In this module, you will focus on the concept of linear change by exploring the problem Stacking Cups.

This unit focuses on the CAHSEE problem:

What is the slope of a line parallel to the line y = 1/3x + 2?

A. -3
B. -1/3
C. 1/3
D. 2

As you progress through this module, you will deepen your content knowledge on the knowledge and skills important in understanding the concept of linear change, including constant rate of change, the slope of a line, the y-intercept, and the slope relationship of parallel and perpendicular lines. In addition, you will observe several instructional strategies to assist students in mastering these types of problems.

The major California Mathematics Content standards addressed in this question include:

Algebra 6.0. Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).

Algebra 7.0. Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.

Algebra 8.0. Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.


In Module 5.1: Linear Change, you will:

  • Deepen your understanding of mathematical concepts in Algebra, including the connection between:
    • slope
    • y-intercept
    • constant rate of change and
    • parallel lines
  • Develop skills in new instructional strategies, including:
    • stimulating student engagement while setting up a mathematical task;
    • organizing materials and students for hands-on mathematical tasks;
    • using strategic questioning to further students' thinking; and
    • using multiple representations to facilitate development of conceptual understanding.