## Expressions, Equations, and Inequalities

**Promoting Mathematical Proficiency**

Some experts assert that middle school teachers should be focused on the big ideas of number systems, of number theory, of symbolic representation, and theory of equations to teach algebra topics. With this focus, teachers are able to develop students' understanding of the structural aspects of algebra. These big ideas will soon come to replace the notion that the essence of algebra is memorizing procedures and rules, a notion that has thus far hindered this country's effective instruction of algebra. As part of this expansion of big ideas and number systems, students are introduced to rational numbers, both positive and negative, in this grade.

The standards, set forth by the National Council of Teachers of Mathematics' Principles and Standards for School Mathematics (2000), for grades six through eight have expectations that would “stretch the middle-grades program beyond a preoccupation with numbers,” showing recognition of the necessity that students gain facility in algebraic thinking. “In algebra the focus is on proficiency in recognizing and working with linear relationships and their corresponding relationships in tables, graphs, and equations; such proficiency includes competence in solving linear equations.” The Standards propose that students develop a deep understanding of rational number concepts, and become proficient in rational number computation and estimation.

**Teaching Model 23.3:** Equations With Rational Numbers