Trying to find math inside everything else

No Right Answer

2012-08-20

A bit ago I got yelled at by a commenter on Kate’s blog who claimed that being always right is why we like math. The problem with that point of view is that, while yes, you can always be right while doing computation, math isn’t just computation. So the other day I was talking with a friend of mine, and that prompted me to post the following tweets:

My friend Phil (@albrecht_letao) responded to the question, and he came up with an answer of $20/hr. When I worked it out with my friend, we came up with $14.25. Does that mean one of us is wrong, since we got different numbers?

No, of course not. What happened is we approached the problems in different ways. Phil only calculated the monetary value: with his amount, my friend would earn the same amount of money she does now. He figured this was an important way to look at it, for paying bills and whatnot. Our calculation came from thinking about how her time is being compensated. Since those 16 hours are being wasted (she has to work them for free; actually, she pays to lose that time), we calculated her “real” hourly rate and used that.

There can be more answers than even these two, depending on what you think is important. But it’s a clear example of a problem, solved using math, with no one right answer. That’s what math is about. I tweeted it thinking maybe it could be a problem worth considering in class, to show that essential idea to students.

What do you think?

P.S. The right answer, of course, came from @calcdave:

 

Category:

anywhere, math

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Totally Radical

2012-07-23

So I’ve been working on creating this board game, Totally Radical. (Tagline: Don’t Be a Square.) After some play-testing and adjustments, and bouncing ideas off of other teachers, I’m ready to post about it.

(But first, thanks to my co-teacher Sarah for helping come up with the game, my coworkers Cindy and Jenn and my Tweeps Max, Jami, and Jamie for playtesting.)


The idea behind the game came before I didn’t really have a good application for simplifying radicals. But I’ve been annoyed at how I see math games designed: do some math action and, if you are correct, you then get to do some game action. While this is certainly how some games work (like Trivial Pursuit), it just separates the math from the game and makes the math seem worthless. So I wanted a game where the math action WAS the game action.

You can read the rules of the game right here: Totally Radical Rules. During the game you have a choice of 5 actions: 3 involve actions we take when simplifying (breaking a number into two factors, taking a root and putting it outside the radical symbol, multiplying two terms together) while two are purely game actions (draw a card, play a special “Action” card).

Other touches of note: the factor cards are exactly half the size of the radicand cards, so that students break up “larger” numbers into “smaller” ones.

You can use factor cards on their own or combined into multi-digit numbers, like so:

(the top would be two factors, 2 and 5, and the bottom would be one factor, 25)
The numbers in the radicand cards are not just simple numbers. There’s prime numbers, composite numbers that can’t be simplified, perfect squares, as well as numbers that can be simplified (going all the way up to 250).

So, how can get this game, you may ask? Two ways!

Make It Yourself

If you want it for free, or are just in that #Made4Math mindset, you can print out the following files on card stock:

Prototype Factor Deck

Prototype Radicand Deck

Cut the cards out and label the backs. Print out the instructions (found here). You’ll also need to make a board: 4 big radical signs (I also recommend cardstock.) That might look something like this:

(I also drew in spots to put the card decks in).

Don’t want to make it or want the awesome one pictured above? Then go for option 2:

Buy It

I found this great website called The Game Crafter where you can send in artwork, pick out the pieces, etc, and they will print and construct the game for you. So if you click the button below, it should bring you to the shop to buy it.

TOTALLY RADICAL
DON’T BE A SQUARE

Category:

games, math

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Twitter Math Camp

 

I’m back from Twitter Math Camp, which was one of the most amazing experiences I’ve ever had. I’ve never made friends so easily, but I was so exhausted afterwards, because we pretty much spent 96 non-stop hours together (except for sleeping time). When people asked me if I had vacation plans this summer, I mentioned I was going to St. Louis for “a conference” and was told it didn’t count as vacation. But oh, it totally did.

 

I’m not sure whether I should blog about the conference or the after conference. I’m a terrible note-taker, so I’m sure others will better be able describe what went on, but highlights include spontaneously lesson-planning with Karim of Mathalicious, community-building and website ideas with Sam Shah, Megan‘s totally awesome Interactive Notebooks talk. But honestly some of the best sessions were the My Favorites… sessions, where people just went up for a few minutes and shared something awesome they did. And it was so much awesome. I also loved how, when something great was said, everyone in the room would say “Someone tweet that.”

 
As for after-conference events, Pi Pizzeria was actually quite good (and so I appreciate a Deep Dish Pizza as being something tasty, but not pizza). The brewery tour was nice, even though is was super-hot and I don’t like beer, but as before, the company was so good. Anyone going to St. Louis (or anywhere close) needs to visit the City Museum, an amazing experience, even if Max Ray did almost lose his wallet from up high. And I was convinced to go see Magic Mike by Julie and Sam, and seeing it with them and the other tweeps (like Marsha) made it hilarious. (Julie taught the whole audience a special dance!)

 

I think the thing that sums it up the most was our final activity:

 

I’ll post about my talk and what I shared later. Have a lot of chores to do now.

 

Category:

conference, TMC

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My Prototype Has Arrived

2012-07-13

About a month ago I made the following tweet:

I’m still waiting to hear back from some of the play-testers, so a more in-depth post will have to wait, but I’m really excited because the prototype I had made arrived in the mail today!

 

 

I think I’ll bring it to Twitter Math Camp, see if the people there have thoughts.

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games

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Lab –> Lecture –> Assessment

2012-06-26

Next year, the weekly schedule at my school is going to be 2 double periods for a particular class (alternating sections on an A/B day schedule) with a single period for every section on Wednesday. Because of the new schedule, I wanted to make a new structure for my class, which is the title of this post: Lab –> Lecture –> Assessment.

There are roughly 30 proper weeks of learning in the year, so I figured I would have 30 Learning Goals to cover, and do one each week. I would introduce each learning goal with a “math lab,” which may be an actual lab (like the popular M&M Lab for exponential growth/decay) or a 3 Act problem or something else that the students can really engage in before getting down to the nitty-gritty and symbolic way mathematicians deal with the problem.

The next double wouldn’t necessarily just be lecture, but it would be the abstraction of what we did the lesson before, including lecturing on technique and practicing what we’ve learned. Then assessment could be any number of things, but will almost certainly involve a targeted quiz.

Seems like a good structure, right? Problem is, while I have a lot of good labs and problems for most of the topics (and will keep improving), not all of them do. Particularly:

  1. Radicals – Simplifying & Arithmetic
  2. Unit Conversion
  3. Solving in Terms Of
  4. Box-and-Whisker Plots / Percentiles
  5. Scientific Notation
  6. Statistics Vocabulary (univariate/bivariate, etc.)

 

So my major goal this summer will be to develop something for each of those. The rest I can fall back on what I have, even if I don’t come up with something new/better. But these have nothing. My first task/idea is to develop a board game about radicals. That’s still under development. Any other suggestions would be appreciated.

Category:

labs, math

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Math Practical

2012-06-16

I was proctoring the Earth Science Regents exam today, and after the students finished I had to direct them to go take the Practical part of the exam in another room. And it got me thinking: why is Earth Science the only exam with a practical? Certainly at least the other sciences should.

Then I thought, well, the foreign language exams do have practicals: they have both a listening section and an oral section, as well as reading and writing. That’s everything. Same for the English exam. And, in a way, the social studies exams do to, in that the DBQs could be considered practicals in that historians work by analyzing various documents. (Though a research aspect would be more pactical.)

So then that got me thinking about having a Math Practical as an exam. It’s totally doable, and I think it would be an interesting idea. How would it work? Here’s an example:

Student goes into a classroom. The proctor hands over supplies: a measuring tape, a clinometer, a Home Depot circular, and a calculator. The exam question is simple: how much would it cost to paint this room? And included must be a margin of error on their calculation. So they need to measure length and width properly, use a clinometer and trigonometry to get the height of the room, calculate surface area, calculate and subtract non-painted areas, turn that surface area into gallons of paint, and then that into a cost. They may even need to calculate exposed surface area of things like cylindrical pipes, too. It’s all math content, but something that is actually done.

Maybe I’ll implement it next year as an exam. If only I didn’t teach trig and surface area right before the Regents….

Category:

assessment, math

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Have Fun With It

2012-06-10

Earlier this year, there was a little Bard panel for the current students that I was invited to as an in-service teacher to speak at (with others). The session was about being an LGBTQ teacher, since those pre-service teachers wanted to know how go about it. (Are you out to your students/coworkers, etc.) I told them that I was out to my students, but only when it was relevant. I wasn’t going to announce it on the first day, but it would come up at some point, and I would be truthful. My students last year found out pretty early, because someone asked in Advisory and it spread around.

This year, though, while a handful of students had asked privately, and while there were some rumors from the 10th graders, they mostly didn’t all know until February. So when I taught my statistics unit in November, I decided to have fun with it. I was doing Dan Meyer’s How I Met Your Mother lesson and updated it a bit. See, I wouldn’t just use Dan’s list of fabricated ex-girlfriends. (For one thing, the start dates are too early.) So I made my own, see if you can spot it:

 

 

 

 

 

 

 

Yeah, I specifically chose all the names so they were all androgynous. And during the lesson I only referred to them as my “exes” (much like Ramona Flowers did in Scott Pilgrim) and using “they.” So I never assigned gender to the people. The students did, though, and I thought it was super interesting to see who assumed they were girls, who assumed they were guys, and who actually caught on that all the names could be either (only 2 or 3 did).

Just playing that tightrope game made me smirk throughout the whole lesson. Mostly because it was just a game, as walking that tightrope while trying to actually hide your sexuality would be terrifying. But since I wasn’t trying to hide, it was fun. And that was my advice to those Bard pre-service teachers: have fun with it. Because if you’re comfortable enough to have fun with it, they’ll be comfortable, too.

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LGBTQ

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My Final Exam

2012-06-08

My second post was about the game Facts in Five and how I thought the scoring system would be helpful for my assessments. I had also been having thoughts about the way to measure synthesis while using SBG. So I thought having a final exam specifically designed to measure synthesis would be the best way to go about it. Here’s how I went about it. (This was the final for the Fall semester, since for the Spring they have the Regents.)

In each bin, I put a slip of paper containing a question. Students will go to the bins and choose which questions they would like to answer, and compile them into a coherent exam.

Those aren’t fractions on each bin label, though. They denote which Learning Goal each question consists of. Instead of having each Learning Goal have its own questions, they mix. But each goal still has 4 questions that apply to it, like so:

Not every topic can be combined with others, but now the student can choose which goals to work on: either they can try to improve a Learning Goal that they got a lower grade on, or pick ones they did well on and show they can perform Synthesis, which is above mastery. But, of course, all of these questions are harder than what they’ve done before.

To score the exams, I use the same scoring system as in Facts of Five, with students squaring what they get right in each Learning Goal. So they will get more points by focusing on completing a goal, instead of jumping around. An example:

Here this student got a decent score by focusing on completing four of the learning goals (9, 11, 16, and 18), and receiving assorted other points.

I definitely like the idea here, but I do need to refine the delivery. It was hectic. But I did not want to print out all 44 questions for everyone, when not everyone will do all of them. That would be a lot of paper. Suggestions are welcome.

Category:

assessment, games

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The Monty Hall Problem

2012-06-06

(Step one in going through a bunch of posts I’ve wanted to make.)

After reading this post on the Monty Hall problem last year, I decided to do a lesson on it. And it worked out okay. But, as Riley Lark did in that post, I did it at the end of the probability unit. So this year, I decided to go for it and do it first. And I must say it worked out quite well, because from the get-go it shows them that what they think about probability isn’t quite right.

First, to play the game itself, it’s good to have a little showboat, plus something that is easy to reset. So I built this:

Image

(It’s a display board and I cut the doors open.) So it was much easier to play the game from the stay, and to keep my hands hidden as I do things behind the doors.

The other thing I did was, before we discussed the theoretical solution, I had them experiment. I gave each pair of students 3 playing cards, 1 red (for the car) and 2 black (for the goats), so one player played host while the other switched or stayed.

The main thing to learn is you really need to MAKE them switch, because teenagers are stubborn and are sure they were right the first time. But only staying won’t show all the necessary results.

Category:

lessons, math

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Algebra Taboo

2012-06-01

I remember reading about the idea of Math Taboo on Sam Shah’s blog, this post by Bowman Dickson. I feel like I had the idea independently, but it seems like many people have, by doing a cursory Google search of the phrase.

Unfortunately, there are lots of posts ABOUT math taboo, but no real materials provided. If I have seen anything, it’s a lesson plan on having the students make their own. Or I saw one for sale, but it was for the elementary level. So I made one myself.

My co-teacher and I went through all the Integrated Algebra regents given since 2008 and pulled out any words that it’s possible a student might not know. I also went through my own lessons and pulled out any vocabulary I had given them. Below is the .pdf for printing your own (I used card stock and laminated), and two .doc templates if you’d like to make more, or alter the ones I have. I made a total of 126 cards (63 double sides – maybe slightly overboard).

Since I found no others, it makes sense to share.

Downloads

Math Taboo (full pdf)

Math Taboo Pink  Math Taboo Blue (doc template)

Category:

games, lessons, math

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