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November 2011, Volume 17, Issue 4

 FEATURES No Child Left UnchallengedDarin BeigieDesign lightbulb questions for your students using these six simple methods. A Fruitful Activity for Finding the Greatest Common FactorCarol J. Bell, Heather J. Leisner, and Kristina ShelleyAs students fill baskets with differing numbers of fruit, they develop the concept of GCF—often before learning the formal definition. Second Look:Factors and Primes Fractions: How to Fair ShareP. Holt Wilson, Cynthia P. Edgington, Kenny H. Nguyen, Ryan S. Pescosolido, and Jere ConfreyDevelop and strengthen students’ rational number sense with problems that emphasize equipartitioning. Your Inner English TeacherConrado L. Gómez, Terri L. Kurz, and Margarita Jimenez-SilvaBy using deliberate strategies to adjust the phrasing of word problems, teachers can provide a richer mathematics experience for ELLs.

 Departments On My MindOn My Mind: Teaching to Intuition Informing PracticeInforming Practice: Specializing: An Entry Point for Problem Solving Quick ReadsQuick Reads: Experiments on the Surface Area of a Sphere Cartoon CornerCartoon Corner: The Longest Yard Solve It!Solve It!: Push-up Pete Solve It!Solve It! Student Thinking: Average Jeans Palette of Problems/Menu of ProblemsPalette of Problems - November 2011 Mathematical ExplorationMath Explorations: Games to Support Decimal Number Reasoning Window on ResourcesWindow on Resources: Books - November 2011 Math for RealMath for Real: Choose My Plate!

 Second Look - Factors and Primes Building Numbers from PrimesUse building blocks to create a visual model for prime factorizations. Students can explore many concepts of number theory, including the relationship between greatest common factors and least common multiples. Making Connections with Prime NumbersPrime numbers and their connections to related topics. Investigating Prime Numbers and the Great Internet Mersenne Prime SearchMiddle school students learn about patterns, formulas, and large numbers motivated by a search for the largest prime number. Activities included. Teacher to Teacher: Dialogue: A Route to ACT-ive LearningAn innovative method to introduce the concepts of greatest common factor and least common multiple. Students engage in a scripted performance, using factor cards and prime factorization to find GCF and LCM. Script is included. Illuminations Lesson: The Venn FactorStudents use a Venn diagram to sort prime factors of two or more positive integers. Students calculate the greatest common factor by multiplying common prime factors and develop a definition based on their exploration. 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.