 comments from a pack of great teachers, creative task designers, and math education researchers.

That's why I blog now. Why do you?

Featured Comments

John Stevens:

I started blogging way back in 2012 because I needed a way to reflect. I was in a very, um, rough patch in my teaching career and needed a way to get some thoughts out there. I was reading all kinds of other blogs and seeing what others were doing, stealing material from people left and right. Therefore, my blog was a way to thank people for giving me cool stuff.

Fast forward to 2014 and things have changed. I’m still reading blogs and stealing left and right, but I’m also trying to give back a little. As information kept pouring in, I started to get some ideas of my own. Sure, some of them are awful, but I’m proud of Barbie Zipline and some others. At this point, it’s still a 70/30 take/receive deal, but I’m all for it.


I feel like I’m currently struggling to answer this question – which is probably why my blogging rate has been downwards of around once a month these days.


So many of the good teacher moves are invisible, and as I begin to blog I aim to capture some of the techniques that I have used to engage students. I often pass along worksheets and activities for teachers to use, but sometimes what I really want to pass along are the questioning techniques used throughout the lesson, along with a structure to ensure that students are discussing mathematics instead of working in isolation. Blogging allows for this extra commentary.

Michael Pershan:

When I started blogging, I desperately needed to validate my experiences. I was teaching in big ol’ NYC, but at a private school with just one other math teacher. I needed to know: Was my teaching weird? Was I actually figuring things out about teaching, or just headed down my own idiosyncratic path? I wanted to say things that made sense to other people, so that I could be really sure that they made sense to me.


My blog is for figuring things out, so that someday I’ll be able to help teachers and kids out in a real way.

Chris Hill:

I used to blog because I felt like I was coming up with some innovative lessons and I was learning some new approaches.

Recently I haven’t blogged because I’ve been handicapped into traditional direct instruction lessons (through resources and student culture). Maybe when I’m not in a different school every year (or when I’m excited about the school where I teach) I’ll start blogging again.

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