Nancy J. Schmitt
Many students taking Algebra I struggle with the concept of the coordinate plane and recognizing the x and y axis and coordinates of a point.
The first activity of this unit will address this skill with an activity based on translations of a triangle in the coordinate plane.
The second activity will examine a scatter plot and a line graph. Understanding the independent variable and the dependent variable will be emphasized. Causality and identifying key words in a word problem will also be investigated. What question is being answered? What do the data mean? Is it truly a relationship between the variables that makes sense or is the relationship forced?
One example of forced data collection is how many steps you take to get to a store from your car and data on how much money you spend in the store. Does it make sense that how much money you spend at a store is dependent on the number of steps you take to a store from your car?
An example of data that makes sense is how much time is spent studying for a test and how many answers are correct. Can the line be extended (extrapolated) and do the data make sense? Do you expect to get more answers correct on a test if you study a longer period of time? The concept of slope of a line and how it correlates to the data is also discussed at this time.
The next activities are extrapolation and line-fitting. The students take existing graphs and predict values of dependent data, based on given independent data. They will extend the line (extrapolate) or create a line on scatter plots. As part of this exercise, the students will look at the data and determine if there is a trend, and whether it is linear. Can a prediction be made based on the data? When considering data from the stock market, it is easy to believe that you can make predictions based on past information. It appears to make sense, but there are many external factors that make predictions anything but foolproof for the stock market.
Lines of best fit will be applied by eye to the data. These lines will be tested against lines of best fit created by regression models on graphing calculators or computer graphing software if it is available.
Because there will likely be a wide range of technology available to both students and teachers, this unit will provide for a wide range of methodologies. However, if teachers are most comfortable with pencil and paper, the bulk of the unit can be undertaken with these tools. Pencil and paper will also be beneficial to the students who have begun to rely on the calculators to do all of the work in creating the graphs and have lost the ability to create the graphs. In all cases students will be encouraged to interpret the meaning of graphs.
Because it is useful for the students to be able to create graphs on graphing calculators for when they are taking the PSAT, SAT, ACT or CAPT (Connecticut Academic Performance Test ) tests, the ability to use the calculators as a graphing tool is also supported here. In addition, calculators and technology may act as a bridge for the students who have special education requirements, where working with paper and pencil may prove so time consuming that the intent of the graph is lost in the arduous process of creation.
