Overview
Receive an equation, or build your own equation, and solve for x in a simple, step by step manner.
Curator: Darrell Glover
Brief Description of Tech Tool:
This tool allows users to solve simple algebra equations in a step by step process. Users can choose from computer generated one step (singular x) or two step (multiple of x or Ax) equations or they can generate their own by choosing the values of such equations themselves. The user then follows the program's process to solve the equations. First, model the equation with the x, +1, and -1 blocks. Second, cancel out the +/- 1's to isolate x. Third (if necessary), divide the x term by the appropriate constant. Last, enter and check the answer for x. The user knows that they are on the right track by keeping the scale balanced; if the scale is out of balance then the setup or answer is incorrect.
Technical & Cost considerations: This is a free tool from the popular Math Playground website. It is very simple to use, loads quickly (even with a slower internet connection), and should easily work on most computers.
Evaluation
1. What mathematics is being learned?
Standards
Common Core:
- Write, read, and evaluate expressions in which letters stand for numbers.
- Understand that a variable can represent an unknown number
- Solve equations in one variable
- Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
- Write expressions in equivalent forms to solve problems
NCTM:
- Represent and analyze mathematical situations and structures using algebraic symbols:
- Understand the meaning of equivalent forms of expressions and equations
- Write equivalent forms of equations and solve them with fluency
Proficiency Strands
- Procedural Fluency - by following the step by step process, the user builds their proficiency at manipulating simple algebraic equations
- Strategic Competence - by using the tool, the user builds up the ability to identify simple algebraic equations that can be easily manipulated to find the value of x
2. How is the mathematics represented?
The equations used in this tool are represented in a virtual manipulative way. The scale is a familiar way to represent the idea of keeping the equation balanced and moves as the user adds/subtracts tiles from each side. Likewise, the addition/subtraction of +/- 1 tiles to each side dynamically shows how they cancel out the tiles already there. Therefore, the concept of isolating x on one side of the equation translates quite well (the tool instructs such as step one) however, how that is done (adding/subtracting a number to both sides of the equation) is only partially perceived. The user adds the necessary +/- 1 tiles to isolate x but the user can easily fixate on simply cancelling the +/- 1 tiles out versus realizing that an integer is being added/subtracted to each side of the equation to do so. This also goes for the step of dividing by A when the equation reaches the form Ax = B. The tool tells the user to divide and annotates lines to evenly divide the remaining +/- 1 tiles amongst the remaining x tiles, however, it is not explicit that the user is to divide by A. Somebody who is unfamiliar or a novice at solving such equations can likely get the correct answers without knowing what he/she is doing exactly. Consequently, given a similar problem on paper, the user may not be able to apply the steps appropriately to find the correct answer.
3. What role does technology play?
This tool would be great for introductory lessons in solving simple algebraic equations. The step by step instructions and friendly interface (with clickable tiles that automatically cancel each other out) make the process of solving such equations easy to follow. However, as noted above, translating these exercises to paper might take a bit of extra instruction due to way the process is represented. The idea of keeping the equation balanced (represented by the scale) gives the user a visual way to stay on the correct track versus a solely numerical representation that might by seen when simply doing similar paper and pencil exercises.
Affordances of Technology for Supporting Learning
- Computing & Automating - this tool automates the act of isolating x and dividing by A for an equation in the form Ax = B
- Representing Ideas & Thinking - this tool represents the idea of a balanced equation through the visual representation of a scale; the scale stays level as long as the equation is balanced
4. How does the technology fit or interact with the social context of learning?
This tool can be used by individuals or small groups (probably no more than three people unless used by the teacher in front of the classroom). While the tool is useful for individual work and only one person at a time can interact with the tool, the nature of the exercise modeled by the tool does lend itself to use in small group discussions.
5. Additional Comments
One note about the create your own equation section - the user is able to choose the values for A, B, and C for an equation in the form Ax + B = C however, the values available to choose from are fairly limited. The range of available values for one constant vary based off of the values chosen for the other constants; this keeps the tool focused on simple equations with small integer answers.