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September 2012, Volume 19, Issue 2

 FEATURES Show Me a SignJohnnie WilsonObserve a first-grade teacher’s use of gesture as a mathematics teaching and learning tool in his classroom. An Appetite for FractionsTrena L. Wilkerson, Tommy Bryan, and Jane CurryUsing candy bars as models gives students a taste for learning to represent fractions whose denominators are factors of 12. Candy bar template and student activity sheet Second Look:Understanding Fractions Memories of a Chicken-and-a-Half - Reflect and DiscussSteven M. SchulmanStep in and out of an impromptu fifth-grade math lesson with an experienced teacher, and renew your appreciation for students’ algebraic thinking. Will CCSSM Matter in Ten Years? - Reflect and DiscussMatthew R. LarsonHow might we use a historical perspective to make the outcome of implementing the Common Core State Standards for Mathematics better than the reform efforts that have preceded it?  Podcast from NCTM's 2012 Annual Meeting in Philadelphia, PennsylvaniaAchieving Uncommon Results with CCSSM Presenter: Matt Larson Slides of presentation (PDF)

 Departments news&viewsnews&views - September 2012 Problem Solversproblem solvers: problem: Firefighters to the rescue Problem Solversproblem solvers: solutions: Hockey-stick fundraiser Math by the Monthmath by the month: Be a math sport technology from the classroomtechnology from the classroom: Pattern-block frenzy Reviewing and Viewingreviewing and viewing: Something for everyone backtalkback talk: The king’s really big bowl

 Second Look - Understanding Fractions Creating, Naming, and Justifying FractionsFor students to develop meaningful conceptions of fractions and fraction operations, they need to think of fractions in terms other than as just whole-number combinations. The authors suggest two powerful images for thinking about fractions that move beyond whole-number reasoning and can be used in the classroom to help support the teaching of fractions. Fair Shares, Matey, or Walk the PlankTeaching young children to create equal-size groups is your treasure map for building students’ flexible, connected understanding of and reasoning about ratios, fractions, and multiplicative operations. Fractions and the funky cookieA mathematics specialist has great success using a pattern-block configuration to help a small group of fifth graders understand that fractional parts of a whole unit must be equal in size. That’s just the way the funky cookie crumbles. Investigations: Fraction ActionAn activity about Fractions focused on teaching numbers and operations. Illuminations Unit: Eggsactly with Fractions Number and Operations Standard for Grades 3-5In grades 3–5, students' development of number sense should continue, with a focus on multiplication and division. Their understanding of the meanings of these operations should grow deeper as they encounter a range of representations and problem situations, learn about the properties of these operations, and develop fluency in whole-number computation. An understanding of the base-ten number system should be extended through continued work with larger numbers as well as with decimals. Through the study of various meanings and models of fractions—how fractions are related to each other and to the unit whole and how they are represented—students can gain facility in comparing fractions, often by using benchmarks such as 1/2 or 1. They also should consider numbers less than zero through familiar models such as a thermometer or a number line.