# Exploring and Understanding Patterns, Functions and Modeling for Elementary Teachers (Math 106)

MATH 106- 001 Instructor: Janet Sipes janetsipes@math.arizona.edu

## COURSE OBJECTIVES:

Upon completion of this course students should be able to:

- Solve story problems using multiple strategies
- Explain numerical and geometric patterns through words and symbols
- Interpret graphs in multiple contexts
- Understand the difference between arithmetic thinking and algebraic thinking
- Make connections across multiple representations (graphs, tables, words, and algebraic expressions)
- Describe real world situation through different types of functions (linear, quadratic, and exponential)
- Understand the concept of mathematical model
- Apply the modeling cycle to real-world situations
- Communicate mathematical ideas and develop an ability to explain and justify their own reasoning
- Examine how mathematical ideas are represented in multiple ways, in particular through the use of technology or hands-on manipulatives
- Develop a familiarity with materials and methods that are consistent with current mathematics teaching approaches for algebra at the K-8 level

## PREREQUISITES

PPL 30+ or MCLG 40+ or SAT I MSS 530+ or ACT MATH 21+ . Test scores expire after 1 year. Some students may need to take Math 100 first.

## COURSE POLICIES

General Math 106 Course Policies

General Math 106 Course Calendar

## COURSE MATERIALS

The following course materials are required for Math 106:

- Textbook: Patterns, Functions, and Models
*[Custom edition for Math 106 from UofA bookstore]* - Calculator
- Geometry Tools: ruler (cm and inches), protractor, compass, triangle squares.
- Others: Pencils, colored pencils, markers, graph paper, scissors, eraser and/or whiteout

## HELP SESSIONS

Besides your instructor's office hours, you are encouraged to make use of the Math 106 Help Sessions. These will take place in MTL 123. The times will be announced at the beginning of the semester (and posted below in Useful Links). These help sessions are excellent occasions to get together with classmates to work on your homework and “talk Math 106.” During these Help Sessions a Math 106 or 302A/B instructor will be available for questions and guidance.

## COURSE FORMAT AND TEACHING METHODS

- This course explores algebraic thinking from early childhood through middle school, with a focus on the different conceptions of algebra, including generalized arithmetic; thinking in patterns and functions; and modeling. We will examine the different topics in K-8 algebra from an advanced perspective. MATH 106 is an activity-based course.
- This course will approach mathematics with the idea that everything in mathematics makes sense, and that you (and your future students) are capable of understanding all of K-8 mathematics. The class is organized to provide a friendly, intimate, non-competitive atmosphere in which you can feel free to explore, discuss, and learn Mathematics in a small group situation.
- You are expected to come to class prepared. Time in class will be spent primarily on working on and discussing problems and activities.