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April 2012, Volume 17, Issue 8

 FEATURES Less is MoreRong-Ji ChenProvide less guidance to students and engage them in challenging mathematical tasks. What Is the Difference? Using Contextualized ProblemsErik S. TillemaReal-world situations involving layers of subtraction will help students in their future work with algebra. Second Look:Subtracting with Integers Where Are the Congruent Halves?Samuel ObaraTry this activity that requires creating two polygons from one to apply knowledge of congruency and transformations and develop spatial reasoning. Putting Mathematical Discourse in WritingSararose D. Lynch and Johnna J. BolyardA problem-solving pen pal project between preservice teachers and sixth graders presented a lens through which a sixth-grade teacher could view students’ work and her instruction. Closing in on ProofDavid A. CofflandQuestions about closure on sets of numbers provide a context for hypotheses and proofs.

 Departments Readers WriteReaders Write - April 2012 On My MindOn My Mind: Mom and Dad Math Solve It!Solve It!: Trains of Thought Cartoon CornerCartoon Corner: All Shook Up Palette of Problems/Menu of ProblemsPalette of Problems - April 2012 Quick ReadsQuick Reads: Map Coloring: A Student’s Perspective Window on ResourcesWindow on Resources – April 2012 Math for RealMath for Real: The Caterer’s Dilemma

 Second Look - Subtracting with Integers Subtraction of Positive and Negative Numbers: The Difference and Completion Approaches with ChipsAn illustration of how the difference and completion (or missing addend) interpretations of subtraction may be used with chips of two colors to understand subtracting negative and positive numbers. Several visual representations are provided. The Value of Debts and CreditsPromote discussions on integers in real life by using positive and negative numbers in the context of net worth. Integer Operations Using a WhiteboardIntegrating interactive whiteboard technology in a unit on adding and subtracting integers enhances student engagement and understanding. What Are You Worth?Use concepts from finance, specifically, assets and debts, to give students a real-world understanding of integer concepts and operations. Illuminations Lesson: Zip, Zilch, ZeroPositive and negative numbers become more than marks on paper when students play this variation of the card game, Rummy. Engaged in a game involving both strategy and luck, students build understanding of additive inverses, adding integers, and absolute value. Number and Operations Standard for Grades 6-8In grades 6–8, students should deepen their understanding of fractions, decimals, percents, and integers, and they should become proficient in using them to solve problems. By solving problems that require multiplicative comparisons (e.g., "How many times as many?" or "How many per?"), students will gain extensive experience with ratios, rates, and percents, which helps form a solid foundation for their understanding of, and facility with, proportionality. The study of rational numbers in the middle grades should build on students' prior knowledge of whole-number concepts and skills and their encounters with fractions, decimals, and percents in lower grades and in everyday life. Students' facility with rational numbers and proportionality can be developed in concert with their study of many topics in the middle-grades curriculum. For example, students can use fractions and decimals to report measurements, to compare survey responses from samples of unequal size, to express probabilities, to indicate scale factors for similarity, and to represent constant rate of change in a problem or slope in a graph of a linear function.