1 Pennies, Pressure, Temperature, and Light: Inverse Functions Resource Type: Lessons Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: The major goal of this lesson is to collect data from a variety of experiments, determine what type of model best fits the data, and explain why. Students explore a variety of relationships using pennies, pressure, temperature, light, and pendulums to determine the algebraic equation that best represents the pattern modeled by the variables involved in... 2 Stressed to the Breaking Point: Multiple-Variable Functions Resource Type: Lessons Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: How does the amount of weight that can be supported by a spaghetti bridge relate to the width (number of spaghetti strands) and the length of a bridge? Students gather data comparing the amount of weight that can be supported, the number of strands of spaghetti used, and the length of the bridge.... 3 Shrinking Candles, Running Water, Folding Boxes Resource Type: Lessons Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: This multi-day activity has students look for functions within a given set of data. After analyzing patterns in the data, students should be able to determine the type of function that best represents the data.... 4 Whelk-Come to Mathematics Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: In this investigation students explore the possible reasons behind the observation that northwestern crows consistently drop a type of mollusk called a whelk from a height of 5 meters to break its shell. Students are given activity sheets and a graphics calculator.... 5 Shedding Light on the Subject Resource Type: Lessons Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: In this 4-lesson unit students develop and analyze exponential models for the behavior of light passing through water. Students begin by considering how light intensity changes from near the surface to the bottom of the ocean.... 6 Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body Resource Type: Lessons Discipline: Mathematics, Science Grades: Grades 8–12 Professional Commentary: This three-part activity illustrates the use of iteration, recursion, and algebra to model and analyze the changing amount of medicine in an athlete's body. The activity is adapted from High School Mathematics at Work, a publication from the National Research Council.... 7 Powerful Calculators Throw Teachers a New Curve Resource Type: Professional Resources Discipline: Mathematics Grades: Grades 8–Postsecondary Professional Commentary: Graphing calculators are sophisticated devices that can run small computer programs and draw the graph represented by complex equations in an instant. In the last few years, they have become mandatory in many high school mathematics classes and can be used on the SAT and advanced placement exams and other standardized tests.... 8 Modeling Orbital Debris Problems Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: In this week-long unit, students examine the problem of space pollution caused by human-made debris in orbit to develop an understanding of functions and modeling. The unit provides students an opportunity to use spreadsheets, graphing calculators, and computer graphing utilities.... Resource Type: Content Supports -- Activities and rich problems Discipline: Mathematics Grades: Grades 7–12 Professional Commentary: How does one go about finding the volume of an irregular shape? Students get a preview of integral calculus as they compute volume of a solid as the sum of volumes of slices of the solid.... 10 Intermediate Value Theorem Resource Type: Content Supports -- Reference materials Discipline: Mathematics Grades: Grades 12–Postsecondary Professional Commentary: This website poses and solves the classic hiker problem: A hiker starts on a path from the bottom of a mountain at 6:00 a.m. and arrives at the top of the mountain at 6:00 p.m.... |