Vienna University: Differential Geometry and Geometric Structures
Differential Geometry and Geometric Structures is one of six research units which comprise the Institute of Discrete Mathematics and Geometry of the Vienna University of Technology. From this website, visitors can read about members and their research activities and download select publications (in German and English). They have also developed some software, which is in German, for use in geometry courses in Austrian schools. The Picture Gallery offers a collection of world Map Projections creat
Your sense of taste
This brief illustrated resource about the sense of taste is part of a feature that explores how humans experience flavor. The five taste qualities--including umami--are mentioned. The resource also corrects the misconception that humans can only taste certain food qualities at specific regions of the tongue. A set of connected, labeled diagrams of the tongue, taste buds, the brain, and facts about taste are noted in a sidebar. One fact compares the average number of taste buds in humans, chicken
Popping the Kernel : Modeling the States of Matter
Constructing models can help students understand the particulate nature of matter. This article discusses how to use popcorn to engage students in model building and to teach them about the nature of matter.
Air pollution is a growing problem today. This lesson plan is designed to teach students about the problem, its effects on our environment and health and the latest methods designed to combat air pollution. The objectives of this lesson are (1) to define air pollution, (2) to identify major causes of air pollution (e.g., automobiles, burning garbage, electric power plants emissions, industrial boilers and certain consumer products), (3) to identify the effects of air pollution (health effects in
Teacher's guide to the infrared
This is a page from a larger website, Seeing our World Through a Different Light, sponsored in part by NASA. This page contains side by side standard and IR photos to illustrate how IR photos show heat. It describes and compares visible light and infrared light. An explanation, accompanied by photos, of how infrared cameras work is also provided.
Expedition to the Poles
In this lesson students will pretend they have just returned from a year in the Arctic or Antarctic. They will look at Web sites about these regions and expeditions to them, and they will create posters illustrating their experiences. Students will conclude by writing paragraphs explaining what it would be like to visit the polar region that they did not focus on in this lesson. As they complete this activity students will research the characteristics of the polar regions and the things they wou
Biology is the science of life, the branch of the natural sciences that studies living organisms.
BBC historic figures : Isaac Newton
This concise biography includes an image of Newton and related links in the right navigation bar including: one to an article Newton papers revealed; The Newton Project; and to a lengthier biography, Isaac Newton.
Tortoise and Hare Race
users step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence of an infinite sequence of numbers.
Variation about the mean
This workshop session, part of a free online course developed for elementary and middle school teachers, explores the mean in depth. Participants work together to investigate the mean as the balancing point of a data set and come to understand how to measure variation from the mean. Video segments, interactive practice, problem sets, and discussion questions involve participants in active exploration.
This Java applet enables students to create tessellations, which are patterns on a plane that do not overlap. The student selects a hexagon, rectangle, or triangle to distort by dragging edges and the newly formed corners. Users can select colors for the pattern, and a button displays information in a second window. The window lists the coordinates of the vertices, angle measures, side lengths, area, and perimeter for the shape. From the applet page, What, How, and Why buttons open pages that ex
The National Math Trail
The National Math Trail makes available problems created by K-12 students as they explore their communities and ask math questions that relate to their own environments. Teachers submit the problems to the site, along with photos, drawings, sound recordings, and videos. Problems can be accessed through an interactive map of the United States.
Observe solar eclipses
This Earth science animation helps students compare three types of solar eclipses: total, partial, and annular. The introduction explains how the type of eclipse is determined by variations in distance and alignment between the Earth, sun, and moon. The animation follows the events of all three eclipses concurrently. Movie controls allow students to repeat, pause, or step through the animation, which can give students more time to compare the eclipse sequences. Copyright 2005 Eisenhower National
A Maths Dictionary For Kids
An animated, interactive dictionary for students which explains over 400 common mathematical terms in simple language. Includes definitions, animated examples, interactive activities, practice and lots of different calculators.
Early algebra, early arithmetic : class materials
This site contains access to over 50 lessons developed as part of a research project that examines how students develop algebraic thinking. The lessons offer teachers in grades 1-6 and parents ideas for situating arithmetic in the context of algebra. The aim of the lessons is to inspire teachers to try new approaches to teaching mathematics. The first lesson is very detailed and provides an introduction to the concepts in later lessons. The use of lessons in sequential order allows students to s
Helping Children Learn Mathematics
Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how were teaching this discipline. Helping Children Learn Math
Etymologies of Algebra, Geometry, Trigonometry
What are the origins and roots of the words geometry, algebra, and trigonometry?
Ecological Footprint: Only One Planet
This two-minute sound segment discusses the concept of your ecological footprint. This is the amount of nature it takes to support your lifestyle. The speaker explains that if we divide up the total ecologically productive space on the planet by the number of people, what we get is five acres per person. In the United States, on average, we use about twenty-five to thirty acres per person to provide all of our services. This site is from an archive of a daily radio program called Pulse of the Pl
Measurement is best learned through direct applications or as part of other mathematical topics. A measurable attribute of an object is a characteristic that is most readily quantified and compared. Many attributes, such as length, perimeter, area, volume, and angle measure, come from the geometric realm. Other attributes are physical, such as temperature and mass. Still other attributes, such as density, are not readily measurable by direct means.
The life sciences investigate the diversity, complexity, and interconnectedness of life on earth. Students are naturally drawn to examine living things, and as they progress through the grade levels, they become capable of understanding the theories and models that scientists use to explain observations of nature.