To Graph Oneself
How do you spend each day?
Imagine a sea of lines going in different directions at different angles, some twisting and turning, others marching straight on forever. Where could you ever fit into this world? The truth is that lines in the Cartesian Coordinate system describe who we are and what we do on a daily basis. They may become useful to us as they describe everything that goes on around us - the rate at which the kitchen sink fills, the pattern of an animal's breath, and even the amount of time we spend on various activities in our lives. It is the latter that we fill focus on in this activity, for it is near and dear to us. How do you spend each day? Do your activities vary from day to day, or do they remain roughly the same? If one's life is defined by what they do, how is your life defined? To answer these questions and describe the trends of your life we have the tool of graphs at our disposal.
Phase One: Gather Data
1. Record your activities for one week. Keeping a notebook with you can help you to accomplish this. Label the kind of activity and the starting and stopping time for each activity.
2. At the end of the week, total the amount of time you spend on each activity. Pick the top five activities you spend the most time on.
3. Look back at your recordings of these top five activities and create a chart for the amount of time you spend on each activity during each day of the week. The rows of your chart should be the days of the week, i.e. Monday, Tuesday, etc. The columns of the chart should be headings for each activity labeled Activity A, Activity B, Activity C, Activity D, and Activity E. (Note: to protect your privacy you do not need to write the actual activities. You may write which activity matches which label in a private place for your own records i.e. Activity A = Bike riding).
Phase Two: Create Graphs
1. On a sheet of graph paper, create a graph for Activity A. Use each day of the week as a unit on the x-axis. The y-axis should be the amount of time spent doing the activity in minutes. Thus, if I spent 120 minutes (two hours)reading on Monday, I should go to Monday on the x-axis and up 120 on the y-axis.
2. On a separate sheet of graph paper, create a graph for Activity B.
3. Repeat step 2 for Activity C, Activity D, and Activity E.
Phase Three: Analysis
1. Draw a line of best fit on the graph for each activity. Predict what kind of graph represents each activity.
On the back of each graph, write a write-up of steps 2-9 2. For each activity, put the x and y values in your calculator (for the days of the week, use Monday = 1, Tuesday = 2, etc.). For each activity, use various lines of best fit until the R value is close to 1 or -1. Find the kind of line of best fit that best fits each graph - record the equation generated by the calculator and the kind of curve for each line of best fit.
3. What kind of graph is each of your graphs for each activity?
4. For each graph, describe what happens to the amount of time you spend on the activity as the week progresses.
5. For all activity graphs that are linear, find the slope of each graph. Is the graph increasing, decreasing, or constant?
6. For all activity graphs that are parabolic, find the axis of symmetry for the parabola. Is it a maximum or a minimum?
7. If your graph has roots, what might this mean?
9. Predict what might happen for each activity on the eighth day. If an activity is unpredictable, describe why it is unpredictable.
Home Link
Unit 3 of Welcome to the Graphs of Life: Analyzing Graphs of Own Creation