Overview

This unit continues our focus 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 unit, you will deepen your content knowledge on the slope of parallel and perpendicular lines and develop instructional strategies to assist students in mastering these kinds 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 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.

Algebra 9.0. Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.

Objectives

In Unit 5.2: Hikers Beware!, you will:

  • Deepen your understanding of mathematical concepts in Algebra, including:
    • Clarifying the concept of y-intercept
    • Clarifying the meaning of negative slope
    • Interpreting the intersection of two lines
  • Develop skills in new instructional strategies, including
    • Creating a classroom environment that builds students' motivation to learn mathematics.
    • Promoting meaningful discourse in mathematics classrooms.
    • Utilizing culturally responsive pedagogy to engage all students
    • Scaffolding students in their development of problem solving strategies.
    • Analyzing student thinking to inform instructional decision-making.
    • Using focusing rather than funneling questions.
    • Structuring the sharing of student work in terms of mathematical flow.