1 Do I Have to Mow the Whole Thing? Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: This lesson offers several practical examples of inverse variation. Students collect data and generate graphs before finding specific equations for inverse variation relationships.... 2 Very Varied - Inverse Variation Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students learn about inverse variation by exploring the relationship between the heights of a fixed amount of water poured into cylindrical containers with different bases. The lesson begins with a review of direct variation and contrasts the properties of direct variation with those of inverse variation.... 3 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.... 4 Be Direct - Oil Spills on Land Resource Type: Lessons Discipline: Mathematics Grades: Grades 8–11 Professional Commentary: This lesson teaches students about direct variation by allowing them to explore a simulated oil spill using toilet paper tissues (to represent land) and drops of vegetable oil (to simulate a volume of oil). The lesson involves mathematical concepts ranging from area and volume to graphing, linear regression, and lines of best fit.... 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.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 7–8 Professional Commentary: Students build a family of cylinders, all from the same-sized paper, and discover the relationship between the dimensions of the paper and the resulting cylinders. They order the cylinders by their volumes and draw a conclusion about the relationship between a cylinder's dimensions and its volume.... 7 A Distant View: Exploring the Principles of Telescope Optics Resource Type: Lessons Grades: Grades 8–12 Professional Commentary: Students see real-life applications of rational functions and the Pythagorean Theorem, as they investigate the essential concepts of how lenses work to magnify vision, and then build simple telescopes to demonstrate their understanding. Discussion questions, suggestions for assessment, additional activities, interdisciplinary connections, and Internet extensions are included in the lesson plan.... 8 More Nonlinear Functions: Patterns, Functions, and Algebra Session 8 Resource Type: Content Supports Discipline: Mathematics Grades: Grades 8–Postsecondary Professional Commentary: This site follows ORC # 11076, Nonlinear Functions, by considering cyclic (or periodic) functions and inverse relationships. The site includes problems, applications, suggestions for homework, solutions to the problems, applets, and illustrative video clips.... |