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March 2013, Volume 106, Issue 7

 FEATURES Visible Thinking in High School MathematicsEmily SlimanChalk Talk and Claim-Support-Question are two routines for developing students’ ability to use multiple representations and encouraging classroom discussion. Equivalence Relations across the Secondary School CurriculumLisa BergerAn analysis of problems from state assessments and other sources helps preservice teachers discover analogous mathematical representations. Why Is the Midpoint an Average?- FREE PREVIEW!Lingguo BuThe relationship between a midpoint and an average showcases the interplay between procedural knowledge and conceptual knowledge in learning mathematics for teaching. Sorting Out Ideas about FunctionAmy F. Hillen and LuAnn MalikA card-sorting task can help students extend their understanding of functions and functional relationships. Second Look:Functions Truth and Beauty: Mathematics in LiteratureMarion D. CohenStudying mathematics-related fiction and poetry helps students develop an appreciation for both mathematics and literature and an understanding of the connection between the two.

 Departments Reader ReflectionsReader Reflections - March 2012 Sound Off!Sound Off!: Least Common Denominators and the Common Core Media ClipsMedia Clips: A Rare July? // Fibonacci Takes to the Air Mathematical LensMathematical Lens: Transformational Geometry at Guilin Garden, Shanghai Calendar ProblemsCalendar and Solutions – April 2013 Activities (for students)Activities for Students: Classifying Triangles and Quadrilaterals Delving DeeperDelving Deeper: Rolling the Dice For Your Information/Products/PublicationsFor Your Information - March 2013 The Backpage: My Favorite LessonThe Back Page: My Favorite Lesson: A Quarter on Trial

 Second Look - Functions Inverse Functions: What Our Teachers Didn’t Tell UsThe concept and notation of inverse functions—often tricky for students—become less so when using real-world data and a strategy of solving for the dependent variable. Choreographing Patterns and FunctionsYoung students dance their way through a multifaceted differentiated approach to early algebra instruction. The Back Page: My Favorite Lesson: A Graphic Organizer for Polynomial FunctionsA graphic organizer can help students analyze polynomial equations. Illuminations Applet: Function MatchingSee how well you understand function expressions by trying to match your function graph to a generated graph. Choose from several function types or select random and let the computer choose. Algebra Standard for Grades 9-12Instructional programs from prekindergarten through grade 12 should enable all students to— Understand patterns , relations, and functions  Represent and analyze  mathematical situations and structures using algebraic symbols Use mathematical models to represent and understand quantitative relationships  Analyze change in various contexts