Algebra Tech Tool: Illuminations-Line of Best Fit

In Project-Based Learning, students are constantly gathering data about their project and making decisions based off of it. Linear data is a fairly common type of data that is extracted from projects, either by design or by chance. Once you know that a set of data is or should be fairly linear, it is helpful for students to look at and analyze the data to make inferences from it. Think of the Barbie Bungee project some students do, where they are trying to figure out how many rubber bands should be on Barbie's bungee to make sure she has a great thrill but doesn't die. Students could run this experiment and gather their data and use a tool, like the one presented here, to make inferences about how many rubber bands would be needed for different drop heights. Without further ado, here is an excellent source for finding the Line of Best Fit!

Overview

Name & Link to Tech Tool or Tool homepage: Illuminations-Line of Best Fit

Brief Description of Tech Tool: This tech tool allows students to explore creating a line of best fit. Students are able to input their own data, and can then guess their own line. Students then check their line with the actual line of best fit created by the program.

Evaluation

Description of Learning Activity

Students have the ability to practice their critical thinking about data with this interactive applet provided by Illuminations. The "Line of Best Fit" activity enables students to work with their own sets of data to plot their coordinates. Students then create a "guess" line which they can manipulate by either changing the numbers in the linear equation or dragging the line to come up with their own line of best fit. From there, they can ask the computer to show them the true line of best fit.

1. Learning Activity Types

Using this activity, students are given a more practical method of "guess and check" problem solving for the line of best fit. Students are able to practice creating their own line of best fit and are also able to explore the concept. Students could use poorly aligned coordinates and really well aligned coordinates to better understand an "r" value.

2. What mathematics is being learned?

NCTM Standards

NCTM-DA&P-Select methods

• Select and use appropriate statistical methods to analyze data
• Develop and evaluate inferences and predictions that are based on data

Proficiency Strands

• PS-conceptual understanding
• Students are working on representing various information in different ways and seeing the usefulness behind each of the representations. Students are practicing with data as a coordinate point, a table, and a graph. Students are also practicing with lines as equations and graphs and are interpreting the various components of those lines as they change one or the other.
• PS-procedural fluency
• Students are becoming more adapt at creating graphs as well as creating equations for lines to best fit the graph.

3. How is the mathematics represented?

Students are working with graphical and numerical representations of numbers in a virtual manipulative that allows them to change the scenario and what they are seeing at any given time. Without technology, students wouldn't be able to test out as many ideas as to the "line of best fit" as easily, and would not see the effect of small changes as readily. However, with the technology, students do not get the same practice of plotting points and understanding the coordinate plane that they would if they were to do a similar activity by hand.

4. What role does technology play?

• Computing & Automating - This tool is very handy for quickly plotting data and creating lines of best fit, tasks that can take up quite a bit of time in the classroom when done by hand.
• Representing Ideas & Thinking -
• Accessing Information -
• Communicating & Collaborating -
• Capturing & Creating - Students can use this tool to create a graph of any data of their choosing and can then create a line of best fit for the data.

5. How does the technology fit or interact with the social context of learning?

For this tool, students could be working individually or in pairs analyzing the same data set. Students could talk together to discuss what they believe would be the best line of fit and why, and then could check it against the "real" best line of fit, as given by the computer. However, this technology would not work well for groups larger than two, as there would not be enough work to do or exploration to support large-group collaboration or discussion on an activity.

6. What do teachers and learners need to know?

Students should be familiar with the idea of "line of best fit", as well as the various aspects of an equation for a line. Students also need to be familiar with a coordinate plane and how to input and graph points of data. Students should feel comfortable with basic computer skills: mouse control and typing, but do not need to be "tech savvy" to be successful at using this applet. Teachers should be walking around and facilitating students when using this applet, as well as monitoring their use and discussions, and should expect to model its use with a projector before having students explore.

How this Supports & Supplements PBL/PrBL

As I mentioned at the beginning of this post, a lot of math projects that are designed contain some sort of linear data. This could be because linear data is very prevalent in the world and is easily relatable to students. I plan on using this tool to help with the same project I mentioned above, the Barbie Bungee. My goal is for students to be able to compare their results with one another and make inferences as to why their results were different and what their results would be if they wanted to drop Barbie from a height 2x or 3x greater than the height we dropped (would it change the equation proportionately?).