Barbie Bungee Lesson 2
Find the line of best fit for the Barbie Bungee data, interpret the slope and y-intercept, and understand the correlation coefficient.
In Lesson 1 students collected data relating the number of rubber bands attached to Barbie and the lowest point that Barbie's head reaches. Remind students of the predictions they made in their previous work.
Display the data from one of your groups using Residuals and Linear Regression.
“What pattern do you notice in these data?”
In front of the class, model the features of the applet. Add a movable line. Allow a student to move the line to where they believe it is a “best fit”.
“The vertical distance from each point to the line is the error from the prediction made using the line of best fit (a residual). Some residuals are positive (the point is above the line), and some residuals are negative (the point is below the line). We square each residual to make all of the values positive. Now we would like to find the line that minimizes the sum of the areas of the squared residuals.”
Allow another student to move the line to try to minimize the sum of the areas of the squared residuals of the area.
Have groups of students explore with the movable line before sharing the “Show line of best fit and residuals”.
Click “Show line of best fit and residuals”.
In the same groups from Lesson 1, students will input their data into the NCTM applet or into L1 and L2 on the graphing calculator. They will find the line of best fit using the NCTM applet of their graphing calculator (STAT, CALC, LinReg(ax+b)). Students will then work through the Lesson 2 Student Activity Sheet in their groups. In this worksheet, students will think about the physical interpretation of slope and y-intercept. They will also find the correlation coefficient (r) for their data set.
The activity sheet is intended for students to work through in groups. The teacher is walking around and listening to the group discussions. Prompt and cue with ideas or questions to check for and deepen student understanding.
Here are some questions you ask students as they are working in groups:
If necessary, connect slope to the definition that students know from previous learning. Most students know slope as the riseover the run or the change in y over the change in x. In this context, the slope is the predicted change in the lowest point of Barbie's head for every additional rubber band that is added.
If necessary, connect y-intercept to the definition that students know from previous learning. Most students know the y-intercept as the y-value when the x-value is zero. In this context, the y-intercept is the predicted lowest point of Barbie's head for zero rubber bands. This corresponds to the height of Barbie.
The correlation coefficient, r, is a measure of the strength of the linear relationship. Scatter plots with a positive linear relationship and very little scatter are close to 1. Scatter plots with a negative linear relationship and very little scatter are close to -1. Scatter plots with very little linear relationship and lots of scatter are close to 0.
Leave your thoughts in the comments below.
Nice worksheet. Thanks for the comments to teacher (in red).
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