Students work on the Think About It problem with their partners today. On the worksheet, the question of "How did each class do?" is open to interpretation. Students may think about this problem in a variety of ways. My goal is for my kids to think about the task using all of the tools they've learned to use to analyze data sets so far: mean, median, mode, range, and inter-quartile range. Here, you can see a student work sample.
After pairs have had a few minutes to interact with the data, I ask students to share who they thought did better. Students might say Class 1 did better because they have more students who got 100%. Another student might say that Class 2 did better because even though they do not have as many students with 100%, they have fewer students with a score below 60%.
I then plan to ask students for the means of the data sets, which are the same. I'll frame the lesson by telling students that even though these data have the same mean their distributions are very different. Today we are going to learn how to calculate a statistical measure called the mean absolute deviation that can tell us about variability within a data set.
To start the Intro to New Material section, I have students fill in the guided notes with me. We will focus on the idea that Mean Absolute Deviation (MAD) is a way to examine variation from the mean, or how far away each data point is from the mean.
The steps to finding the MAD of a data set:
Before we circle back to find the MAD for the classes in the Think About It, I ask students a series of questions to help them internalize the concept of the MAD:
One key point that I make sure comes out during our conversation is that MAD is a way to examine variation from the mean, whereas range and IQR describe (or summarize) variability from the median. Then we calculate the MAD for the data sets in the Think About It problem.
Since this concept is challenging for my students, I then guide them through the second example.
To help students gain some momentum, I next have them work in pairs on the Partner Practice problem set. As students work, I circulate around the room and check in with each group. I am looking to see that students accurately determine the MAD. They also need to accurately interpret the MAD given the context. You can see a partner practice sample here.
Teacher's Note: My students have access to calculators as they work. I am watching to make sure that students are showing their work at each step. At a minimum, I want to see the numerator and denominator of the fraction, before they divide.
After 10 minutes of work time, students work on the Check for Understanding problem on their own. As students work on the CFU, I circulate and check in on students' work. If there are any misconceptions, I'll note the students' names on my clipboard, so that I can check in with those students early on in Independent Practice.
Students who are struggling to interpret the MAD could look at the data on a dot plot. Here they will be able to see more clearly when data is more spread out. Any who struggle with the required computation, I will encourage to cross out each value once they've entered it into their calculators.
Next, students work on the Independent Practice problem set. Below are some notes about how students may explore some of the problems on this practice.
After the Independent Work time, students have the opportunity to discuss their responses to Problem_6 with their partners. Students are able to share their thinking, hear the thinking of a peer, give and receive feedback on their work, and ask clarifying questions.
Students then independently work on the Exit Ticket to close the lesson.
An exemplar response for Problem 2 would resemble: Group 2 was more consistent on their test because the MAD was 3.3%, whereas the MAD for Group 1 was 16.7%. This means that on average, students in group two were within 3.3% of the average test score, so the scores were clustered more closely. Students in group 1 were on average within 16.7%, which means the scores were more spread out than group 1’s scores.