Sack+Race

Sack Race



This applet revolves around the concepts of slope, systems of equations, and piecewise linear functions. Two functions are provided, each representing a relationship between distance and time. Users are able to manipulate one of the two functions according to directions provided in a PDF. Teachers could also easily create their own direction for this applet. By manipulating the starting point of the function and the slope of different pieces of the function, the corresponding animation of the sack race is altered. This allows students to gain a better understanding of rate of change and how graphs correspond to real world phenomena. The line can also be manipulated so that the two linear equations intersect. This will enable the animation of the sack race to reinforce the idea that a solution to a system represents when two equations or positions are equal. There are many possibilities for this applet which furthers understanding of real world application through rate of change, piecewise functions, systems of equations and the connection between a graph and its corresponding animation.


 * Grade Level:** 8-11
 * PSSM Content Standard:** Algebra
 * Math Content:** Slope, Piecewise Functions, Systems of Linear Equations

Evaluation & Annotations

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

This resource focuses on linear equations and their connections to real world phenomena. Students are able to manipulate the speed (slope) of two individuals in a sack race as well as their starting point (y-intercept) through an animation. Once this is accomplished, students can view the corresponding linear equations which were created by the situation in conjunction with the animation of the actual sack race. This enables students to understand the connection between a real world event and corresponding linear equations which represent the event. Depending upon the manipulation of the starting points and speed of the two individuals, this applet can be used to further thinking about slope or systems of equations. This resource definitely creates a relational understanding for students. The connection between motion and the graphs of two individuals creates a deep understanding for students far beyond instrumental understanding.


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

This resource fosters learning through exploration. There are directions provided with the applet, which require students to manipulate the situation and analyze the corresponding graphs. However, the beauty of this applet is that it is very simple for teachers to base a lesson upon as well. Teachers can easily build a lesson around the power of the animation of the applet. In either case, the underlying assumption about the nature of this learning is that student understanding of linear equations needs to be grounded in real world situations where students have the opportunity to manipulate variables are reflect upon the outcomes.


 * 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?**

Technology plays an integral role in the power of this applet. The dynamic software present in this applet allows students to manipulate the speed and the starting points of the two individuals in the sack race. Furthermore, the technology provides students with a real time view of the sack race and its corresponding graphs. The dynamic software creates a powerful exploitative learning experience that would not be possible without such technology. Without this applet students would not be able to see the connection between the actual event of the sack race and the graph. And without this technology student manipulation and subsequent analysis of graphs would be very cumbersome and much less powerful.


 * 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 applet focuses on many central features of the algebra curriculum. Students in Pre-Algebra, Algebra I, and Algebra II strive to understanding linear equation in the context of real world situations. This applet does a wonderful job of accomplishing that. Students in Algebra I and II also dedicate time to systems of equations, which this applet can easily focus upon. While this resource does provide powerful dynamic software, there is no inherent direct instruction on slope and systems of equations. Therefore, this resource should be used to supplement existing lessons on the aforementioned topics.


 * 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?)**

This resource would be a great tool for collaborative work. Whether using the instructions that adjoin the applet or creating new instruction and prompts, teachers should utilize the applet for exploration. In some manner students should be manipulating the variables of the situation, and making and testing conjectures about how the graphs will be affected. This is a great opportunity for students to work collaboratively and discuss the accuracy of their conjectures, and the patterns and properties of linear equations that arise. Especially with the complexity of the connection between the real world sack race and the linear equations, it would be highly beneficial for student reflect and have the support of peers to deepen their understanding.


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

As previously mentioned the applet does not need to be used in conjunction with the prompts provided by Simcalc. Teachers have the potential to create their own lessons around slope, piecewise functions, and systems of equations rather easily. While the directions provided by Simcalc do not take differences in ability into account, teachers have the potential to create hints for struggling students or provide varying levels of difficulty with separate prompts and questions. The Sack Race does take difference in learning style into account. Students are provided with several graphical representations, an animation of the race, as well as thorough written directions targeted at furthering understanding of the graph and animation. Simcalc certainly made a concerted effort to create an exploration for the multiple intelligences 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)?**

Prior to using this resource, students need to have an understanding of linear equations. It would be highly beneficial for students to have knowledge about slope-intercept form. This would allow students to dedicate more energy to the connection between the real world animation and the graphs, as well as on systems of equations. Furthermore, an understanding of slopes and y-intercepts would create a richer dialogue for students as they collaborate. Teachers need to be aware that students need this foundation and need to implement this resource at an appropriate point within the curriculum. Teachers additionally need to act as facilitators during activities with this tool, given that the power behind the tool is it explorative nature. There are specific technology requirements for using this resource. There are sufficient directions provided by Simcalc on how to use the applet, which could be highly beneficial for students as they use addition Simcalc resources in the future.