February

We have been studying linear regression this semester.  We did Double your pleasure and the Balloons.  We also did Random Squares and Rolling Down the River to learn the importance of randomization.  Next the students designed projects in groups of 2 or 3.  When they collected their data they had to prove they did so in a true random way.

Requirements for the project were a combination of things we used this summer.  The following is the list of things they were to include and explain in their written and presented project:

1. Raw data – include how it was obtained
2. Explanatory Variable
3. Response Variable
4. Scatter Plot
5. Least-square regression equation
6. Explanation of the slope and y-intercept
7. Correlation Coefficient
8. Proportion of variation
9. Lurking variables
10. Outliers
11. Influential Points
12. Residual Plot
13. Other statistics that might pertain to their particular data

I was impressed with the quality of their work.  Their project data did not always give the best result but they still learned a lot about statistics.

November

Random Rectangles
I did this lesson with seventh at the beginning of the year and now with the eighth. It went much more smoothly.  With the 7th graders, I was very unsure of how far we would get with a certain concept, so I was much more able to have guidelines to go by.  I gave them very specific instructions to follow and knew what size of chunks to undertake during 1 class period.  We are starting the rolling river activity tomorrow, and I preceded this by giving them part of today to generate the random numbers needed.  Tomorrow I will give them handouts and we won’t need to mess with the calculators. 
The students learned to use the calculator very quickly and they are also learning about random, populations, samples, mean, etc.  Great lesson, and thus far there won’t need to be any corrections.

We had studied comparing 2 variables including correlation coefficient and linear regression lines.  This month they were to come up with a project question, conduct a survey and report their results.  Before we started the project I wanted them to realize the importance of random sampling. We first did the Random Rectangles activity.  I really liked the lab worksheet with this activity.  It made it clear about the difference between subjectively and randomly chosen rectangles.  An added bonus was the part showing the importance of sample size.  I liked the way it demonstrated the Stratum and Cluster methods.  I think the students got a much clearer picture from this.

We also did the Rolling Down the River exercise.  This really made the differences between convenience, simple random and stratified clear for all of my students.

Next time I would allow more time to “explore” the answers.  Because of these activities, I was pleased with their linear projects.  It was obvious they spent more time thinking about sampling techniques.

Students were given the Random Rectangles Data Sheet.  They were to subjectively select five rectangles and find the area.  Then they were to find the mean area.  As a class, we collected the means from each student.  We found the class mean, median, and quartiles 1 & 3 so that we could then make a line plot & box & whisker plot.  We then compared the subjectively found areas to a true random selection.  The problem that I experienced was that my first class selected rectangles that gave almost the exact same values as a true random sample.  The point was to show them that we don’t do a good job of selecting true random samples, but they actually did.    In the future, I might combine data from more than one class so that the subjective random and the true random will not be so close.