Module 3: Representing Equalities and Inequalities in Middle School Mathematics

Shultz, H., Costa, V., and Ellis, M. (2005). Module 3: Representing Equalities and Inequalities in Middle School Mathematics. In V. Costa, M. Bonsangue, and H. Shultz (Eds.) (2 nd ed.).  Professional Development Resources Online for Mathematics [Online Course].  Available from www.pdrom.coursepath.org/.

Motivating CAHSEE Problem

If x is an integer, what is the solution to |x - 3| < 1?

1. {-3}
2. {-3, -2, -1, 0, 1}
3. {3}
4. {-1, 0, 1, 2, 3}

What is the y-intercept of the line 2 x - 3 y = 12?

1. (0, -4)
2. (0, -3)
3. (2, 0)
4. (6, 0)

California
Mathematics Content Standards

• Algebra 1, Standard 3.0: Students solve equations and inequalities involving absolute values.

• Algebra 1, Standard 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). 

Math Concepts

• Attending to CAHSEE examination problems
• Sequencing of problem examples from more simple to more complex
• Providing both geometric and algebraic representations of the problem
• Modeling of checking solutions
• Providing alternative  methods of solving the problem

• Finding x - and y -intercepts, given a linear equation in the form Ax + By = C
• Carefully consideration of the purposes of homework and the sort of feedback provided to students
• Using x - and y -intercepts to graph a line

Instructional Strategies

• Using a real-life example that extends throughout the lesson
• Inviting student verbalization of problem-solving and thinking to increase conceptual understanding
• Using advance or graphic organizers to support teaching and learning
• Using the textbook and resources to deepen understanding of math concepts and skills
• Supporting struggling readers and English Learners

• Providing multiple representations of mathematical relationships
• Teaching students to solve the problem to the point of answering the question posed
• Using note-taking strategies to help students organize, retrieve, and use mathematics content
• Using textbook and publisher resources to deepen understanding of mathematical concepts and skills
• Analyzing data to determine student achievement of objectives
• Reflecting on lesson implementation to identify strengths and areas of needed improvement, and to make a plan for future implementation