InterMath Workshop Support

Program:	InterMath - Algebra
Location:	Washington/Wilkes County
Date:	Spring 2007
Instructors and Contact Info:	Al Lapointe: lapointe@uga.edu Susan Sexton: sextons@uga.edu

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 mathematics-specific 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 technology-enhanced mathematical investigations
• Develop a network of peer educators available for continued support during and following the workshop

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.

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 standards-based reform documents, such as the NCTM standards

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

ASSESSMENT

Participants will be assessed on the content and quality of their online portfolios. Feedback and suggested modifications for a select number of write-ups 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 write-ups, the participants will also create a mathematics lesson that integrates technology and algebra for use in their own classroom.

COURSE OUTLINE

January 29, 2007: Class 1 (3:30pm ≠ 7:30pm)

Welcome to InterMath!

Introduction to Excel and Graphing Calculator

February 12, 2007: Class 2 (3:30pm ≠ 7:30pm)

Topic: Variables and Expressions

Explore "End Behavior with a Constant Ratio"

Explore Working with Zero

February 26, 2007: Class 3 (3:30pm ≠ 7:30pm)

Topic: Relationships Between Varying Quantities

Explore the need for a variable in a general solution with InterMath Exploration: Consecutive Odds or Evens

Explore the manipulation of four variables with InterMath Exploration: Unusual Property

Explore Excel with InterMath Exploration: Raised to the 100th

Explore more with variables with InterMath Exploration: Hypatia's Triumph

March 12, 2007: Class 4 (3:30pm ≠ 7:30pm)

Topic: Algebraic Expressions

March 26, 2007: Class 5 (3:30pm ≠ 7:30pm)

∑ Proportional Reasoning

April 16, 2007: Class 6 (3:30pm ≠ 7:30pm)

∑ Linear Equations & Inequalities

April 30, 2007: Class 7 (3:30pm ≠ 7:30pm)

∑ Different Types of Equations & Inequalities

May 14, 2007: Class 8 (3:30pm ≠ 7:30pm)

∑ Systems of Equations and Inequalities

May 23, 2007: Class 9 (8:30am ≠ 2:30pm)

∑ Introducing Functions and their Movements

May 24, 2007: Class 10 (8:30am ≠ 2:30pm)

∑ Exploring Different Functions

May 25, 2007: Class 11 (8:30am ≠ 2:30pm)

∑ What did we forget?

MATHEMATICAL CONTENT EXPLORED THROUGH THE INVESTIGATIONS

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 multi-variable)
• 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