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February 2013, Volume 19, Issue 6

 FEATURES A Pathway for Mathematical PracticesMelanie Wenrick, Jean L. Behrend, Laura C. MohsSee how the NCTM Process Standards in action integrate Common Core State Standards in a second-grade classroom. Surviving an Avalanche of Data- FREE PREVIEW!Lyn D. EnglishHelp first-grade students learn to competently generate, test, revise, and represent data before being formally taught to do so. So, Here’s the StoryLynn ColumbaIt is a “read”-letter day when storybooks, thinking strategies, and physical materials can use a splash of whimsy and fun to introduce multiplication facts to third graders. Appendix: A table of multiplication strategies, directions for creating a pocket multiplier, and a list of additional resources Using Technology to Teach EquivalenceRochelle Goldberg Kaplan and Sandra AlonReflect and DiscussProfessional development equips practitioners with skills to enhance student learning. Appendix: Lesson-planning steps as well as Reflect and Discuss questions Second Look:Equality

 Departments A pedagogical analysis of back talk: Abby and the number line news&viewsnews&views / coaches' corner - February 2013 Problem Solversproblem solvers: problem - The inaugural address Problem Solversproblem solvers: solutions - Valentine’s Day probability Math by the Monthmath by the month: Get Your Bearings Technology/Technology Tipstechnology from the classroom: Collaboration 2.0 Reviewing and Viewingreviewing and viewing: For your resource library backtalkback talk: David’s problem solving

 Second Look - Equality Fostering Relational Thinking while Negotiating the Meaning of the Equals SignHow third-grade students developed an understanding of the equals sign and began to use relational thinking as they discussed true/false and open-number sentences. The sequence of instructional activities and children’s responses to them are provided. Balancing Act: The Truth behind the Equals SignThe 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 EquationsGiven 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 equation-solving 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 - NumbersUse 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 - ShapesBuild 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 built-in sets or a random set. Number and Operations - Pre-K through Grade 12Instructional 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