
Relative Ratios
Alexander Sabatino Jr. 


68 
Four 45minute classes 

This is an interactive, mediarich 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 K12
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 uptodate 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 34 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

