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**Earth and space science**

**Mathematics**

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In this lesson, learners will first watch a video about the orbit and formation of the MMS satellites to learn about their flight configuration. After, they will research similar facts about other types of satellites. Next, learners will compute the... (View More) volume of MMS' tetrahedral flight configuration and investigate how the tetrahedral volume changes as the satellites change positions. Finally, they will create a report that outlines their findings. This activity requires student access to internet accessible computers. This is lesson three in the MMS Mission Educator's Instructional Guide, which uses examples from the mission to introduce mathematics (focusing on geometry) in a real-world context. The lessons use the 5E instructional cycle. **Note: MMS launched March 12, 2015. For the latest science and news, visit the MMS Mission Website under Related & Supplemental Resources (right side of this page).** (View Less)

This is an online set of information about astronomical alignments of ancient structures and buildings. Learners will read background information about the alignments to the Sun in such structures as the Great Pyramid, Chichen Itza, and others.... (View More) Next, the site contains 10 short problem sets that involve a variety of math skills, including determining the scale of a photo, measuring and drawing angles, plotting data on a graph, and creating an equation to match a set of data. Each set of problems is contained on one page and all of the sets utilize real-world problems relating to astronomical alignments of ancient structures. Each problem set is flexible and can be used on its own, together with other sets, or together with related lessons and materials selected by the educator. This was originally included as a folder insert for the 2010 Sun-Earth Day. (View Less)

This is a lesson about using the light from the star during an occultation event to identify the atmosphere of a planet. Learners will add and subtract light curves (presented as a series of geometrical shapes) to understand how this could occur.... (View More) The activity is part of Project Spectra, a science and engineering program for middle-high school students, focusing on how light is used to explore the Solar System. (View Less)

Learners will build an open spectrograph to calculate the angle the light is transmitted through a holographic diffraction grating. After finding the desired angles, the students will design their own spectrograph using the information learned. The... (View More) activity is part of Project Spectra, a science and engineering program for middle-high school students, focusing on how light is used to explore the Solar System. (View Less)

This math problem determines the areas of simple and complex planar figures using measurement of mass and proportional constructs. Materials are inexpensive or easily found (poster board, scissors, ruler, sharp pencil, right angle), but also... (View More) requires use of an analytical balance (suggestions are provided for working with less precise weighing tools). This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications. (View Less)

In a mechanical demonstration of the Pythagorean theorem, this example provides a practical, hands-on method for deriving square roots using a carpenter's square. This resource is from PUMAS - Practical Uses of Math and Science - a collection of... (View More) brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications. (View Less)

Mathematicians often argue that anything which can be represented numerically or algebraically can also be represented geometrically. This is perhaps true even to the extent that simple numeric calculations can be demonstrated geometrically. This... (View More) example illustrates one such geometric process of addition. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications. (View Less)

This article is about the isoperimetric theorem. It states the theorem, explains its history and uses examples and exercises to demonstrate it. The resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created... (View More) by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications. (View Less)

This math problem demonstrates the concept of geometric progression, through an example of a million dollar contract between an employee and an employer. Application of the concept of geometric progression to social cause activism is addressed. This... (View More) resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications. (View Less)