I begin class today by showing students images or actual copies of three histograms they have recently worked on (the pulse histograms, timing 5 seconds, and the length of their strides). I start the discussion by asking students what they notice about the histograms. Specifically, what do they all have in common? Once students are able to identify that they are all highest in the middle, symmetrical, and tapering at both ends, I introduce them to the normal distribution and bell curves. I follow the Normal Distribution presentation to lead this opening discussion.
Once students have a conceptual understanding of the normal distribution, they will take a look at four different situations, sketch accompanying histograms, and try to decide if they think the data is normally distributed or not. There is a great activity titled "What's Normal?" with four different scenarios in the IMP Year 1 textbook (2009) on page 313. It is also easy to make up other scenarios that would be interesting to students, such as:
I make sure that students understand that they only know the situation; they do not have the real data in front of them. So, they have to imagine what a histogram representing the data set might look like. Another important factor that they will have to consider is how to scale their x-axes.
This activity gives students a good opportunity to practice SMP 3: Construct viable arguments and critique the reasoning of others. This time they are constructing arguments about data they are making assumptions about, rather than looking at real numbers. This activity usually leads to a rich discussion as we discuss why students portrayed the situation in the ways they did.
Once students have sketched out histograms and decided whether or not they think the data would be normally distributed for the different situations, I have students share out their work. What’s Normal? follows the scenarios outlined by the IMP activity (see IMP Year 1 textbook (2009), p. 313), but it's easy to change the titles to reflect other scenarios I may have created. I find students are particularly interested in talking about income distribution and age of population distribution as they may be unaware of how these histograms skew. I may vary the length of discussion on each issue and some of the social causes behind them depending on how much time we have in class.
I want to be sure that students realize if categorical data is used, the resulting graph cannot show a normal distribution. I make sure they are clear that numerical data must be used. I allow students to construct their own arguments about other situations and determine whether or not they believe they are normally distributed (or close to it).
In closing, I give students time to reflect on what they have learned about normal distribution. I might give them a 3-2-1 exit ticket and ask them to reflect on the following prompt:
This material is adapted from the IMP Teacher’s Guide, © 2010 Interactive Mathematics Program. Some rights reserved.