Module 1: Operations and Applications with Rational Numbers in Middle School Mathematics

Shultz, H., Bonsangue, M., Costa, V., and Cho, G. (2005). Module 1: Operations and Applications with Rational Numbers 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 http://www.pdrom.coursepath.org/.

Motivating CAHSEE Problem

The diameter of a tree trunk varies directly with the age of the tree. A 45-year-old tree has a trunk diameter of 18 inches. What is the age of a tree that has a trunk diameter of 20 inches?

1. 47 years
2. 50 years
3. 63 years
4. 90 years

11/12 - (1/3 + 1/4) =

1. 1/3
2. 3/4
3. 5/6
4. 9/5

California
Mathematics Content Standards

• Number Sense (6th) 1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages.
• Algebra and Functions (6th) 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.
• Algebra and Functions (7th) 1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs.

• Number Sense (7th) 2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division.
• Algebra and Functions (7th) 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results.

Math Concepts

• Attending to CAHSEE examination problems during regular lessons
• Solving direct variation problems through unit rates and proportions

• Attending to CAHSEE examination problems
• Using the vertical format to simplify fractional expressions
• Sequencing lessons to move toward complexity of multiple step problems by requiring multiple layers of mathematical knowledge and skills
• Making warm-ups relevant to the lesson and using them as entry-level assessments

Instructional Strategies

• Giving careful attention to flow of the lesson
• Using poetry or literature to support teaching and learning of mathematics
• Supporting content-specific vocabulary development

• Emphasizing the natural ways in which mathematics and what goes on in mathematics classrooms are advantageous to ELs
• Utilizing active engagement strategies of speaking, writing, signaling, and thinking.
• Increasing comprehensible input , student interactions , and student thinking skills
• Using student whiteboards in ways that promote a positive learning environment and support deeper understanding of the concepts and skills addressed in the lesson