[following up from here]
Appeal To Their Intuition
"How much cash is this?" Take guesses. The student risks nothing with a guess but that investment pays off huge for the teacher over the life of the exercise because the student wants to know who guessed the closest.
Again, ask "how much cash?" but also ask "how heavy?" Show them the weight. (I zeroed out the jar from every weight measurement you'll see here. Don't worry about it.) Spitball some ideas for determining the value of those coins. You're trying to motivate the idea that the weight of the coins ties directly to how much the coins are worth. Pull up the relevant Treasury website.
Then mix in some nickels. Scoop out a small sample. Play with that. Set up a proportion between value and weight.
Now you have pennies, dimes, nickels, and quarters. I took nine sample scoops, everything from small to big.
I formatted these at 4×6 so I could print them out at our local one-hour shop for a few bucks and put one in front of every student.
Throw A Curve Ball
Some will finish quickly. You tell them you have a jar of coins that weighs 5,500 grams. You reach in and pull out 14 nickels. How much is the jar of coins worth?
They'll run these calculations and come up with an estimate of $55. You tell them it was really $34, which is huge error. Ask for sources of error. Then toss this up and talk about it.
Confirm The Answer
$84.00, if you were curious.
It's essential to give some kind of visual confirmation of the answer, both so we can give credit to good initial guesses and so we can talk about sources of error. (ie. "who was off by the most? did sample size matter at all?")
- Show them CoinCalc, the backend of which does exactly what we've done here.
- This activity follows-up nicely on the goldfish activity, where we used a small sample of fish to determine the total population of a lake.
- We yield the floor to Jason Dyer and anybody else who would like to debate the question, "why are we doing this digitally?"
Here's the entire learning packet [62MB].
[followed up here]
Let's push this forward. The question is "how much cash?" The reference point is CoinCalc.
Your challenge is to outline the supporting materials so that this activity will a) scale from easy to hard, b) throw a few curveballs at the students who figure out its mechanics quickly, and c) offer visual confirmation of the answer to provoke a discussion of sources of error.
If you then consider the fact that a) it's easier to mix coins than unmix them and b) it's easier to tally the value of a roll of coins than a pile of loose change, you'll understand why producing this unit took a week of detailed planning and an afternoon of careful shooting.
[click for high-res]
I withdrew $100 in pennies, nickels, dimes, and quarters from my bank account last week. I walked out of the bank holding a plastic sack full of change, feeling like some kind of underachieving bank robber.
I did this because I live in mortal terror that if I ignore the WCYDWT fairy even one time, she will leave me for another math teacher and whisper interesting ideas in his ear. For this reason, I put her ideas into some kind of play as fast as I possibly can.
I was just thrilled she didn't tell me to literally rob the bank. I mean, it's conceivable.
Posted in uncategorized on October 5th, 2009 41 Comments »
Whatsup: I can’t wait to see you waste another Saturday of your life collecting data on self-checkouts. You should like write a book or something. I’ve been waiting for a resolution all my life, and here it is! Clap your hands, people! This guy’s a nerd!
Some big-boy blogs picked up my grocery express lane post, including Lifehacker last week, from which a few careerist trolls have now immigrated, allowing me a glimpse at the kind of shower mold real bloggers deal with daily.
"Don't feed the trolls" is sound policy which I'm ignoring here not because I'm looking for affirmation from my usual enablers but because I get this from my students all the time, both personally, about world-record math and graphing stories, but also in the abstract, in our show-and-tell post-mortems. We have watched some incredible videos lately — Rube Goldberg machines and time lapse photography, for instance — and if a video smacks even slightly of concentrated effort or advance planning, someone will inevitably scoff that the subject has a) "too much time on his hands" or b) "no life."
Ten times out of ten.
And I would so much rather my students understood the value of turning stupid ideas into reality than the entire sum of Algebra. It's so obvious to me that the kind of person who would create a cocktail-mixer from balsa wood and twine is simply blowing off steam that life will eventually focus in a direction that will be extremely a) constructive, b) profitable, or c) both. I can't make this obvious to my students. After six years I lack a succinct, meaningful response to my students' defensive, clannish embrace of mediocrity, though I'm grateful for this tweet, which comes pretty close:
dwineman: You say "looks like somebody has too much time on their hands" but all I hear is "I'm sad because I don't know what creativity feels like."
Posted in uncategorized on October 3rd, 2009 30 Comments »
I need to clarify my professional situation, which is nothing like my announcement last spring that I was quitting teaching to pursue a doctorate.
- I am teaching two math classes. The same remedial Algebra at the same high school.
- I am working for Google. I have deferred graduate school for a year and accepted a ten-month position as a "curriculum fellow" at Google's campus in Mountain View, CA. I start Monday, which means my understanding of the job is informed only by the application process and not yet by any actual experience. Regardless, I'm ecstatic. Google wants to hire competent programmers, obviously, so they're reaching out to university CS professors and down to high school math teachers, which is my angle. I will be working with a handful of other math teachers to embed the Python programming language into traditional math curriculum for adoption on the sort of scale you'd expect from Google. I am realistic. The challenges are immense but so are the possible returns. It isn't my ideal full-time job developing WCYDWT math curriculum next to an on-call barista but it's really close.