Mammals-Slope

=**Slope Activity with Mammal Data**= Back to Scatterplots The goal of this activity is to showcase how TinkerPlots can be used to address the CCSS Grade 8 Statistics and Probability Standards.

The Mammals Slope activity develops student understanding of the concept of slope. This activity uses the following TP tools: Plot, Diagonal Reference Line, Ruler, Case Table, Formula Editor. Suggested questions and sample screen shots are shown.

Part I
1. Open the Mammals file from the Sample Document | Science and Nature folder. Create a scatterplot with height on the horizontal axis and sleep on the vertical axis. Drag a white icon up and/or right until all of the icons are fully separated. 2. Lock the axis endpoints at x=0 and y=0 by double clicking on each of the zeros. 3. Place a diagonal reference line into the plot to represent the overall trend of the data points. To move the reference line up and down, grab the middle. To rotate the reference line, grab one of the ends. Note that you do not need to intersect any of the points (mammal icons) when you place the reference line. Note that the equation for the reference line is shown at the lower left side of the plot. 4. Snap the horizontal ruler tool to the Ground Squirrel (0.3, 15) and the African Elephant (4.0, 3) icons. Make sure the difference is measured from the squirrel to the elephant (positive). The number sentence 4.0 - 0.3 = 3.72 is shown below the reference line's equation. Figure 1. Scatterplot with diagonal reference line and ruler tool.

Part II
1. Click off the plot to deselect the mammal data. Then, drag a case table from the shelf into the work space. The case table should be empty. 2. Type "mammals" in the first column label and "dif_ht" in the second column label. In row one, type "squirrel to elephant" and record the difference of 3.72 meters (only type the number). 3. Switch the ruler tool to vertical distance. Be sure to note that the direction of the difference is from the Squirrel to the African Elephant so the sign is accurate (negative). 4. Add a third variable to the table titled "dif_sleep" and record the difference of -12 hours of sleep per day (only type the number). 5. Add a fourth variable labeled "rate_of_change" to the case table. 6. Select Table | Options and Show Formulas. A new row will appear in the case table where formulas can be added. 7. Enter a formula for the rate of change in the cell directly below the label "rate_of_change". [Ask your students which variable should be in the numerator, before entering the formula. This can provide a good teaching moment.] 8. Compare the ratio from the chart to the value in the equation shown on the plot. What do you notice? Figure 2. Squirrel to Elephant rate of change.

Part III
1. Move the ruler tool to a second set of points. The Owl Monkey (0.4, 17) and the Bottle Nose Dolphin (3.5, 5) are shown in Figure 3. 2. Record the horizontal and vertical differences in the case table. 3. Compare the rate of change for these pairs of mammals. Figure 3. Monkey to Dolphin rate of change.

Part IV
Compare the values in the equation shown in the plot to the rate of change values shown in the case table, are they close? The goal of this activity is not to have these values match exactly, the goal is to illustrate where the slope comes from. Some folks will want to see the exact slope. This can be done in TinkerPlots, but not directly from the plot. It is important to develop this concept through investigations, before the least square regression line is formally introduced.

Analysis of rate of change in this problem: As the height of the mammals increases by one meter, the number of hours of sleep per day decreases by about three and a half hours. pdf of this webpage