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October 2011, Volume 105, Issue 3

FEATURES

A New Recipe: No More Cookbook Lessons
Suzanne R. Harper and Michael Todd Edward
Cookbook materials can be readily transformed into lessons that reflect a genuine inquiry approach.

An Ap“peel”ing Activity
Joshua A. Urich and Elizabeth A. Sasse
Students peel oranges to explore the surface area and volume of a sphere.
Second Look:
Volume and Surface Area

Geometry and the Design of Product Packaging
Cindy M. Cherico
Simulating a real-world marketing situation, students examine the mathematical calculations that play an integral part in product design.

Korean College Entrance Exams: An Inside Look
Dae S. Hong and Kyong Mi Choi
The mathematical concepts, skills, and problem-solving methods that Korean students need to know in preparation for high-stakes testing.

Counting Priests, Paladins, and Pets
Scott McClintock
Virtual worlds, such as the one inhabited by the players of World of Warcraft, can serve as sampling grounds for students who are video gamers.

Second Look - Volume and Surface Area

Mathematical Lens: House, Amherst, Massachusetts
This 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 Biology
Exploring relationships between size and heat loss in dogs teaches students about the ratio of surface area to volume.

Activities for Students: Monod's Nightmare Problem
An 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 Kites

Each 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 9-12

Instructional 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.