Analyzing Linear Practice Data with Center and Spread
Lesson 9 of 20
Objective: SWBAT interpret differences in center and spread for three different data sets.
Two days ago, students made predictions about how they would fare on Linear Practice #3 (LP3), before having one more go at that challenge. When today's class opens, I present each class with their real results from that third and final trial, and instruct students to construct a box plot of the data. Students should be able to sketch this final box plot on their Comparing Box Plots handout from two days earlier, and to compare the real data to the predictions they made then. Engagement is high as students complete this task, because the data comes directly from within the class and because kids want to see how well their predictions held up.
We have some fun as I ask, "How did we do?" I mean this question is both ways: how did everyone fare on LP3, and how accurate were the predictions made by students? Just like that, we're comparing box plots, and interpreting the data!
When students are done constructing their box plots, I spend a few minutes talking about representations of data on the number line. I start with measures of center. "What are the three measures of center?" I ask, and noting how quickly and comfortably students can answer this question, I ask which of the three we can see on a box plot. In this particular representation, of course, we can see the median but not the mode or mean. If students are confident with what we've done so far today, I might ask them to calculate the mean of the LP3 scores, and then to plot a point representing the mean on their box plots, which can lead to a discussion of how we might intuitively estimate where the mean falls in a data set.
Each of the three types of stat plots we're currently studying - box plots, dot plots, and histograms - have strengths and weaknesses relative to each other. I want this conversation to move in that direction, but I also want students be the ones having such ideas.
After discussing center, we move on to spread. I ask students to name the two measures of spread that we're studying here - range and IQR - and then to show how these two measures appear on a box plot.
On the flip side of the Comparing Box Plots handout, students can record the center and shape for each data set. They should have done this for Linear Practice trials #1 and #2 in a previous class, so now they can record the data for LP3. As this happens, I again reiterate that the mean and mode are not visible in the box plots on the front of this page. The data is displayed at the front of the room however, so students should be able to make these calculations.
You'll also notice that I've left room for shape at the bottom of this handout. If there is a critical mass of curious students, I'll address this topic, but this year I let it slide in most of my classes. I've chosen instead to stick to the intuition available when we compare and interpret differences between center and spread, and to give shape a passing treatment for now.
Now we step back from the curriculum for a few moments to celebrate successes and build some community. First, I give some "data driven shout outs". As shown on these slides, I recognize students who improved the most from Linear Practice #2 to Linear Practice #3, and to the students who got the most work done on yesterday's Delta Math assignments. I'm emphasizing improvement and hard work, and as a result, there are students in every class who get a shout out even though they're not the type to usually earn such recognition, and this goes a long way toward building community. I can count on kids wanting to take pictures of their name on the board, so they can go home and share that success.
Next, we choose a mascot. One of the questions on yesterday's survey asked students to suggest a mascot for their class. I post a list of all student responses, and then run a few rounds of voting until we've identified a winner. It's lighthearted and fun. One of my favorite constructs is to ask the class if they'd "really like to be known as __________________," and I fill in the blank with the most absurd option.
Once the kids make their choice, it gives me another way to refer to a class. Moving forward it's so much more fun to greet my "Ninjas" every morning than "Period 1 Algebra".
Kids are usually excited to see the data from yesterday's survey, and often the first few sections of today's lesson can pass pretty quickly. So in my back pocket I've prepared some results from yesterday's survey for our perusal.
If it's an especially task oriented class, I ask kids to make a dot plot of one of these sets. If they like to shoot the breeze and talk about ideas, then I just post each for a few minutes and we chat about what we see. I find that it helps to mix the pace once in a while, and today's loose, Friday agenda serves to build an upbeat culture that we can maintain no matter how hard we have to work.