Linear: temperature vs. volume of gas in a closed container
10oC, 500 ml; 20oC, 520 ml; 30oC, 531 ml; 40oC, 558 ml;
What I like about this one is extending the line backwards until V=0. The resulting temperature is very close to absolute zero. These are kid-found numbers and yet we get within 10o of the accepted absolute zero. That's definitely cool.
The freestyle skiers and motocross users have a program that allows a video to be converted into stop motion or for two videos to be superimposed, called Dartfish. They use it at the Olympics to show two racers running a course simultaneously. Search Google images for Dartfish and racers and then combine the pictures and a grid. Make sure to tell them to mark the centers of gravity. Or not. Make it interesting with one of Dan's Pictures that doesn't have the complete arc.
Then, here's a set of points. Figure out which regression gives you the highest value of R^2 -- 2nd catalog > Diagnostics ON
x: -3, -2, -1, 0, 1, 2, 3
y: 3, -8, -7, 0, 7, 8, -3
An additional note for anyone using TI: In all of these, I have them put the equation into the y= list. I let them retype a couple times, then mention that (Stat, Calc, 4) LinReg (VARS, Y-Yars, Y1) Y1 will automatically put the equation into Y1 if it is empty. Use a different Y if Y1 isn't empty. Then you can have the points and the regression showing together. This stunt works with any of the regressions.
I got into the spirit and wanted a total list for future reference so I copied the comments from folks who chimed in. I kept those who provided links or a different thought and trimmed the rest. I did not check the links and did some editing ...
Read more below the jump:
Kate: This is the best of what I have so far:
* period vs length of a pendulum (quadratic)
* square footage vs price of residential real estate in Manlius (messy, but linear)
* the growth of the population of Facebook (exponential)
* time vs distance and cost vs distance of various airline flights (linear)
Calculus Dave said...
A teacher at my school uses the pseudoscience of "biorhythms." Kids can then find their own and follow it up with keeping track of "good days" and "bad days."
Dan said...
Percentage of the moon illuminated vs. calendar day. [data]
Duration of a plane flight v. miles traveled. [data]
Sue VanHattum said...
I use minutes of daylight in trig class. [Data is here.]
Scott said...
Sunrise/sunset times. The available data might be "too accurate" for your taste. I had kids record data one year, but I didn't keep up with it well enough and we had to fill in with newspaper stuff. Anyway, it came out pretty nice, and we talked about daylight savings (a transformation!) and latitude. Another thing about sunset is that kids can decide if they want to hang on to hh:mm (for ease of communication) or instead go for minutes since midnight (for ease of functional notation).
samjshah said...
An idea related to that, that I had this year (but didn't get to do) was going to be called something like: "FORREST GUMP, SLOW DOWN AND WALK"
1. Have students go on Google Maps and plot WALKING directions from the school to like 25 destinations -- maybe 1/3 near and 1/3 in the state and 1/3 far. Disneyland. The local pizzeria they love. Mt. Rushmore. The state capital. Etc. Then they plot the DISTANCE vs. TRAVEL TIME.
Talk about why the data is linear, what the slope means, what that means Google is assuming about walkers, what a proper domain is for that function, what doesn't fit the pattern, what's a good way to graph all these different distances (feet vs. miles) etc
samjshah said...
Also, they can find data for Moore's Law!
http://samjshah.com/2009/02/24/moores-law/
David said...
Force vs. displacement of a spring?
nyates314 said...
Potentially exponential (or maybe logistic if resources are running out?) - world or US population. The US page has a link to historical population estimates. I used the US data for a logistic growth regression as part of a project.
As part of a different project, I have students model Olympic speeds or distances with a linear regression (speeds getting faster with time). It's often interesting to compare men's and women's regression lines for the same sport.
Terry Kaminski said...
Using the internet, students need to find data on tide levels at 2 different locations in Canada. Go to a search engine and search for Tide Tables. Look for Canadian Tide Tables. Need to find data that is sinusoidal (This is important. Not all tidal data is sinusoidal). Create a table of the data for each location for a 24 hour period, a graph of the data, form a sinusoidal regression.
Jasmin Loire said...
I don't exactly know how you'd gather the data, but I'm thinking (with my science teacher mind) that something like Wein's law may be useful. It states that the intensity of light or heat drops as 1 over the square of the distance from the light/heat source.
Perhaps a thermometer and a nice roaring fire and taking temperature data and various distances out (not up)?
Or if you had a photometer, then light intensity as you moved away from a flashlight.
It would certainly explain patterns that they wouldn't even realize they see.
I forget if this works the same for sound decibels or not, but it would then explain why you need to be close to the earbuds to hear the song.
Terry Kaminski said...
You can also look at the average monthly temp. for a city in Canada, Northern Europe or Northern US. There is enough of fluctuation in this data over 12 months that it makes for good sinusoidal data.
Mrs. H said...
Kate, two things my kids have found interesting are the relationship between "dog years" and "human years" and another one that generated a lot of discussion was the relationship between birth year and life expectancy. We found data from 1900 to present and had a good time discussing the data. One interesting thing I discovered was an article that stated that the current generation is the first generation which will have a lower life expectancy than their parents. I think they were blaming it on obesity.
Sarah Cannon said...
To add to Nick's population, my kids were fascinated by Breathing Earth last year. It's running on equations and all already, but at least could be an exercise in deriving them. (Okay, really, this probably motivates more of writing an equation given pieces of info, but I saw population and got excited.)
Cal said...
For sinusoidal I give them my natural gas bill from my house; it gives the volume used and is typically a good fit. I also have the death numbers for our province, also sinusoidal.
samjshah said...
Another idea... for those who like chemistry... atomic number vs. atomic mass.... linear...ISH.
Frank Noschese said...
If you have the time and/or resources, I would have the kids generate data via experiment. You can check out some great ones here:
http://jwelker.lps.org/labs/index.html
Simpler ideas...
Linear: Superball bounce height as a function of drop height. Why is the slope less than one? What does the slope mean?
Inverse: Length vs. width for a paragraph of text. See Measuring Paragraphs from eeps.com
Quadratic: Length of hanging slinky vs. number of hanging coils
Inverse Square: Do this experiment (perf board version), but put the perf board on an overhead projector that's on a cart. Wheel the cart from one end of the room to the other and take data as you go.
Linear Indirect: Mass of a bag of Starburst candies as a function of how many candies we've eaten. (I'd use Starburst since they are individually wrapped.)
eeps.com has more fun data at their Data Zoo
Re: Pendulum -- Be sure to plot length on y-axis and period on x-axis if you want a quadratic (even though this goes against traditional independent and dependent variable graphing kids learn in science class).
JYB said...
I usually opt for sneaky "value of education" types of graphs or social good stuff. Like years of education vs. income or life expectancy.
Or we do a survey of time spent studying vs. test score.
A few years ago after our kids got their reading level scores we plotted it versus a whole bunch of self reported stuff. Not surprisingly, reading level correlated most highly with time spent reading for fun. Students were astonished.
Got this link from freetech4teachers today.
Then there's gapminder data.
Of course, who can forget the relationship between pirates and global warming.
mgolding said...
Total resistance vs number of resistors in parallel (rational). Get an ohmmeter and a bunch of the same size resistor. String 'em up and measure.
Dan M. said...
There are a bunch of activities that were developed for teaching regression by Statistics Canada - they have been posted around the web in a few places:
http://www.keypress.com/x2812.xml
http://www.teacherweb.com/ON/Statistics/Math/photo1.aspx
Two things you won't like about these: they are Canadian, and they tend to use Fathom (rather than TI) as the technology of choice. Still, I think they are worth a look. It has been a few years since I've used these activities, and I can't say for sure if there is something there that would be useful to you.
Matt said...
You can try the DASL website, they have a lot of data some of it linear.
http://lib.stat.cmu.edu/DASL/
Aniko said...
Measuring reaction time: students create a chain by holding hands and pass a "hand squeeze" along it. The time to reach the last person is proportional to the length of the chain. The slope is the reaction time of one person.
Lsquared said...
My data is your data:
http://www.box.net/shared/zrjxkzpn9z
A couple years back, I collected data with a class where we had CBR's and CBL's: attachments for a TI graphing calculator that let you collect data directly to the calculator. I've got balls bouncing (quadratic) water cooling (exponential) and fluorescent lights flickering (periodic). Enjoy!
Daniel A. Kaufmann said...
1) # of books read in a year vs. # of facebook friends.
2) # of texts sent/day vs. most expensive cell phone bill
Kevin said...
I have not used it, but this looks like a very interesting (and free) way to explore patterns in data:
http://ccsl.mae.cornell.edu/eureqa
Maybe it will get past the problems people were talking about with projecting their TI calculators.
John Gale said...
Crayola's Law?
http://www.crayola.com/colorcensus/history/chronology.cfm
http://www.weathersealed.com/wp-content/uploads/2010/01/crayons_big2.png
and an argument between Ray Kurzweil and Kevin Kelly on
extrapolations of exponential curves.
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