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
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
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 standardsbased 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 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.
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 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