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**Earth and space science**

**Mathematics**

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This is a set of one-page problems about the scale of objects in images returned by spacecraft. Learners will measure scaled drawings using high-resolution images of the lunar and martian surfaces. Options are presented so that students may learn... (View More) about the Lunar Reconnaissance Orbiter (LRO) mission through a NASA press release or by viewing a NASA eClips™ video [4 min]. Common Core State Standards for Mathematics and English Language Arts are identified. This activity is part of the Space Math multi-media modules that integrate NASA press releases, NASA archival video, and mathematics problems targeted at specific math standards commonly encountered in middle school. (View Less)

This is a set of one-page problems about calculating the volume of objects. Learners may calculate the volume of an asteroid, Vesta, or the stacking of satellites inside an atlas V rocket nose cone. Options are presented so that students may learn... (View More) about the Dawn mission to asteroid Vesta through a NASA press release or about NASA's investigation of comets by viewing a NASA eClips™ video [5 min]. Common Core State Standards for Mathematics and English Language Arts are identified. This activity is part of the Space Math multi-media modules that integrate NASA press releases, NASA archival video, and mathematics problems targeted at specific math standards commonly encountered in middle school. (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 math-science integrated unit about spectrographs. Learners will find and calculate the angle that light is transmitted through a holographic diffraction grating using trigonometry. After finding this angle, the students will build their... (View More) own spectrographs in groups and research and design a ground or space-based mission using their creation. After the project is complete, student groups will present to the class on their trials, tribulations, and findings during this process. 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)

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 this activity, learners draw a circle with a single focus, an ellipse with two foci close together, and an ellipse with two foci far apart, and compare the shapes. Learners then measure the Sun in four images each taken in a different season,... (View More) comparing the apparent size of the Sun in each image to determine when Earth is closest to the Sun. This is the second activity in the SDO Secondary Learning Unit. The activity is reprinted with permission from the Great Explorations in Math and Science (GEMS). (View Less)

Math skills are applied throughout this investigation of windows. Starting with basic window shapes, students determine area and complete a cost analysis, then do the same for windows of unconventional shapes. Students will examine photographs taken... (View More) by astronauts through windows on the Space Shuttle and International Space Station to explore the inverse relationship between lens size and area covered. This lesson is part of the Expedition Earth and Beyond Education Program. (View Less)

This is a book containing over 200 problems spanning over 70 specific topic areas covered in a typical Algebra II course. Learners can encounter a selection of application problems featuring astronomy, earth science and space exploration, often with... (View More) more than one example in a specific category. Learners will use mathematics to explore science topics related to a wide variety of NASA science and space exploration endeavors. Each problem or problem set is introduced with a brief paragraph about the underlying science, written in a simplified, non-technical jargon where possible. Problems are often presented as a multi-step or multi-part activities. This book can be found on the Space Math@NASA website. (View Less)