Day 150 Mean Absolute Deviation Day Two

6th Grade Math Standards: 6.NS.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

The Learning Objective: Find the mean absolute deviation of a data set

Quote of the Day: "Watch your thoughts for they become words. Watch your words for they become actions. Watch your actions for they become habits. Watch your habits for they become your character. Watch your character for it becomes your destiny."

Agenda:

1. Review the quiz
2. Mean absolute deviation recap - the third page on the link with a thumbs up and thumbs down
3. Try one mean absolute deviation problem. I chunked it by stepping in for students after each step in the problem.
4. At the start of the second class do May Mayhem (4 problems on distributive property, dividing fractions, dividing decimals in a real-world context, and surface area)
5. Go back to mean absolute deviation the last thirty minutes of class with the data set 1, 2, 3, 4, 5, 6, 7

Homework: Find the mean absolute deviation of a data set (either 1, 2, 3, 4, 5, 6, 7 or one slightly more complicated).

The Assessment: After each step on mean absolute deviation students could circle a thumbs up or down as to whether or not they understood the step. This confirmed for me that students struggled most with the second step of finding the distance each data value is from the mean.

The May Mayhem assessment proved once again that students struggle with distributive property, but we continue to grow with the concept. We spent three full days on this topic earlier in the year, another day with a quiz on it, part of another class reviewing that quiz, and revisited this topic several times in March Madness and through weekly quizzes. This is undoubtedly one of the hardest topics for the sixth grade mind to master and retain. It's easier when they have numbers, but even then I'm not sure students understand beyond the fact that they can attain an answer to the question 3 (2 + 4). They fail in large numbers to recognize that 3 x 2 + 3 x 4 is an equivalent expression. They simply get stuck on the idea that the value of the expression is 18.

The percentages were higher today on all questions, but that's because I was answering many questions the students had before they were clicking in. That's part of the job as teacher of course, but I just feel it's necessary to point this out since all topics in May Mayhem are supposed to be review.

Glass Half-Full Take: Given the data set of 1, 2, 3, 4, 5, 6, 7 I had just about a whole class successfully find the mean absolute deviation provided that they could view their notes. I had no issue with them using notes - I know most people in our country would not be able to identify what a mean absolute deviation is.

One Regret: Given that the distributive property is still an issue after all we have done this year, perhaps we should have done something more hands on or created a lesson that is more engaging, but I reached out to my Twitter followers and asked if they had ideas. We took their ideas of creating a problem on the floor and having the students jump from the outside of the parenthesis to the inside. We used algebra tiles. We weaved it back into weekly quizzes and warm up problems. We even exaggerated the idea by having students solve a really long problem such as 5 (2 + p - r + 3). None of it worked. It's hard to have regret about the effort, but I do want to make a note that I want to go back to this strand of the standards and try something even more creative next year. Maybe I will do something like this where I have sixth graders go around asking clueless seventh graders to apply the distributive property.

Link of the Day: I really got a kick out of the link above. If you need a laugh it's good. The one with Robinson Cano is also really funny.