Algebra Syllabus
1. PROGRAM TITLE: InterMath  Algebra
2. GOALS ADDRESSED
Participants will:
 Expand and strengthen their mathematical knowledge and capabilities, specifically in the domain of algebra by investigating challenging algebra problems
 Engage in problem solving by identifying patterns, forming conjectures, and developing proofs through the use of technology
 Use mathematicsspecific technologies such as dynamic geometry software, graphing programs, spreadsheets, and the Internet to explore algebra investigations
 Write and post online solution processes to the investigations using web page development software
 Develop middle school mathematics instructional activities and strategies that incorporate technologyenhanced mathematical investigations
 Develop a network of peer educators available for continued support during and following the workshop
3. IMPROVEMENT PRACTICES
Participants will gain knowledge and practice in developing instructional activities and strategies for teaching algebra in the middle school classroom in order to positively affect student achievement. Participants will also improve their own mathematical competencies in the area of algebra.
4. COMPETENCIES
Participants will be able to:
 Select and use appropriate technological software to explore, analyze, and represent algebra problems
 Communicate their mathematical thinking by expressing their reasoning, analysis, and extensions of the mathematical concepts associated with an investigation in written, verbal, and visual forms
 Modify algebraic investigations for appropriate use in the middle school classroom
 Make connections between InterMath experiences and standardsbased reform documents, such as the NCTM standards
5. PERFORMANCE INDICATORS
As a result of this course, participants will demonstrate their ability to:
 Incorporate technology into the learning and teaching of algebraic concepts
 Communicate mathematical understanding of a variety of algebraic concepts in the form of an online portfolio of investigation solutions
 Plan middle school instructional activities based on InterMath experiences
6. PREPARATION PHASE
Dates: XXXX 2005
Instructor: Dr. Wilson/Dr. Gootman
Location: UGA campus
Strategies: Internet exploration, electronic and classroom discussions, lectures, exploration of mathematical investigations, investigation writeups, collaborative brainstorming, lesson planning, presentations
7. ASSESSMENT
Participants will be assessed on the content and quality of their online portfolios. Feedback and suggested modifications for a select number of writeups will be provided throughout the workshop. Assessment will be based on use of representation, analysis, appropriate selection and use of technological tools, creation of extensions, and accuracy of mathematics. In addition to the investigation writeups, the participants will also create a mathematics lesson that integrates technology and algebra for use in their own classroom.
8. COURSE OUTLINE
I. Class 1
A. Introduction to InterMath
B. Introduction to Technology
C. Work through an algebra investigation as a whole class using technology
D. Discuss the components and structure of a writeup (including extensions)
II. Class 2
A. Participants engage in investigations of Variables and Expressions.
B. Participants add writeups to their online portfolios
C. Participants work on variable and expression investigation, spreadsheet skills, and/or other topic covered in class
III. Classes 34
A. Participants engage in the Patterns investigations
B. Participants begin their first web page writeups to include in their online portfolios
C. Continued technological teaching and support (especially with Excel and the structure of a writeup)
IV. Class 5
A. Introduction of graphing program
B. Class works through an algebra investigation together that uses the graphing program technology and graphing calculators
C. Participants explore investigations using graphing software and graphing calculators
D. Participants add writeups to their online portfolios
V. Classes 67
A. Participants engage investigations of Equalities and Inequalities
B. Participants add writeups to their online portfolios
C. Revisit and revise a writeup
VI. Class 8
A. Participants engage in investigations of Functions
B. Participants add writeups to their online portfolios
VII. Class 9
A. Participants begin Linear Function and Linear Inequalities investigations
B. Participants add writeups to their online portfolios
VIII. Class 10
A. Participants continue Linear Function and Linear Inequalities investigations
B. Introduction of dynamic geometry software
C. Participants add writeups to their online portfolios
IX. Class 11
A. Participants engage in investigations of Nonlinear functions
B. Discuss and brainstorm ideas about modifying InterMath experience for a middle school mathematics classroom
X. Class 12
A. Participants engage in investigations of Polynomial Functions
B. Participants add writeup to their online portfolios
C. Adapt an InterMath investigation into an instructional activity for middle school students Whole class or small group activity
XI. Class 13
A. Participants engage in investigations focused on Inverses of Functions and Systems of Inequalities in Two Variables
B. Participants add writeups and middle school lesson plan to their online portfolios
XII. Class 14
A. Each participant creates a technologyenhanced mathematical investigation for their own classroom
B. If the activity was implemented in the classroom, participant will discuss what went well, what was difficult, what can be improved, etc.
C. Each participant will take a mathematics exam
9. MATHEMATICAL CONTENT EXPLORED THROUGH THE INVESTIGATIONS
(Click Here to see a list of selected InterMath investigations clustered for Algebra )
Patterns
 Model and solve contextualized problems using various representations, such as graphs, tables, and equations
 Recognize, investigate, analyze, extend, and generalize numeric patterns
 Formulate a rule for a pattern
 Understand the concept of variable
 Evaluate expressions and solve equations (single and multivariable)
 Explore the concept of linear combinations
 Explore problems associated with converging and diverging sequences and series, including arithmetic, geometric, recursive, infinite, and the Fibonacci sequence
 Investigate patterns related to Pascal's Triangle
 Consider patterns and relationships associated with square and triangular numbers
Functions and Equations
 Represent the concept of function verbally, numerically, symbolically, and graphically
 Apply algebraic ideas such as the Pythagorean Theorem and trigonometry to geometric problems
 Understand linear function concepts, such as slope and intercepts
 Formulate the equation of a line in various forms
 Study quadratic functions and parabolic graphs
 Investigate tangent lines and their equations
 Solve a system of equations
 Solve problems associated with linear inequalities
 Generalize the effects of a graph as the coefficients of its equation are modified
 Find the roots of a function algebraically and graphically
 Determine the minimum and maximum values of nonlinear functions
 Explore converging and diverging end behavior of a function
 Solve equations graphically by considering intersecting functions
 Solve equations numerically and symbolically
 Translate verbal expressions into algebraic expressions/sentences and vice versa
Graphing
 Investigate quadratic functions and properties of parabolas
 Analyze the slopes of parallel and perpendicular lines
 Solve for an equation graphically
 Find the equation of a circle centered at the origin or centered at the coordinate (h,k)
 Transform a graph by modifying its equation
 Use and apply the distance formula
