InterMath  Workshop Support  

GOALS ADDRESSED
Participants will:
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:
PERFORMANCE INDICATORS
As a result of this course, participants will demonstrate their ability to:
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.
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 classIII. 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 portfoliosV. Classes 67
A. Participants engage investigations of Equalities and Inequalities
B. Participants add writeups to their online portfolios
C. Revisit and revise a writeupVI. Class 8
A. Participants engage in investigations of Functions
B. Participants add writeups to their online portfoliosVII. Class 9
A. Participants begin Linear Function and Linear Inequalities investigations
B. Participants add writeups to their online portfoliosVIII. Class 10
A. Participants continue Linear Function and Linear Inequalities investigations
B. Introduction of dynamic geometry software
C. Participants add writeups to their online portfoliosIX. Class 11
A. Participants engage in investigations of Nonlinear functions
B. Discuss and brainstorm ideas about modifying InterMath experience for a middle school mathematics classroomX. 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 activityXI. 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 portfoliosXII. 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
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 vers
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