Algebra+Balance+Scales

Algebra Balance Scales



"Algebra Balance Scales" presented users with the opportunity to input a problem and model the step by step actions of solving the problem. Students are able to create and input a problem with one constant and one coefficient on each side of the equation. By dragging variables and numbers to each side of the balance scale the equation can be represented visually. Once the problem is modeled there is an option to continue to solve the equation. The applet presents the user with the option of adding, subtracting, multiplying, or dividing an amount from both sides of the equation. Once this is entered the balance scales will reflect the step taken. This allows students to understand if their step progressed the problem towards a solution or was unnecessary. When the equation is solved the applet will notify the user that the solution is correct. The steps are kept displayed at the top of the balance scales which allows students to see the order of all of the steps taken to arrive at the solution.


 * Grade Level:** 7-9
 * PSSM Content Standard:** Algebra
 * Math Content:** Solving Linear Equations, Properties of Equality

Evaluation & Annotations
This resource focuses on solving linear equations. Students are able to create their own equations with variables and integers on both sides. Tiles are used to represent the variables and integers of the equations. The applet provides students with the option to add, subtract, multiply, or divide from both sides of the equation. Weather the step is correct or incorrect the applet adds or subtracts the appropriate tiles and alters the equation so that students can understand if their step made progress. This applet demonstrates relational understanding. Students are able to visually see how the properties of equality work and are able to gain an understanding of how certain actions will not progress the problem. Furthermore, the applet will forbid the student from subtracting a variable or integer from both sides when it is not present on both sides. This further demonstrates to students that select steps are unnecessary. While relational understanding is the focus of this applet, there are still areas that are lacking. Students are not able to use negative integers with the applet and are not able to insert an equation which will yield a negative answer. Although the applet explains why it is not accepting such equations, this could be confusing to students.
 * What is being learned? What mathematics is the focus of the activity/technology? Is relational or instrumental understanding emphasized?**


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

Learning takes place through solving equations with multiple representations. The main idea behind this applet is that as students are solving linear equations they are able to symbolically and visually understand how the properties of equality are being applied. Students are able to perform operations and view the results with the equation and with the tiles. This assists students in understanding how select steps may simplify the problem and other steps will complicate the problem. The underlying assumption is that students will be more successful with solving equations when presenting with an activity that makes the process less abstract and more visual.


 * 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 fosters the multiple representations that make this applet unique. The dynamic software integrated into this applet allows students to perform operations to both sides of the equations and subsequently witness the changes symbolically and visually (with the tiles). Without this technology students would be able to perform the steps, yet would not be able to immediately witness the result through multiple representations. Furthermore, without this technology there would be the chance that students are combining like terms incorrectly. This applet ensures that the step is chosen is accurately reflected.


 * 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 a great tool to supplement the existing curriculum. Solving linear equations is a crucial component of the Pre-Algebra and Algebra I curriculum. This tool would greatly assist students in understanding the properties of equality and the steps to solving a linear equation. Students would still need a formal lesson on solving equations with variables on both sides; however this tool would be a great addition to provide students with practice. Many students perform the steps in solving equations, yet do not really possess a relational understanding the rationale behind the steps. This resource would foster such a relational understanding. Its implementation would be best in the middle of a lesson on solving equations with variables on both sides. It should be introduced before students are dealing with decimals, fractions, and negative integers, since the applet does not allow their inclusion.


 * 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 could be used individually or collaboratively. In either case the problems presented would need to be carefully constructed due to the limitations of the applet, which were previously mentioned. The applet could be used for independent practice. The resource would ensure that students are not receiving incorrect answers and the multiple representations would provide students with a visually representation, allowing them to understand the affects of their steps. If the students are presented with a multitude of problems to use, this could be an effective independent practice tool. While it is not the intention of this applet, student collaboration with this tool could be successful. Like independent work, there would need to be additional resources provided. To foster student dialogue and reflection there would need to be questions posed that groups of students could debate. Students would need to be presented with questions as to why certain steps would not be helpful and why others would be disallowed by the applet. Collaboration would be best if students were required to think deeper, instead of simply being required to solve problems.


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

This resource presents learning opportunities in visually and symbolically. Students that struggle with the abstract aspects of mathematics are able to use the tiles to comprehend what the steps of solving a linear equation actually represent. Therefore, this applet provides learning opportunities through multiple representations. The applet is lacking written explanations; however it does provide two means with which to understand solving equations. The applet does not take differences of learner's abilities into account. Given the fact that the applet does not provide the questions, there is no way to accomplish this. Instead, the burden of differentiating the difficulty of questions falls upon the teacher who will be supplying the problems to 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)?**

Students need to be able to solve one and two step linear equations before attempting to use this applet. There needs to be a foundation of using the properties of equality before attacking equations with variables on both sides. Additionally, students need to possess a basic understanding of solving equations with variables on both sides. This resource does not supply students with directions on how to solve equations; therefore this needs to be addressed prior to using the applet. Teachers need to be cognizant of these prerequisites and need to carefully construct a lesson pr practice with this applet. As previously discussed, this applet does not allow equations with decimals, fractions, or negative integers to be inserted. Also, the equation does not allow equations with a negative solution to be inserted. While there are not specific technological requirements for suing this applet, the resource provides directions on how to operate its features. Students should be able to comprehend the features of the applet; however it would not be a bad idea for teachers to briefly touch upon how to use the applet.