# Around a Circle: Measuring a Geometric Figure

Your textbook has many, many problems on finding the measurements of a circle, so I looked for problems that are off the beaten track. The result is an unusual set of applications to the circle, therefore challenging but intriguing, I think, for middle school classes. Let your colleagues know of your own ideas  and comments on this topic. Just add a note below.

Discovering the Value of Pi
Students measure the diameter and circumference of several circles, using a handy applet, record their data and reach conclusions about the ratio of circumference to diameter. A genuine guided exploration!

Windshield Wipers: It’s Raining! Who Sees More? The Driver of the Car or the Truck?
In this activity, students compare the areas cleaned by different wiper designs. An animation shows the movement of the two windshield wipers, each cleaning off a different geometric shape on the window. Students are encouraged to draw the shape cleaned by each wiper and find its area.

The Great Circle
By clicking on two cities on a world globe, students see two line segments connecting the cities, one showing the great circle route (the shortest) and the other showing the route on a flat map. An interesting  and visual application of real-world math.

Three Piece Circle Puzzle
Students create the puzzle themselves, using compasses, and are challenged to find the area of each of the three pieces. You will need to guide your eighth- and ninth-grade students through the given solution.

# Connecting Classrooms, Sharing Real Data

This article first appeared in Beyond Penguins and Polar Bears online magazine April 1, 2008. The article has been modified to include middle school math and science examples. All versions of this article are licensed under a Creative Commons License.

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Collaborative and real-time data projects engage students in collecting and sharing local data; communicating with other students around the world; using and analyzing “pooled” data from web-based databases; and accessing unique, primary source information. Even though there is no substitute for direct experiences and active investigation, extending the realm of inquiry through electronic communications can greatly enrich and extend an inquiry approach to science and math teaching.

These kinds of projects are highly motivating to students because they bring classrooms together from across the country and globe in shared learning experiences. Students are required to go beyond their own experience, to share with others, and to consider alternative points of view. Not only do students share data, they share perspectives and cultures. What could be more exciting?

Some wonderful collaborative and real-time data projects have been available online for years. To get a feel for the breadth of available projects, try a few searches in the Internet Projects Registry from the Global School Network (GSN) and in the KIDPROJ index of projects. You will find lists of projects from around the world that cover many disciplines. You can search for projects specific to your curriculum and students’ age levels and even design, post, and moderate a project that your class and others can join. You can also subscribe to both web sites’ listservs to get e-mail updates on new projects when they are listed.

Featured Projects

K-12: Track Spring’s Journey North
Teachers and students in K-12 classrooms are invited to participate in Journey North’s annual global study of wildlife migration and seasonal change. A free Internet-based citizen science project, Journey North enables students in 11,000 schools to watch the wave of spring as it unfolds. Students monitor migration patterns of monarch butterflies, hummingbirds, whooping cranes, and other animals; the blooming of plants; and changing sunlight, temperatures, and other signs of spring. Students share their local observations with classmates across North America and beyond, and look for patterns on real-time maps. As they put local observations into a global context – and connect with field scientists – participants are better prepared to explore how climate and other factors affect living things.

Each Journey North study features many entry points and resources that address learning standards: Journey North for Kids reading booklets and lessons, stunning photos and video clips, weekly migration updates, interactive maps, instructional units, and compelling migration stories.

Center for Innovation in Engineering and Science Education: Collaborative Projects

Noon Day Project
The goal of the Noon Day Project is to have students measure the circumference of the earth using a method that was first used by Eratosthenes over 2000 years ago. Students at various sites around the world will measure shadows cast by a meter stick and compare their results. From this data students will be able to calculate the circumference of the earth.

International Boiling Point Project
The purpose of this project is to discover which factor in the experiment (room temperature, elevation, volume of water, or heating device) has the greatest influence on boiling point.

Down the Drain
How much water is used in homes everyday? Would you be surprised to learn that according to the USGS the average American uses between 80-100 gallons (approx. 300 – 375 liters) of water per day? Do people in other parts of the world use more or less water than Americans? This collaborative project helps students find out the answers to these questions. By collecting data on water usage from people around the world students will be able to see how their water use compares to others and determine what they might do to use less water.

Center for Innovation in Engineering and Science Education: Real Time Data Projects

Wonderful World of Weather
By using hands-on activities and real-time data investigations, students can develop a basic understanding of how weather can be described in measurable quantities, such as temperature, wind, and precipitation. The real-time data lessons also address topics such as climate, cloud classification, and severe storms. Students use the Weather Underground web site to collect and analyze weather from around the world. Three sets of activities are included: Introductory Activities, Real-Time Data Activities, and Language Arts Activities. A Literature Connection page with selected prose and poetry with a weather or season theme is a part of the site.

Musical Plates
Earthquakes, a scientific and physical phenomenon, affect our lives in many ways. In this project, students use Real-Time earthquake and volcano data from the Internet to explore the relationship between earthquakes, plate tectonics, and volcanoes.

This multidisciplinary Internet-based learning experience has been designed to expose students to real world problem solving through unique uses of instructional technologies. In particular, students will use real time data from the Internet to track a real ship at sea, determine its destination and predict when it will arrive. In addition, they will have the opportunity to monitor the weather conditions at sea and predict when rough weather might impact on the ship’s arrival time. The focus is on math concepts and navigation.

The GLOBE Program
The GLOBE (Global Learning and Observations to Benefit the Environment) Program brings together students, teachers, and scientists from around the world to learn more about the environment. Students use established protocols to collect environmental data locally. The data are shared using a global database to further the understanding of Earth as a system. For a school or classroom to submit data for any of the projects, at least one teacher must be trained in the GLOBE science measurement protocols and education activities by attending a GLOBE Teacher Workshop.

However, data from around the world has been archived since 1995 and can be accessed and downloaded by country, state, or region, or specific school by anyone. The Teacher’s Guide, which contains hundreds of lessons, protocols, and field guides, is searchable by grade band and concept.

ePals
ePals offers K-12 students and teachers around the world a free and safe environment for building and exchanging knowledge based on protected connectivity tools, evidence-based curricula and authentic, collaborative learning experiences. The ePals Global Learning Community is the largest online community of K-12 learners, enabling more than half a million educators and millions of students across 200 countries and territories to safely connect, exchange ideas, and work together. ePals projects cover the topics of global warming, habitats, maps and others.

# History to Enrich Mathematics Learning!

Although the NCTM Standards do not have student expectations for learning mathematics history, exposure to this history can help students see real-world connections in mathematics.

Approximating Pi
Mathematics and science owe a great deal to Archimedes, including a way to approximate pi. Here is historical information along with an applet to approximate pi using the perimeter lengths of polygons inscribed within and circumscribed around a circle.

The Beginnings of Probability
Teachers can share some of this mathematics history as they work with students to compute probabilities for simple compound events, an NCTM expectation for students in grades 6-8.

The Golden Ratio
This rich site connects linear measurement, ratio and proportion, art, and mathematics history.

Measuring the Circumference of the Earth
This Internet project is hands-on, real-world, and historical. Students join with classes around the world to repeat the experiment of Eratosthenes — measuring the shadow of a meter stick and making calculations to approximate the circumference of Earth.

Pythagorean Puzzle
The Pythagorean theorem is at the intersection of algebra and geometry. At this site, learn about the life of Pythagoras and the development of the Pythagorean theorem. And use an applet to explore the meaning of the most famous equation in algebra.

Manipula Math with Java: Pythagorean Theorem
Here is another applet offering a more sophisticated approach to affirm in a visual way the validity of the Pythagorean theorem.

Tortoise and Hare Race
Uing an applet, students can vary parameters for the race. There is information about Zeno’s paradox along with exploration questions for students that can lead to a discussion about infinity.