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  Lesson Plans
Relative Ratios

Alexander Sabatino Jr.
OverviewProcedure for teachersStudent Resources and Materials
Grade Level
 6-8
Time Alloment
 Four 45-minute classes

Overview

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.


Learning Activities

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

Standards

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.

Media Components

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.


Materials

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