        Relative Ratios Alexander Sabatino Jr.    6-8 Four 45-minute classes This is an interactive, media-rich lesson in which students examine proportions. By experiment, students will discover that proportions are made up of equal ratios each containing the same building blocks. Using video, students will discover that proportions are direct relationships, and understand how they are used to estimate quantities and find missing numbers. Using the Internet, students will apply their knowledge of direct relationships and proportions to problems in planetary science. Finally, students will demonstrate their ability to use proportions by determining if human bones are a good predictor of height. This lesson utilizes reading, writing, and mathematical skills in an interdisciplinary format. Students will be able to: Explain the nature of direct relationships Explain the nature of proportions Test if two ratios are in proportion Explain why two ratios are in proportion Find missing information to complete a proportion Apply proportions to solving problems. Predict the height of a person using anatomical measurements in proportion National Council of Teachers of Mathematics grades K-12 http://www.nctm.org/standards/standards.htm Numbers and Operations Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Algebra Represent and analyze mathematical situations and structures using algebraic symbols. Use mathematical models to represent and understand quantitative relationships. Measurement Understand measurable attributes of objects and the units, systems, and processes of measurement. Data Analysis and Probability Develop and evaluate inferences and predictions that are based on data. Problem Solving Solve problems that arise in mathematics and in other contexts. Apply and adapt a variety of appropriate strategies to solve problems. Reasoning and Proof Make and investigate mathematical conjectures. Communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. Connections Recognize and apply mathematics in contexts outside of mathematics. Video: Mathvantage #2: Proportional Reasoning Web sites: National Space Science Data Center, NASA, fact sheet http://nssdc.gsfc.nasa.gov/planetary/factsheet/index.html Developed by NASA, this Web page organizes planetary data in one table. This is useful since this type of data is difficult to access otherwise. The NSSDC Web site is full of up-to-date information on the planets. It includes pictures and current celestial events. It is highly recommended to explore. Per class: One pound package each of white and black beans 12 to 15 envelopes or small bags VCR Per group of 3-4 Students Metric ruler (rulers should have millimeter gradations) Meter stick Per student: Calculator Exploring Proportions Activity student organizer Proportional Reasoning student organizer Proportions and Planetary Science student organizer Proportions and Physical Anthropology student organizer