College-Prep Physics: Yesterday we did the Ball Bounce Challenge, and only a couple of groups chose to graph their data. Rather than lecture about qualities of a good graph, I gave students a bad graph that I made (pictured) and asked them to find and list all the things “wrong” with the graph. Then I asked all groups to graph their ball bounce data. (If they didn’t have enough data to graph, then I asked them to graph the data from the bad graph.)
College-Prep Physics: Curve-fitting by hand can be tedious and linerization can be confusing. But curve-fitting with technology has its drawbacks, too — Excel is too unweildy and Logger Pro’s buffet of functions quickly has students blindly finding the function with the lowest R value.
Enter Desmos: While it doesn’t produce pretty labeled graphs like Logger Pro, I LOVE the slider function for curve fitting. (I know Logger Pro can do this, too, but it’s so much simpler in Desmos.) So today, everyone graphed their paragraph data from several weeks ago in Desmos. Then we reviewed the 4 types of functions we’ll be encountering this year and their characteristics:
Then we looked at several data points to see what doubling x (paragraph width) did to y (paragraph height). Did height double (linear), quadruple (quadratic), halve (inverse), or quarter (inverse square)? Now that we knew it would be an inverse relationship, we added to Desmos a “k=1″ line and a “y = k/x” line. Then we dragged the slider for k until we get a good fit for the data.
So in the example in the first picture, we get y = 6.8/x. But what does y represent? What does x represent? What are the units for 6.8? While Logger Pro automatically figures that out, I like that Desmos forces kids to wrestle with those questions. After some analysis, we see the relationship in the first picture to be height = (6.8 cm2)/width.
Now that we walked through that example as a class, we did a follow-up activity which looks at the effect of font size on the height of the paragraph, which I modified from here: http://bestcase.files.wordpress.com/2012/08/paragraphshandouts.pdf
To mix things up, I had each group member analyze a different font. My handout is here: LAB measuring paragraphs FONT SIZE 2014 Low Tech
Once the graphs are done, students get a unique URL for their graph that they can share with me, or download an image of the graph for inserting into Word documents or printing and pasting into lab notebooks.
PS: Sorry for being MIA the previous 9 days. College-prep students were working on their midterm projects for the first 4 days, and the remaining 5 days were midterm exam days where students took buffet quizzes and handed in their projects.
College-Prep Physics: Today I flew down to Orlando for AAPT’s Winter Meeting. While I’m away, students are working on a pen-and-paper lab to find the relationship between the height of a paragraph of text and its width. It’s their first inverse relationship. This should make our future exploration of Newton’s Second Law easier.
You can download the paragraph passages here: http://www.eeps.com/pdfs/paragraphsWithRulers.pdf
And there’s also a more detailed student handout (with different paragraphs though) which has both inverse (height vs. width) and quadratic (height vs. font size) relationships to investigate:
College-Prep Physics: Today we explored graphical relationships for proportional, quadratic, inverse, and inverse square functions using Desmos. Here’s the sheet: MATH RELATIONSHIPS 2014
The goal is for students to be able to determine the type of relationship by looking at data.
Proportional: If X changes by factor of N, Y will change by factor of N.
Quadratic: If X changes by factor of N, Y will change by factor of N2.
Inverse: If X changes by factor of N, Y will change by factor of 1/N.
Inverse Square: If X changes by factor of N, Y will change by factor of 1/N2.
College-Prep Physics: This is a revision of Friday’s graphing lesson that I was able to use with another class today. We compared individual attributes of two handwritten bouncy ball graphs. Compared titles, axes labels, axes scale, BFL, graphing all data vs. average, etc. Because not everyone voted when we did show of hands, I had kids stand on opposite sides of the room to vote on which graph they liked best for each attribute.
Students then made their own Bouncy Ball graph in light of the previous discussion.
NOTE: I need to make a better handout next year. Plus, I never got around to writing the BFL equation and slope calculations for the first graph.
College-Prep Physics: In two of the CP classes, students graphed their ball bounce data. Part of it was for me to see were they are with their graphing skills and help correct mistakes. The classroom arrangement isn’t very conducive to walking around and looking at their work, so I was just talking from the front of the room as questions arose. It wasn’t a great lesson, and I need to revise it for my third CP class on Monday.
I tried using the above visual to show why “zigzag” breaks on graph axis can be bad. The paper folds over to show how the zigzag part is eliminated and creates a false y-intercept. (Thinking about this now, it would be even better if the graph was a parabola or square root. You couldn’t tell if the trend curved or not if the beginning of the graph was zigzagged out.)