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Module Five

MODULE 5: MODELING LINEAR CHANGE IN MIDDLE SCHOOL MATHEMATICS

Ellis, M. , Shultz, H., and Costa, V. (2006). Module 5: Modeling Linear Change in Middle School Mathematics. In V. Costa, M. Bonsangue, and H. Shultz (Eds.) (3rd ed.). Professional Development Resources Online for Mathematics [Online Course]. Available from http://www.pdrom.coursepath.org/

 

Unit 5.1

STACKING CUPS

Unit 5.2

HIKERS BEWARE

Motivating 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

California
Mathematics Content Standards

  • 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.

Math Concepts

 

  • The connection among (1) equal slopes, (2) equal rates of change and (3) parallel lines.
  • Clarifying the concept of y-intercept
  • Clarifying the meaning of negative slope
  • Interpreting the intersection of two lines

Instructional Strategies
  • 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
  • Creating a classroom environment that builds students' motivation to learn mathematics.
  • Promoting meaningful discourse in mathematics classrooms.
  • Utilizing culturally responsive pedagogy to engage all student
  • 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.

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PD-ROM was administered by Orange County Department of Education and California State University, Fullerton. The project was made possible with funding from the Improving Teacher Quality State Grant Program, administered by the California Postsecondary Education Commission (ITQ #240). It was and a collaborative effort of California State University Fullerton Departments of Mathematics and Secondary Education, Orange County Department of Education, and the Corporation for Education Network Initiatives in California (CENIC).
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