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

## 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 MATERIALS

The following course materials are required for Math 106:

Students may use either a Calculator or the Desmos app

Geometry Tool: ruler (cm and inches)

*Other recommended, but not required, materials:*

Pencils, colored pencils, markers, graph paper, scissors, eraser and/or whiteout, protractor, compass, triangle squares

## 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.