Many of my students are upperclassmen and have spent much of their college experience avoiding math courses. In fact, on last year's FCQ (Faculty Course Questionnaire) my students' average rating for the item "Personal interest in this subject prior to enrollment" was a 1.8 out of 6 --

**a response the university tells me is at the 0th percentile across campus**. I like to think of this as a great opportunity in a "nowhere to go but up" kind of way, a chance for me to change the way students think of mathematics and see themselves as mathematical beings. Then again, it's hard to make big changes in only 15 class meetings of 2.5 hours each. If I'm going to make a difference, class has to get off to a solid start.

My opening activity this year started with the preparation of four simple index cards with different distribution shapes:

Four common distributions, clockwise from top left: normal, left skewed, right skewed, and normal. |

I have the benefit of a small class of 14 students. So I cut my graphs into a total of 14 pieces:

14 pieces for 14 students. Note on the bottom I've provided the hints A, B, C, and D. |

When class started, I mixed up the graph pieces and handed one to each student. Then I told the class to find the other people in class who had the graph pieces that aligned with theirs. Once they had a completed graph, form a group at one of the tables and discuss which of the following they thought their group's graph might describe:

- People born each month of the year
- Student GPAs at this university
- Student heights at this university
- Starting salaries of new graduates from this university

So in less than 15 minutes I combined group-making, statistics, and active, student-centered problem solving into one activity.

**This activity also gets students thinking about distribution shapes, which I sometimes worry we ignore in the rush to calculate centers and spreads.**If you're wondering how to adapt this for your classroom, I offer these suggestions:

- If you have a few more students, cut more slices.
- If you have twice as many students, consider making two of each distribution shape and scaling the x-axis to match one of 8 potential descriptions. (i.e., a normal distribution scaled for heights in inches could be distinguished from one scaled for SAT scores.)
- If you want to use this for Algebra 1, you can make graphs that describe things like, "Toni walked to the bus stop at 2 mph, rode the bus at 30 mph to the bike shop, then rode a bike back home at 12 mph." Such an activity begins CPM's
*Algebra Connections*and was the inspiration for my activity. - If you want to use this for Algebra 2 or higher, you can use graphs of functions that students will become familiar with (parabolas, cubics, hyperbolas, etc.). I don't think it's worth fretting over vocabulary at this point -- just give students an opportunity to think about how the functions behave and what phenomena they could possibly model.

Awesome idea! I teach Eighth Grade - Algebra and "Math 8." My brain was already churning out ideas beyond the stats graphs and then you even gave out more suggestions. In general, I love the idea of cutting up the index cards and then "finding" the other pieces of your graph - piecewise situations as well as other functions. Give them "stories" to choose from or have them write their own. Give each group a set of 3-4 "puzzles"' to put together and analyze. . .so many options! Thanks :)

ReplyDeleteThanks, Cindy. The CPM activity I used in the past had students create their own story to go with the graph. I think that would work better for Algebra 1 than it might for statistics since I really wanted my graphs to represent a distribution and not something else. You might also want to check out Dan Meyer's Graphing Stories post for even more ideas.

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