Marcos and I had not used cards in our probability work. We sorted through a deck today, and talked about the features. I asked Marcos a variety of questions about the probability of choosing various cards, both with and without replacement. He answered the questions with relative ease.
I wanted to try a different delivery method for Marcos with our Statistics work. We went onto Khan Academy and watched a variety of videos on analyzing categorical data. It covered basic pictograms, pie, and bar graphs. We also saw how to use Venn Diagrams to represent data, as well as 2-way frequency tables. Marcos successfully answered questions on the topics.
Marcos completed plotting points on his scatter plot for the Age vs. Sleep/Caffeine/Phone use survey. He made generalizations about how each of the activities change with age. The number of hours of sleep per night decreases with age. Cell phone use decreases with age. Caffeine intake varies, although Marcos expected that it would decrease with age, since younger kids need more sleep.
Marcos reviewed all of the survey results, and threw out any data that was incomplete. We discussed how he should plot the data. Our independent variable is age, which ranges from 7 to 65. So we have a large difference in the upper and lower bounds of our domain. I instructed him to scale the x-axis by 2. Marcos decided that he would plot all three pieces of data on the same graph. Our dependent variables have smaller values, ranging from 1 to 11. The graph will look short and wide. Marcos set up the axis and started to plot points. He will continue next session.
Marcos thought of three questions that could be randomly correlated to age. He typed a survey that asked students and teachers for their age, number of hours of sleep they get a night, number of cups of caffeinated beverages they drink in a day, and number of hours spent on their cell phones a day. We made copies and distributed them throughout the school. During our next class, Marcos will make a scatter plot of the data. He will use his graphing calculator to find the line of best fit for the data.
Marcos asked for more time with his test in Algebra, so he continued and finished it during Statistics class today. He scored 35/37, for an overage of 95%.
The graphing of scatter plots can be tedious. Marcos did a great job on his homework, but needed class time to remember how to enter the information into the graphing calculator to find the line of best fit and the correlation coefficient. He completed questions 7-11 in class today. We thought of 3 questions that we can ask the students and staff at Batt that would yield non-linear results. We can use the data to make scatter plots.
Given charts of data that are not linear functions, we can make scatter plots of the data. We then take 2 distinct points from the line and write an equation of the "line of best" fit for the data. The equation has a correlation coefficient which tells us how closely the equation models the data. A correlation coefficient of 1 shows a positive correlation, and the equation is very close to the data. Likewise, -1 shows a negative correlation. The correlation coefficient ranges between 1 and -1. We used the graphing calculator to enter the statistical data, and it calculated the correlation coefficient. We could use the calculator's program to write the equation of the line of best fit. Marcos' assignment is p.352-353 (1-11)
Marcos worked on a practice sheet and completed 36 questions in an hour. He did not think he would be able to do it all at the start of our session. I encouraged him and redirected him along the way. The exercises were in preparation for the work will be do on scatter plots and equations of lines.
