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
Council of Teachers of Mathematics grades K-12
Numbers and Operations
- Understand numbers, ways of representing numbers, relationships
among numbers, and number systems.
- Represent and analyze mathematical situations and structures using
- Use mathematical models to represent and understand quantitative
Data Analysis and Probability
- Understand measurable attributes of objects and the units, systems,
and processes of measurement.
- Develop and evaluate inferences and predictions that are based
Reasoning and Proof
- Solve problems that arise in mathematics and in other contexts.
- Apply and adapt a variety of appropriate strategies to solve problems.
- Make and investigate mathematical conjectures.
- Communicate their mathematical thinking coherently and clearly
to peers, teachers, and others.
- Recognize and apply mathematics in contexts outside of mathematics.
Mathvantage #2: Proportional Reasoning
Space Science Data Center, NASA, fact sheet
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
Per group of 3-4 Students
- One pound package each of white and black beans
- 12 to 15 envelopes or small bags
- Metric ruler (rulers should have millimeter gradations)
- Meter stick
- Exploring Proportions Activity student organizer
- Proportional Reasoning student organizer
- Proportions and Planetary Science student organizer
- Proportions and Physical Anthropology student organizer