Opening this lesson with a review, we asked the students what they remember about mean as a fair-share and the mean as a balance point. Through discussion, we had the students talk about what they remember and how they would express both of the representations. We then gave the students 8 different distributions of a data set, all with the same mean. For convenience, these distributions were all cut out prior to the lesson in order for the students to be interactive with the lesson. After the students were given these 8 distributions, we asked them to put them in order from least variable to most variable by completing a visual observation. Once the students realized that this was difficult to complete, we introduced the total absolute deviation, also known as the TAD. At first, we showed an example of how to compute the TAD using one of the distributions and then instructed the students to complete these computations for each of the other 7 distributions. We explained that the numerical value represented the total distance each data point is away from the mean. We then asked the students to rank these distributions again based on variability. After they completed this, we then asked how the students would be able to rank these distributions if they had data sets with different means and a different number of data points. Through guided instruction, the students were able to determine that the MAD, or mean absolutely deviation, would provide better results. We computed the MAD for one of the distributions and then had the students compute the MAD for the other 7 distributions. Once again, they were asked to rank them in order of least variable to most variable, explaining that the MAD was the average distance each point was away from the mean. Wrapping up this lesson, we were able to have a discussion about how the mean is an important measure and without it, it would be difficult to compute how variable a data set is. For review, we went over the TAD and the MAD again, ensuring that the students had a conceptual understand of what these measures represented. Below, I have attached the distributions that we cut out and used in order to rank variability. I have also attached the lesson outline for the MAD, this was a lesson that was created by Jon Hasenbank and Tara Maynard, I used this lesson to teach the concepts with some modifications.
This lesson aligns with the CCSSM grades 6-8 standards due to it’s connection with variability. The focus of the lesson was for students to understand how the TAD and the MAD account for variability, and eventually can be used to make conclusions about data sets. Overall, this lesson would be rated as a 4. It allowed the students to be introduced to the TAD and the MAD, which they will use later on, but I feel as though it should be focused more on the MAD and how this measure is important in terms of variability. I think it would be beneficial to include data sets with different means and number of data points in order to show how the MAD is a more powerful measure and how it determines variability.