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October 2011, Volume 105, Issue 3

 FEATURES A New Recipe: No More Cookbook LessonsSuzanne R. Harper and Michael Todd EdwardCookbook materials can be readily transformed into lessons that reflect a genuine inquiry approach. An Ap“peel”ing ActivityJoshua A. Urich and Elizabeth A. SasseStudents peel oranges to explore the surface area and volume of a sphere. Second Look:Volume and Surface Area Geometry and the Design of Product PackagingCindy M. ChericoSimulating a real-world marketing situation, students examine the mathematical calculations that play an integral part in product design. Korean College Entrance Exams: An Inside LookDae S. Hong and Kyong Mi ChoiThe mathematical concepts, skills, and problem-solving methods that Korean students need to know in preparation for high-stakes testing. Counting Priests, Paladins, and PetsScott McClintockVirtual worlds, such as the one inhabited by the players of World of Warcraft, can serve as sampling grounds for students who are video gamers.

 Departments Reader ReflectionsReader Reflections - October 2011 Media ClipsMedia Clips: Global Population Explosion // U.S. Population Growth Mathematical LensMathematical Lens: Life Is a Bowl of Mathematics Calendar ProblemsCalendar and Solutions - November 2011 Activities (for students)Activities for Students: Ellipses and Orbits: An Exploration of Eccentricity Technology/Technology TipsTechnology Tips: Teaching Sampling Distributions Using Autograph Delving DeeperDelving Deeper: Teaching the Unthinkable in Introductory Statistics For Your Information/Products/PublicationsFor Your Information - October 2011 The Backpage: My Favorite LessonThe Back Page: Financing a College Education

 Second Look - Volume and Surface Area Mathematical Lens: House, Amherst, MassachusettsThis issue’s photograph is of a rectangular house and target questions focus on mathematical topics that include isometric drawings, area, and proportional reasoning. Students draw floor plans and elevations of the house and use proportional reasoning to estimate measurements from a perspective drawing and calculate the surface area. Mathematical Lens uses photographs as a springboard for mathematical inquiry. The goal of this department is to encourage readers to see patterns and relationships that they can think about and extend in a mathematically playful way. Mathematical Lens is a regular department of Mathematics Teacher. Includes questions for students and answer key. Teaching Proportional Reasoning through Familiar BiologyExploring relationships between size and heat loss in dogs teaches students about the ratio of surface area to volume. Activities for Students: Monod's Nightmare ProblemAn activity about e. coli to focus on teaching volume, surface area, and graphic modeling. Activities are hands-on, open-ended activities that encourage problem solving, reasoning, communication, and mathematical connections. Activities  is a regular feature of Mathematics Teacher and highlights activities that develop conceptual understanding of mathematics topics. The author uses the growth of e. coli to discuss exponential growth. Illuminations Lesson: Tetrahedral KitesEach student constructs a tetrahedron and describes the linear dimensions, area, and volume using non-traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed. Measurement Standard for Grades 9-12Instructional programs from prekindergarten through grade 12 should enable all students to— Understand measurable attributes of objects and the units, systems, and processes of measurement Expections: In grades 9–12 all students should— make decisions about units and scales that are appropriate for problem situations involving measurement.   Apply appropriate techniques , tools, and formulas to determine measurements Expections: In grades 9–12 all students should— analyze precision, accuracy, and approximate error in measurement situations; understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders; apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations; use unit analysis to check measurement computations.