Day 125: Finding the Mean

6th Grade Math Standards: 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
6.SP.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 of a data set

Agenda:

1. Visual example of equal shares in partners (take a stack of 3, 2, and 1 rectangles and make them all have the same number of rectangles). 
2. Derive the formula to find the equal share (introduced now as the mean or average).
3. Work out what happens on a number line and where an average sits relative to the data set (the sum of the distances before and after the average are equal). 
4. We did an original activity in which pairs of students were given 4 index cards. Each index card had one number written on the front and a different number on the back (so 8 numbers in all). Students were instructed they could only use one side of the index card (we used four different colors for each index card and informed students they could only use one color). From there we gave students a scavenger hunt of sorts. They had to find different means by using trial and error (or a better method if they could think of it) to arrive at the means. 

The Assessment: I went around the room as students tried to work out what data set would be appropriate given the mean.

Homework: I gave students six problems in which they had to find the mean.

My Glass Half-Full Take: As I was going around the room to see how students were doing, I got two positives from different students. The first was that one student recognized that by simply multiplying the mean by four he knew what sum to look for. This made it much easier to derive the mean

Another pair of students recognized quickly how to use trial and error, and got the first three means I asked for without any difficulty. I changed the task for these two students. For them I asked them to find how many different combinations of means could we come up with given the rules of this activity. They only could list 9. I went through a method using variables to demonstrate that there will over 9 and asked them to come up with what they thought it could be for homework. I canceled their normal homework because I knew the task was so easy for the two of them. I told them both not to spend more than 15 minutes and that it was ok not to have the answer as long as I could see the effort.

One Regret: I think I might laminate the index cards next year so that we can take out the aspect in which students have to write what numbers go where. It will save 5 minutes and a small tree.