Distance+Rate+and+Time

Distance, Rate, and Time



This resource presents students with a bank of application problems involving distance, rate, and time. The applet takes the students step by step through the problems. Each problem begins with the given. Next, the applet describes the symbolic representation of two aspects of the real world phenomena alongside written rationale. Finally, the applet constructs an equation and solves for the missing information. After following through this process several times students become aware of the steps and work towards predicting the next step and the rationale before it is provided by the applet. The major aim is enabling students to decode application problems and construct expressions and equations that lead to a solution. Following the applet there is a link to another page which explains distance, rate, time, and their connectedness in greater depth.


 * Grade Level:** 8-9
 * PSSM Content Standard:** Algebra
 * Math Content:** Solving Linear Equations, Distance/Rate/Time, Word to Symbol Translations

Evaluation & Annotations

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

This resource first and foremost educates students about translations from words to symbols. The applet provides an extremely deep bank of application problems, which enables students to become aware of key words which translate to symbols. Word to symbol translations in this manner is instrumental understanding. Yet there are also in depth explanations provided by the applet for each step in solving the problem. This fosters a relational understanding, as students are able to gain a deeper understanding of why distance, rate, and time is translated into addition, multiplication, and equivalence. In addition to translations from words to symbols, students are reviewing aspects of solving linear equations. Many of the problems require use of the distributive property, combining of like terms, and the application of properties of equality. While the applet does not break down each step of solving the equation, it requires students to perform the steps on their own, which ultimately requires practice with linear equations.


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

With this applet learning takes place through practice. With the large volume of practice problems, students are exposed to numerous situations involving distance, rate, and time. Students are given explanations for how the various aspects of a given problem can be translated into an expression, how expressions can be combined, how the problem can be solved, and what the answers really means. More importantly, the applet provides students with rationale for many of the vital steps of the problem. The underlying assumption is that through detailed explanations and through extensive practice students will become capable of translating situations into expressions, solving, and understanding the rationale behind each step along the way.


 * 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 is essential to this resource. The use of technology provides students with an extremely large bank of application problems with varying situations. This makes it very difficult for students to simply memorize the steps to apply without understanding the rationale behind them. In other words, this deters instrumental understanding. The technology also provides step by step guidance for the crucial aspects of the problem. Students are able to attempt to solve each step of the problem individually prior to clicking the "next step" button. The technology therefore offers a surplus of guided practice problems with which students can easily check their accuracy. The disadvantage of the technology is that it does not provide steps and explanations for many of the basic steps used to solve equations. This resource would not be successful for students struggling with solving equations because there is no support for that aspect if the problem. Rather this resource is intended for students that have mastered the solving of equations and are seeking guidance and practice on application problems.


 * 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 would be best used for individual practice that would supplement an existing curriculum. It could be given to advanced students during a lesson on solving linear equations. Having them practice real world application would allow them to act in their zones of proximal development instead of being stuck at a slower pace. This applet could also be given to students that are struggling during a lesson on distance, rate, and time. This resource could act as a stand alone instructional resource with a large amount of practice problems. In either case this resource would not replace classroom curriculum. While it does provide explanations, students still would benefit more from a teacher who would be able to answer direct questions, while initially covering the concepts of distance, rate and time. This applet certainly would enhance students learning and understanding at a relational level.


 * 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 technology would best be used for individual students. The nature of the resource allows students to determine the steps for the problem and check their answers with the resource and its explanations. This is a great tool for self-evaluation. This distance, rate, and time applet could be used with partners, which would foster a discussion of the correct steps and would enable the students to assist one another if the equation was not solve accurately. Either approach would be beneficial, yet this is truly a great resource for students seeking individual practice at home.


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

One of the drawbacks of this applet is the lack of acknowledgment of difference of learners. Like much of mathematics there is more than one approach to solving many of the problems that the applet presents. Yet only one solution is presented for each problem. This is problematic as students may assume that another approach, which they are more comfortable with, would not be acceptable. Yet, presenting multiple approaches to each problem would also be problematic, as it would make the problems more convoluted. The decision to present one route to the solution is understandable, yet come with drawbacks. As far as acknowledging differences in learning styles - the applet does seek to address learning verbally through text and through symbols. However, there are no visual representations for real world problems that present rich opportunities for images.


 * 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)?**

In order to successfully use this applet, learners need to have mastered solving linear equations. The applet does not provide detailed steps for distributing, combining like terms, and solving linear equations. Without this ability students will not be able to solve the problem, even if they fully understand how to translate the application to symbols and the rationale behind the process. It is crucial that students meet that prerequisite. Students also need to have a basic understanding of distance, rate, and time prior to using the applet. This resource is not designed as an introductory tool for a lesson on distance, rate, and time. Rather students need to understand the basics and use that as a base to solve the application problems that are presented. As far as technological requirements to use the applet, there are none. Students should be able to easily follow the simple directions provided. Teachers need to be aware of the placement of their students and implement this resource when students are at the appropriate level. This is a great tool for bridging solving equations to solving real world application problems if it is incorporated into the curriculum when students are prepared.