One of my day jobs, at least. I put this together for a thematically appropriate Pi Day quiz for the site that I work for. If you haven’t played a Word Ladder quiz before, the concept is that each correct answer changes exactly one letter from the previous answer.
…it’s also an important concept that many of my physics students have studied recently.
Conceptually, torque is the quantity required to make an object rotate around a given point. I’m being very careful to avoid phrases like “how hard you have to turn something”, because there are ways to increase your torque without increasing the force you’re applying.
Distance from the point the object is rotating around is also a factor, as evidenced by the device I found in my parents’ kitchen.
The science museum that I volunteer at recently opened up the traveling math exhibit that I’ve been looking forward to for a while. One of the activities features a piece of equipment that, as a physics student/teacher, is near and dear to my heart: the motion sensor. As you walk towards and away from the sensor, it records how far away you are and plots this distance on a graph.
It’s a nifty setup that gets people thinking about how motion can be described both visually and mathematically, but it does raise the question: how does the sensor know how far away you are?
The explanation is best illustrated with a game of catch.
…a fraction’s a fraction, no matter how small. It’s mildly irritating that many people seem unaware of this.
To fill the silent void of an empty house during this stint of unemployment, I’ve been rotating through the options that YouTube, NetFlix, Hulu, and various network sites have to offer. Nothing too heavy; it’s generally just background noise as I work on job applications, knit, write this blog, etc. You may recall that I’m a huge fan of game shows and cooking shows, and Food Network’s Cutthroat Kitchen fills both of those niches nicely.
If you’re not familiar with the premise of the show, four contestants each have $25,000 to bid on opportunities to sabotage their opponents. After each round of cooking, one contestant is eliminated until the last chef standing wins the amount of money he/she has remaining. To add a bit of dramatic flair (and likely a bit of a psychological element), the contestants are issued their auction money in the form of 250 hundred-dollar bills.
Naturally, many of the contestants are giddy at the opportunity to hold that amount of cash: “I’ve never held this much money before, not even a fraction of it!”
Um, yes, you have. Have you held a one dollar bill? Then you have held a fraction of 25,000 dollars: 1/25,000. A fraction is just any portion of a whole, regardless of how small. (It can even be more than the whole, if you’re willing to get into improper fractions.)
A child holding his or her first penny still has a fraction of 25,000 dollars, even if it’s a little trickier to convey. A penny is generally expressed as .01 of a dollar, so we could write the fraction as .01/25,000. However, fractions are more intuitive when there are no decimals within them; .5/2 is equivalent to 1/4, but the latter is much easier to picture. To get rid of the decimal in that case, we multiplied the top and the bottom by 2. (Recall that 2/2, 3/3, 42/42, etc., are all equal to one, so multiplying by them does not change the value of the fraction.) Since .01 x 100 = 1, we can multiply the top and bottom of .01/25,000 by 100 to get 1/2,500,000. It’s a small fraction, but a fraction nonetheless.
…and, thanks to the magic of post scheduling, this post is going up at exactly 9:26AM on 3/14/15.
To be honest, I initially wasn’t sure what my Pi Day post should be about. I’ve already written about pie and circumference; what aspect should I cover now? The answer struck me as I recalled a question on a job application I filled out recently. I was asked what my educational philosophy was and how I had demonstrated this in previous positions. After years of studying and working in education, my response felt hackneyed, but it really is my philosophy: people learn better when they see and experience concepts rather than just memorizing facts and formulas. This requires hands-on activities and real world demonstrations. So how can we apply this to pi?
The essence of pi is that it’s the ratio between the circumference of a circle and its diameter. We don’t have to put blind faith in this formula, because we can test it for ourselves.
You will need:
- a variety of round objects
- a flexible tape measure (think sewing box, not tool box) OR ribbon, a marker, and a ruler
1. Take a round object. Use the tape measure or ribbon to measure across the diameter of the object; if using the ribbon, mark the length of the diameter with a marker and use the ruler to measure this length.
It’s Girl Scout Cookie Season, which means…arithmetic? It’s one of the few occasions that requires me to pay cash to someone who isn’t standing in front of a register, and I was happy to see that the mom handling the money started making change for my 20 without reaching for any sort of computational assistance.
I love calculators as much as the next person (probably more, actually), but there’s a time and a place for them, and basic arithmetic isn’t it. Back in the day, kids would complain about having to learn how to do arithmetic. “We have calculators for this,” they’d exclaim, and teachers would respond that no one carries a calculator with them at all times. Fast forward twenty years, and now we have calculators built into our phones. But who really wants to whip out their phone every time they want to multiply three times four or subtract twelve from twenty? I can tell you that, based on my experience as a teacher, tutor, and general math-doer, it’s much easier, faster, and more reliable to apply basic arithmetic facts than it is to break out a phone, open up an app, and punch the correct buttons on a touchscreen.
This is especially true when dealing with hordes of cookie fiends, and extra-specially true in my particular case.
Girl Scout Mom: “Change for a twenty…” Me: “No, I’m buying five boxes. Girl Scout Mom: “Bless you.”
…but a Mobius strip is not a situation; it’s a one-sided object. Having trouble imagining it? Fire up your copy of Mario Kart 8 and play the first course in the Flower Cup…don’t have that? Come over and play it at my house, unemployment is LONELY. Or you can just try this at home.
- a narrow strip of paper at least 15 cm long (around 6 inches, if you insist on not using metric)
- two different colored pens or pencils
- scotch tape
Got all that? Here goes: