This course examines ideas associated with algebraic thinking and algebra. Topics include functions, variables, graphs, equations, linear equations, and systems of linear equations. Emphasis is placed on the interpretation of graphs. The course follows a problem-solving approach, in which participants learn to express the solution to a problem in multiple ways: visually, algebraically, numerically, and verbally (the fourfold way). Prerequisite: Intermediate Algebra

ALGEBRAIC THINKING: PATTERNS (ALG)
Participants examine several problems involving patterns. They express the solutions in various ways, using pictures, numbers, symbols, and words. Participants discuss several key ideas in algebraic thinking.

VARIABLES (VARS)
Participants examine several different uses of variables, and they focus on the importance of specifying variables accurately. Participants learn to recognize the use of letters (which look like variables) as labels in shorthand statements. They use dimensional analysis to convert between units. They discuss both appropriate and inappropriate uses of literal notation in school mathematics.

THE ALGEBRA WALK (WALK)
Participants learn informally about coordinate graphing by forming human graphs outdoors. Participants become familiar with various properties of functions by examining the similarities and differences of their graphs. Participants form graphs corresponding to pairs of simultaneous equations, and they understand the significance of the solution to a system of equations. Participants design a human graph activity appropriate for their own students.

THE PARADE (PARADE)
Snapshots taken every five seconds along a parade route provide a context for the introduction of time-distance graphs. Participants plot information on a “Snapshot Sequence Sheet” and use the visual representation to examine concepts of linear functions and their graphs. Participants focus on interpreting time-distance graphs.

SLOPES (SLOPE)
Participants find slopes of lines, first on a grid and then on a coordinate graph. They see how a line of slope m determines an equation y = mx+b, and how this corresponds to a function rule. They find equations of lines in slope-intercept form y = mx+b using graphs and tables.

EQUATIONS OF LINES (LINES)
Participants use the basic definition of the slope of a line to find equations of lines in various forms. Participants become familiar with the various forms of equations of lines, and they find equations for lines that meet specific conditions. Participants examine the development of equations of lines in their algebra textbooks.

LINEAR SYSTEMS OF EQUATIONS (SYS1)
Participants revisit the parade problem, which was introduced in the Equations of Lines module. Participants use graphing and algebraic techniques to solve various linear systems of equations. Finally, participants apply their knowledge to analyze a real-world application problem.

ALGEBRAIC REASONING PROBLEMS (AR)
Participants solve algebraic reasoning warmup problems by using any problem solving strategy and by expressing their solutions visually, numerically, algebraically, and verbally. Participants present the approaches used in solving the problems and discuss how their own students might solve them.

PATTERN PROBLEMS (PATT)
This module contains a collection of problems that lead to nonlinear functions. The problems provide practice in representing mathematical ideas visually, numerically, symbolically, and verbally (the fourfold way). By exploring concrete situations using a variety of mathematical techniques, participants increase confidence and competence in their ability to apply mathematical problem-solving skills.

POLYNOMIALS (POLY1)
While mathematics teachers are usually quite competent manipulating polynomial expressions, many have not thought extensively about how to use concrete materials to make algebraic manipulations meaningful to students. In this module we use “Algebra Pieces” (available from Math Learning Center) and “Exploring the Unknown,” an instructional unit from MathScape: Seeing and Thinking Mathematically (available from Creative Publications) for this mathematical and pedagogical exploration.

Back to Course Descriptions