InterMath - Algebra

INSTRUCTOR: *Sarah
Ledford*

Email: *sledford@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

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.

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 write-up (including extensions)II. Class 2

A. Participants engage in investigations of Variables and Expressions.

B. Participants add write-ups to their online portfolios

C. Participants work on variable and expression investigation, spreadsheet skills, and/or other topic covered in classIII. Classes 3-4

A. Participants engage in the Patterns investigations

B. Participants begin their first web page write-ups to include in their online portfolios

C. Continued technological teaching and support (especially with Excel and the structure of a write-up)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 write-ups to their online portfoliosV. Classes 6-7

A. Participants engage investigations of Equalities and Inequalities

B. Participants add write-ups to their online portfolios

C. Revisit and revise a write-upVI. Class 8

A. Participants engage in investigations of Functions

B. Participants add write-ups to their online portfoliosVII. Class 9

A. Participants begin Linear Function and Linear Inequalities investigations

B. Participants add write-ups to their online portfoliosVIII. Class 10

A. Participants continue Linear Function and Linear Inequalities investigations

B. Introduction of dynamic geometry software

C. Participants add write-ups 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 write-up 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 write-ups and middle school lesson plan to their online portfoliosXII. Class 14

A. Each participant creates a technology-enhanced 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**

(

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 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