## Lesson Plans: Time that Star!

# Time that Star!

**Suggested grade levels**: 7-12

**Estimated class time**: 2-3 class periods

*Lesson plan by Kara C. Granger of Maria Carillo High School in Santa
Rosa, CA*

## Summary

This lesson examines the idea of periodic behavior and how it is determined from a set of data. The students will examine this concept through a hands-on lab that involves a simple, student-made pendulum which is followed up with critical thinking and performance assessment style questions. Students will also analyze data received from high-energy satellites of various binary star systems' orbital periods or stellar rotation periods.

## Objectives

- Students will recognize a periodicity within a set of data.
- Students will learn how to complete and apply the method of Folding to finding the period of the periodicity.
- Students will apply the method of Folding to determine the periodicity of pendulums, sample data, and orbits of binary star systems.
- Students will learn an appreciation for basic astronomy and astrophysics through the exposure of such topics embedded in this lesson.

## National Education Standards

**National Science Education Standards**

This lesson plan addresses the following National Science Education Standards:

**NS.5-8.1 Science as Inquiry**

As a result of activities in grades 5-8, all students should develop:

- Abilities necessary to do scientific inquiry
- Understandings about scientific inquiry

**NS.5-8.2 Physical Science**

As a result of their activities in grades 5-8, all students should develop an understanding:

- Motions and forces
- Transfer of energy

**NS.9-12.1 Science as Inquiry**

As a result of activities in grades 5-8, all students should develop:

- Abilities necessary to do scientific inquiry
- Understandings about scientific inquiry

**NS.9-12.2 Physical Science**

As a result of their activities in grades 9-12, all students should develop an understanding of:

- Motions and forces
- Conservation of energy and increase in disorder

**NS.9-12.4 Earth and Space Science**

As a result of activities in grades 5-8, all students should develop an understanding of:

- Origin and evolution of the universe

**National Council of Teachers of Mathematics**

This lesson plan addresses the following educational standards from the National Council of Teachers of Mathemantics:

- Process Standards
**Problem Solving**

Instructional programs from prekindergarten through grade 12 should enable all students to:- Build new mathematical knowledge through problem solving
- Solve problems that arise in mathematics and in other contexts

**Connections**

Instructional programs from prekindergarten through grade 12 should enable all students to:- Recognize and apply mathematics in contexts outside of mathematics

- Algebra
**Understand patterns, relations, and functions**

In grades 6-8 all students should:- represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules

- generalize patterns using explicitly defined and recursively defined functions
- interpret representations of functions of two variables

**Represent and analyze mathematical situations and structures using algebraic symbols**

In grades 6-8 all students should:- use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships

- use symbolic algebra to represent and explain mathematical relationships

**Use mathematical models to represent and understand quantitative relationships**

In grades 6-8 all students should:- model and solve contextualized problems using various representations, such as graphs, tables, and equations

- Data Analysis
**Select and use appropriate statistical methods to analyze data**

In grades 6-8 all students should:- b. discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots

**Formulate questions that can be addressed with data and collect, organize and display relevant date to answer them**

In grades 9-12 all students should:- understand histograms, parallel box plots, and scatterplots and use them to display data

## Prerequisites

- Students should know how to graph/plot data and determine the mean from a set of data.
- Students should have been exposed to a variety of astronomy and astrophysical concepts, such as those discussed in the Science section of the Imagine the Universe! Web site. Information in the Introduction section of this lesson's Day 2 can also be used.

## Procedure

This lesson has been developed as a multi-day plan. Each lesson day has been designed to take approximately an hour to complete. The lesson is broken down as follows:

- Day 1: Students complete a hands-on lab involving a pendulum and recognition of periodic behavior
- Day 2: Students apply the method of Folding to determine a period in sample data and from actual satellite data
- Enrichment: Day 2 includes an optional enrichment where students learn and apply the chi-square test to determine the period in a set of data

### Get started on Day 1!

## References

- Kaufmann, William J. III,
*Universe*, Freeman and Company, 1994, pgs. 336-435 - Kerrod, Robin,
*Encyclopedia of Science: The Heavens Stars, Galaxies, and the Solar System*, Macmillan Publishing Company, 1991 - Kondo, Herbert,
*The New Book of Popular Science Vol. 1*, Grolier Incorporated, 1982, pgs. 174-205 - Sanford, Peter W. and Salton, Jane and Laskarides, Paul,
*Galactic X-ray Sources*, John Wiley and Sons, 1982 pgs. 161-162 - Seward, Frederick D. and Charles, Philip A.,
*Exploring the X-ray Universe*, Cambridge University Press, 1995

Data used in this lesson were retrieved from the HEASARC Data Archive.