Second Look  Equality 
Fostering Relational Thinking while Negotiating the Meaning of the Equals Sign How thirdgrade students developed an understanding of the equals sign and began to use relational thinking as they discussed true/false and opennumber sentences. The sequence of instructional activities and children’s responses to them are provided. 
Balancing Act: The Truth behind the Equals Sign The misconceptions that students have when using the equals sign and a lesson that teachers can use in the classroom to give students the foundation for an accurate conception of equivalency. 
Does Understanding the Equal Sign Matter? Evidence from Solving Equations Given its important role in mathematics as well as its role as a gatekeeper to future educational and employment opportunities, algebra has become a focal point of both reform and research efforts in mathematics education. Understanding and using algebra is dependent on understanding a number of fundamental concepts, one of which is the concept of equality. This article focuses on middle school students' understanding of the equal sign and its relation to performance solving algebraic equations. The data indicate that many students lack a sophisticated understanding of the equal sign and that their understanding of the equal sign is associated with performance on equationsolving items. Moreover, the latter finding holds even when controlling for mathematics ability (as measured by standardized achievement test scores). Implications for instruction and curricular design are discussed. 
Illuminations Lesson: Pan Balance  Numbers Use this tool to strengthen understanding and computation of numerical
expressions and equality. In understanding equality, one of the first things
students must realize is that equality is a relationship, not an operation. Many
students view "=" as "find the answer." For these students, it is difficult to
understand equations such as 11 = 4 + 7 or 3 × 5 = 17 – 2. 
Illuminations Lesson: Pan Balance  Shapes Build up to algebraic thinking by exploring this balance tool using shapes of
unknown weight. Challenge yourself to find the weight of each shape in one of
six builtin sets or a random set. 
Number and Operations  PreK through Grade 12
Instructional programs from prekindergarten through grade 12 should enable all students to—
 understand numbers, ways of representing numbers, relationships among numbers, and number systems;
 understand meanings of operations and how they relate to one another;
 compute fluently and make reasonable estimates
