Algebra Online Resources
THE STANDARD (NCTM - PSSM)
Understand patterns, relations, and functions:
Understand patterns, relations, and functions:
- represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;
- relate and compare different forms of representation for a relationship;
- identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
- develop an initial conceptual understanding of different uses of variables;
- explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;
- use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships;
- recognize and generate equivalent forms for simple algebraic expressions and solve linear equations.
- model and solve contextualized problems using various representations, such as graphs, tables, and equations.
- use graphs to analyze the nature of changes in quantities in linear relationships.
ALGEBRA BALANCE SCALES
THE STANDARD (NCTM - PSSM)
RATIONALE:
This virtual manipulative allows you to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, you can choose to perform any arithmetic operation, as long as you DO THE SAME THING TO BOTH SIDES, thus keeping the beam balanced. The goal, of course, is to get a single X-box on one side, with however many unit blocks needed for balance, thus giving the value of X.
What mathematical content is being learned (or intended to be learned)?
RATIONALE:
Solving linear equations by the use of inverse equations is typically taught to students with the “scale” and “balancing” (keep equal) idea behind it. Students have to first click on the correct operational symbol before they enter in a number, so they must understand that if multiplication is displayed, then the inverse operation is division.
Is the focus on instrumental or relational understanding?
The focus is equally both. Students should come into this applet knowing about inverse operations, but “seeing” the connection between the operations can help students make a connection about the steps needed to solve for the variable. After students use this resource to help master their understanding, then it is simply a matter of carrying out procedures (following steps).
What role does technology play?
The technology plays a visual and “hands-on” role in terms of inverse operations used to keep a linear equation balanced. This will allow students to observe the effects of carrying out particular operations by seeing the scale move lower or higher, then students can begin to understand which operation needs to be performed. Another positive aspect to this technology is that the program will allow students to perform incorrect addition or subtraction steps, which only changes the equation, it does not immediately say the step the student performed was incorrect.
What instructional function(s) does the resource serve?
This resource primarily serves a “practicing skills” function, with a small amount of direct instruction in the form of immediate feedback with the entry of an incorrect step, thereby, prompting students to rethink their response.
What kinds of representations of the mathematics are used?
- develop an initial conceptual understanding of different uses of variables;
- understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.
RATIONALE:
This virtual manipulative allows you to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam. Once the beam balances to represent the given linear equation, you can choose to perform any arithmetic operation, as long as you DO THE SAME THING TO BOTH SIDES, thus keeping the beam balanced. The goal, of course, is to get a single X-box on one side, with however many unit blocks needed for balance, thus giving the value of X.
What mathematical content is being learned (or intended to be learned)?
- Use of inverse operations to solve linear equations
RATIONALE:
Solving linear equations by the use of inverse equations is typically taught to students with the “scale” and “balancing” (keep equal) idea behind it. Students have to first click on the correct operational symbol before they enter in a number, so they must understand that if multiplication is displayed, then the inverse operation is division.
Is the focus on instrumental or relational understanding?
- instrumental understanding (carrying out procedures)
- relational understanding (understanding the meaning of mathematical words and symbols; connections among ideas)
The focus is equally both. Students should come into this applet knowing about inverse operations, but “seeing” the connection between the operations can help students make a connection about the steps needed to solve for the variable. After students use this resource to help master their understanding, then it is simply a matter of carrying out procedures (following steps).
What role does technology play?
The technology plays a visual and “hands-on” role in terms of inverse operations used to keep a linear equation balanced. This will allow students to observe the effects of carrying out particular operations by seeing the scale move lower or higher, then students can begin to understand which operation needs to be performed. Another positive aspect to this technology is that the program will allow students to perform incorrect addition or subtraction steps, which only changes the equation, it does not immediately say the step the student performed was incorrect.
What instructional function(s) does the resource serve?
- practice (i.e., practicing skills or knowledge already learned)
- direct instruction/explanation (i.e., explaining or presenting content to students)
This resource primarily serves a “practicing skills” function, with a small amount of direct instruction in the form of immediate feedback with the entry of an incorrect step, thereby, prompting students to rethink their response.
What kinds of representations of the mathematics are used?
- sybolic (i.e., numerals, symbols)
- concrete or real-world objects (e.g., images of base-10 blocks, puppies, or jars)
- dynamic (mathematical ideas represented through motion or sound)
EXPLORING ORDER OF OPERATIONS
Click on image!
This interactive mathematics resource allows the student to explore the order of operations (GEMDAS: grouping symbols, exponents, multiplication, division, addition and subtraction). In the explore mode, there are five levels of difficulty ranging from just 2 order of operation up to all 5. The resource also includes print activities, solutions, learning strategies, and a math game.