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Graphing Activity

September 17, 2012

I posted a photo on my 180 blog last week showing some graphs my conceptual students had to graph by hand, based on data I gave them.  @WillyB asked about the activity, so I decided to write about it.

I made four sets of linear data long ago, so long ago that I don’t remember if I made them or if I “borrowed” them from someone else. I always ask my conceptual students to graph them by hand, and then we use the graphs and the equations the students get for the best-fit lines that they practice drawing to learn about the meaning of a slope and y-intercept. @WillyB asked me if the students collected the data themselves. Alas, no. Here is my data:

1)  A cheerleader is measuring the time it takes for a white carnation flower to turn red when the stem is placed in red dye.  She tries 6 different stem lengths.

stem length (cm)           time (minutes)
4.0                               7.0
8.0                              13.0
12.0                             19.0
16.0                             25.0
20.0                             31.0
24.0                             37.0

2)  A scientist is measuring the number of bacterial cells per square millimeter when cultured in various concentrations of nutrient.  He tries 6 different concentrations.  If you were wondering, “ppm” stands for “parts per million.”

concentration (ppm)           number of cells (cells)
2.0                                        16
4.0                                        28
6.0                                        40
8.0                                        52
10.0                                       64
12.0                                       76

3)  A gardener keeps track of rainfall over a month, and records the total amount of rainfall so far each time he measures it.  Think about what the slope of this graph might mean.

day of the month (days)          amount of rain (cm)
5                                          4.0
9                                          5.6
15                                         8.0
18                                         9.2
22                                        10.8
30                                        14.0

4)  An FBI agent keeps track of how tall her amazing miracle banana tree plant grows as the months pass.  You would think she had better things to do with her time.

time (mo)                    height (m)
1                                0.75
2                                1.00
3                                1.25
4                                1.50
5                                1.75
6                                2.00

I would love to have students collect the data themselves. Last year I did that, having students mine the internet for data of their own choosing and trying to fit the data to a line. Those were honors students. My conceptual students tend to need a less open-ended assignment, especially at the beginning of the school year. I didn’t trust these kids to be able to get good and appropriate data. I think that this may have been a mistake. I should trust my students at any level to be able to do what I ask.

I don’t know if I will be teaching conceptual students next year, but if I do, I think I will try having them collect the data. But I will give them guidelines. I will have them do some sort of product and price comparison. Last year a number of my honors students graphed price vs. the number of crayons in a box, which is fairly linear and has a y-intercept. I might also have them do some sort of average weight and age data for infants. I think I will have to do research in advance to be able to give good guidelines for “what to google.” I’d like to give them three or four quasi-specific types of data to gather, and maybe one open-ended type. I suppose I could incorporate Dan Meyer’s flight data activity into this one, too, rather than doing it as a separate assignment.

I’m open to comments and suggestions!

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