Line+of+Best+Fit

Line of Best Fit



This resource enables user to practice finding the line of best fit for a scatter plot. Students can plot points by entering a coordinate pair or by clicking on the coordinate plane itself. Data can also be copied and pasted from spreadsheets and then plotted. Once points are plotted they can be dragged around the plane. When all of the points are plotted the application allows user to determine their best guess of the line of best fit by manipulating a line which is presented. By clicking the "computer fit" feature students can compare their guess to the least squares regression line. Once the least squares regression line is visible students are able to experiment with the the line by adding and removing points. This enables users to gain a better understanding of how the line of best fit will be affected as the scatter plot changes. This resource also features an exploration which allows students to find the line of best fit with real world data from the NBA and analyze how the removal of data affect the line of best fit and the correlation coefficient.


 * Grade Level:** 9,11
 * PSSM Content Standard:** Algebra
 * Math Content:** Plotting Points, Line of Best Fit, Correlation Coefficient, Slope

Evaluation & Annotations

 * What is being learned? What mathematics is the focus of the activity/technology? Is relational or instrumental understanding emphasized?**

This resource educates students about the line of best fit. Students are able to plot point by clicking or by entering the coordinate pair, which reinforces their knowledge of graphing. Students are then asks to generate the line of best fit by manipulating a line which is presented by the applet. As students manipulate their line the equation of the line can be seen. This reinforces their understanding of slope, y-intercept, and the connection between the multiple representations of a line. Once students select their line of best fit they are able to view the computers line of best fit which is based off of least squares regression. This enables students to check their accuracy. This performing the task and verifying the answer must be considered instrumental understanding. On the other hand, aspects of the resource encourage a relational understanding. The resource additionally features an exploration activity in which students find the line of best fit given NBA players total points and games played. Through this exploration students are able to see the relevance of the line of best fit and understand what it means in a given situation. Higher level thinking questions are also posed in the exploration which further student thinking about how the removal of data points can affect the line of best fit and what it would mean in a real world scenario. This is certainly adding to students' relational understanding.


 * How does learning take place? What are the underlying assumptions (explicit or implicit) about the nature of learning?**

This applet offer opportunities for students to learn through exploration. The exploration activity encourages students to form and test conjectures about what happens to the line of best fit when a data point is added or removed. The applet itself allows students to constantly add new data points and view the manipulation of the line of best fit. This applet can also be used for practice. Students could plot points, generate their own line of best fit and check their accuracy against the computer line of best fit. This would provide immediate feedback. The underlying assumption is that students need to explore the relationship between data points and the line of best fit. The other underlying assumption is that it is vital that students are able to understand the line of best fit in the context of real world problems.


 * What role does technology play? What advantages or disadvantages does the technology hold for this role? What unique contribution does the technology make in facilitating learning?**

Without technology the aims of this resource would not be accomplished. The dynamic software enables students to plot points accurately, manipulate the line of best fit and check their line of best fit. More importantly, the dynamic software allows students to add and remove data points and view the subsequent change in the computer line of best fit. Performing this operation by hand would be nearly impossible and would waste large amounts of time.


 * How does it fit within existing school curriculum? (e.g., is it intended to supplement or supplant existing curriculum? Is it intended to enhance the learning of something already central to the curriculum or some new set of understandings or competencies?)**

This resource should supplement the already existent curriculum. The line of best fit is already of component of most Algebra I and Algebra II courses. For the successful use of this resource teachers would still need to instruct students on the process of finding the line of best fit and the rationale behind it. This applet would best be used as an additional resource to deepen their understanding and practice finding the line of best fit. Students should use the applet to better understand how the line is affected by new data points and how the line of best fit can be applied to real world situations. The resource should also be used for individual student practice supported by the immediate feedback of the computer line of best fit. In either case it is crucial that the teacher plays an integral role in instructing on the line of best fit prior to the implementation of the resource.


 * How does the technology fit or interact with the social context of learning? (e.g., Are computers used by individuals or groups? Does the technology/activity support collaboration or individual work? What sorts of interaction does the technology facilitate or hinder?)**

If the resource is being utilized as an exploration it would best be used in groups or pairs. This would create collaboration and discussion on how the line of best fit is affected as the data points are manipulated. This would also allows students to discuss how the line of best fit can relate to real world issues. If the applet is being used as a means for students to practice finding the line of best fit it could be used individually. The answer is available to students graphically and as an equation. This immediate feedback would allow students to adjust, gauge their progress,and ask for assistance from the teacher if necessary. Unfortunately, there is no tutorial on finding the line of best fit for students to refer. This hinders individual work a bit, yet as long as this is covered in notes prior to practicing the process it should not be a large issue.


 * How are important differences among learners taken into account?**

Difference in learners are somewhat taken into account with this resource. The applet allows students to view the points in coordinate form and on the graph. The applet allows for the lines to be viewed visually and graphically. The exploration enables students to see connections between real world phenomena, graphs, and equations. Considering the limitations of the topic, the applet does a fair job of speaking to multiple intelligences. As far as being adaptable to learners with different levels of mathematical ability, the resource is lacking. There are no available hints or assistance for students struggling to find the line of best fit. As previously mentioned there are no directions for finding the line of best fit at all. Teachers should keep this in mind and perhaps focus on the exploration aspect of the resource with groups of students.


 * What do teachers and learners need to know? What demands are placed on teachers and other "users"? What knowledge is needed? What knowledge supports does the innovation provide (e.g., skills in using particular kinds of technology)?**

To successfully use this applet, students need to be aware of the basics of finding the line of best fit. There is no need to understand the least squares regression line, however students should be able to find the line by eliminating outliers and drawing a line through the center of the relevant points. There is not enough explanation with the resource for students to understand the concept without this prior understanding. Students additionally need to be aware of how to plot points and use slope and y-intercepts of a line to graph. This is not a necessity but with this understanding students will be able to better comprehend the applet. For performing the basic features of the applet (plotting points, removing points, and manipulating lines) sufficient directions are provided. Teachers need to be prepared to act as a facilitator as students explore the line of best fit and need to be accessible to provide guidance if this resource is used as a practice tool.