This course was developed to satisfy the California Commission of Teaching credentialing requirements for teacher candidates. The class provides opportunities for candidates to learn how to teach the basic and essential fundamentals of physical education for K-6th grade students. The central knowledge is about children’s motor skill development along with the emotional and social aspects related to physical activity. Teachers will learn the key aspects of a physical education lesson, which include a warm-up activity, the lesson plan (skill development and game applications), and closure. As a total lesson, at least half the time is spent in moderate to vigorous activity.

The course also addresses classroom management techniques, safety and liability, kinesiology, and instructional techniques. It incorporates discussions of multicultural aspects and special needs populations, and concludes with ideas for integrating physical education with academic subjects such as mathematics, language, and natural and social sciences.

In the first video segment, we analyze the population dynamics for a test-tube of cells that affect each others' likelihoods of replication when they collide. The particular example we use is a prisoner's dilemma, which has the almost paradoxical property that survival of the relatively most fit leads overall fitness to decrease. In the second video segment, we suggest that the population dynamics from the first segment can be related to an analysis that uses payoff matrices found in traditional game theory.

This lesson provides simple activities for younger children to explore balance. Students will demonstrate spatial awareness and the ability to follow instructions. They will experience different movement forms.

Design a scavenger hunt for a family hike. Activity from Weekly STEM in a Bag. Colorado Americorp agents in Araphahoe, Denver, Garfield, Larimer, and Weld Counties. Work supported by the Corporation for National and Community Service under Americorps grant number 18AFHCO0010008. Opinions or points of view expressed in this lesson are those of the authors and do not necessarily represent the official position of or a position that is endorsed by the Corporation or the Americorps program. This resource is also available in Spanish in the linked file.

In this video segment from Cyberchase, Harry decides to train as a firefighter and uses line graphs to chart his physical fitness progress.

Western Mining History presents and article from the Colorado Springs Gazette from September 14, 1878 detailing a road trip through southwestern Colorado. This is a first hand account of the journey. Western Mining History is an historical site that provides databases, information on mining, mining towns, gold and Photos and maps of the western United States. Consider becoming a member or making a donation to help further the work of the site.

This activity engages learners in examining data pertaining to the disappearing glaciers in Glacier National Park. After calculating percentage change of the number of glaciers from 1850 (150) to 1968 (50) and 2009 (26), students move on to the main glacier-monitoring content of the module--area vs. time data for the Grinnell Glacier, one of 26 glaciers that remain in the park. Using a second-order polynomial (quadratic function) fitted to the data, they extrapolate to estimate when there will be no Grinnell Glacier remaining (illustrating the relevance of the question mark in the title of the module).

Western Mining History presents history of freight hauling and supply delivery to early western mining towns. Western Mining History is an historical site that provides databases, information on mining, mining towns, gold and Photos and maps of the western United States. This photo gallery provide an excellent collection of primary sources for historical analysis in the classroom. Consider becoming a member or making a donation to help further the work of the site. Suggested use: Students might compare modern day transportation to the methods of freight transportation used to bring supplies to early mining towns.

Students learn about weight and drag forces by making paper helicopters and measuring how adding more weight affects the time it takes for the helicopters to fall to the ground.

In this lesson and its associated activity, students conduct a simple test to determine how many drops of each of three liquids can be placed on a penny before spilling over. The three liquids are water, rubbing alcohol, and vegetable oil; because of their different surface tensions, more water can be piled on top of a penny than either of the other two liquids. However, this is not the main point of the activity. Instead, students are asked to come up with an explanation for their observations about the different amounts of liquids a penny can hold. In other words, they are asked to make hypotheses that explain their observations, and because middle school students are not likely to have prior knowledge of the property of surface tension, their hypotheses are not likely to include this idea. Then they are asked to come up with ways to test their hypotheses, although they do not need to actually test their hypotheses. The important points for students to realize are that 1) the tests they devise must fit their hypotheses, and 2) the hypotheses they come up with must be testable in order to be useful.

Objectives
-Demonstrate to students the enormous amount of produce that is wasted daily because they do not fit the aesthetic criteria of producers, retailers, and consumers.
-Show students that fruits and vegetables that do not look “perfect” taste the same as ones you find in the store.

I usually begin with a story about lying on a cot looking up at the stars on a dark night in the mountains, seeing countless stars and the hazy Milky Way stretching across the sky. I talk about how they seem to be part of a celestial dome rising very high above me, and I note that I do not have any way to know, as I am looking at the stars above me, how far they are away from me. I talk about how ancient people used and envisioned the stars. I mention the experiment with the Hubble Space Telescope in which the "darkest" and most empty part of space was imaged, and found to contain countless distant galaxies (search on "Hubble deep field" or go to http://www.stsci.edu/ftp/science/hdf/hdf.html).
I mention that this often leads people to consider how insignificant they are in the scheme of things. My feeling is that you are only as significant (or insignificant) as your actions make you.
I then talk a bit about how we now know that "visible" matter is organized into atoms, which are very, very small. In a way, they are like the stars in that they seem to be incomprehensibly small, while stars seem to be incomprehensibly large and distant. I then pose the question, "How does the part of this world that we observe and experience on a daily basis fit into a physical reality that spans from the incomprehensibly small to the incomprehensibly large?"
I pass-out the blank worksheet "Comparison of Lengths Relevant to Our Universe" to every student, and have them organize into groups of 2-3. The task is to fill-in the exponents corresponding to 9 distances listed in a box on the page, and to locate those distances on the logarithmic scale. I give them a couple of minutes to start working with the page, and then interrupt to ask what they need help with. This usually involves determining one of the lengths involving light years on the board. I let them complete the tasks in their small groups, then I ask group representatives to call-out their results.
Working from a set of correct answers, we then discuss the scale. For example, we note that there is a greater difference (in orders of magnitude) between the size of a proton or electron versus the size of a hydrogen atom, and the height of a person and the peak elevation of Mt. Everest. It is usually noted that humans fall near the middle of the length spectrum of the universe, which was also noted by Primack and Abrams (2006). Some students place great importance on this. I tend to note that there is a practical limitation to the size of individual cells that will have predictable functions (they need to be larger than the length scale governed by quantum mechanics) and constraints on the upper size limit of organisms made of cells, which determines where we are on the scale.

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Western Mining History presents Historical|Photographs of Colorado mining towns and mines. Western Mining History is an historical site that provides databases, information on mining, mining towns, gold and Photos and maps of the western United States. This photo gallery provide an excellent collection of primary sources for historical analysis in the classroom. Consider becoming a member or making a donation to help further the work of the site. Suggested use: Students might do a "then/now" comparison of well known towns, analyze the photos for historical details, consider the working conditions for the miners and/or environmental impact of early mines.

This course provides a study of fitness and wellness and their relationship to a healthy lifestyle. Defines fitness and wellness, evaluates the student's level of fitness and wellness, and motivates the student to incorporate physical fitness and wellness into daily living.

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In this learning activity, students analyze an actual dataset of the influence of temperature on tree growth. They use mathematical and statistical concepts like slope equations and lines of best fit to determine the relationship. They are then asked to make predictions about future tree growth under different greenhouse gas emissions, interpreting data from climate models to make these predictions.

Students observe capillary action in glass tubes of varying sizes. Then they use the capillary action to calculate the surface tension in each tube. They find the average surface tensions and calculate the statistical errors.

Using the LEGO MINDSTORMS(TM) NXT kit, students construct experiments to measure the time it takes a free falling body to travel a specified distance. Students use the touch sensor, rotational sensor, and the NXT brick to measure the time of flight for the falling object at different release heights. After the object is released from its holder and travels a specified distance, a touch sensor is triggered and time of object's descent from release to impact at touch sensor is recorded and displayed on the screen of the NXT. Students calculate the average velocity of the falling object from each point of release, and construct a graph of average velocity versus time. They also create a best fit line for the graph using spreadsheet software. Students use the slope of the best fit line to determine their experimental g value and compare this to the standard value of g.

Show Caption
Hide This diagram shows the relationship of Gibbs Free Energy to composition. In this diagram there are two minima represented for free energy which is achieved by unmixing of two distinct phases each with definite composition. The dashed line, which is tangential to the two minima in the free energy curves, gives the composition of the coexisting minerals at a specific temperature. From: Klein, C., and Dutrow, B., Manual of Mineral Science, 23rd ed., J. Wiley and Sons. Used with permission. The phenomenon of solid solution is common in many rock-forming minerals. At high temperatures, thermal vibrations permit accomodation of ions with size differences on the order of 15-30%. However, as physical conditions change, ions no longer fit into similar sites which creates internal (lattice) strain energy. Consequently, the mineral composition must adjust to relieve this strain energy and minimize the Gibbs Free Energy of the system. One possible response of the system is for elements in a crystal to move from one chemical site to another via intracrystalline diffusion. This results in segregated domains that are enriched in one element or another--this is a process called exsolution.
A good example of this process can be seen in the alkali feldspar mineral group. At high temperature the mineral anorthoclase (K,Na)AlSi3O8 shows complete solid solution, i.e. there is a random distribution of K and Na in the alkali sites of the crystal. Upon cooling, Na and K segregate into more ordered domains creating areas that are rich in albite NaAl Si3O8 and microcline KAlSi3O8(see Figure 1).
The purpose of this exercise is to provide a number of activities to demonstrate how exsolution works and to demonstrate complex-system behavior in this relatively common natural phenomenon.

Part I: Images of naturally occurring perthite.
The following images show minerals that have undergone exsolution at different scales. The image on the top left shows exsolution as viewed with a Transmission Electron Microscope (TEM; field of view is 10 microns). The image on the top right is a photomicrograph of exsolution in microcline as seen in thin section (cross-polarized light, field of view is 2 mm). The picture on the bottom left is a hand sample of perthitic microcline as seen in hand sample (field of view is 10 cm). The picture on the bottom right is a picture of plagioclase feldspar showing the "schiller" effect. This is caused by sub-microscopic unmixing of two distinct plagioclase phases in the compositional range of labradorite (An50 - An70) which results in the beautiful play of colors seen in this photo; (field of view of 20 centimeters). This series of pictures is a good example of scale invariance of this physical phenomenon.
Examine perthite textures from hand samples and thin sections from your own mineralogy collection. We can easily envision unmixing of two immiscible fluids--for example oil and vinegar salad dressing. The same thing happens when we unmix (i.e. exsolve) solid phases--the process just takes a bit longer as atoms have to migrate in the crystal lattice by intracrystalline diffusion! How can such a common feature as perthite be understood in terms of complex-system behavior?

Exsolution observed on a sub-microscopic scale in this TEM picture; this microstructure shows unmixing of labradorite in very fine essentially parallel lamellae. From Champness, P.E., and G.W Lorimer, 1976. Exsolution in silicates. Chapter 4.1 in Electron Microscopy in Mineralogy. H.R. Wenk, ed. Springer-Verlag, New York. Field of view is 10 microns.

Perthite observed in thin section. Field of view is 2 mm.

Perthite observed in hand sample. Field of View is 10 cm.

Unmixing of parallel lamellae, as observed in a hand specimen of labradorite from Madagascar. These lamellae act as diffraction grating for white light, producing spectral colors known as labradorescence or the "schiller effect"; the field of view is 20 cm. Photo by B. Dutrow; used by permission.]

Part II: Exsolution Puzzle Exercise.
This exercise is done in groups of 2-3 students. Coins are initially randomly distributed on a chessboard, and are then subsequently moved to create domains of increasing order (regions that are dominated by either pennies or nickels). This is a kinesthetic learning exercise that creates a physical model that simulates how the exsolution process works. (Inspired by Greg Marfleet, Carleton College)

Randomly distribute 20 pennies and 20 nickels on the attached 7x7 chessboard (Microsoft Word 33kB Dec1 10). The random distribution of pennies and nickels is analogous to the random distribution of Na and K in the high temperature alkali feldspar, anorthosite. (See Figure 1)
The goal is to have a given coin completely surrounded by similar neighbors (i.e. 8 nearest neighbors of the same type of coin located on adjacent edges and the diagonal squares. Each student will sequentially move a coin into an adjacent open position (horizontal, vertical and diagonal moves are allowed) to achieve this desired configuration. Perfect ordering of nickels and pennies into discrete domains is analogous to perfectly ordered crystals of albite and microcline. [NOTE: in this exercise we are modeling the diffusivity of only the alkali elements, Na and K. The ordering of Si and Al in the tetrahedral sites of a feldspar crystal is a related, but entirely different process].
Systems tend to minimize Gibbs Free Energy (see Figure 2) on their way towards a state of equilibrium. In this example, the surface area surrounding domains of the segregated compositions (nickels/Na and pennies/potassium) is proportional to the excess Gibbs Free Energy of those domains. As clusters of similar coins evolve (segregate) and get bigger, the bounding surface areas are minimized and the energetics of the system are decreased.

INSTRUCTIONS

For the initial random state, determine the area surrounding each type of element; do this by assuming the unit length along each edge is 1 and add all the surfaces surrounding Na/nickel and K/potassium coins or aggregates of coins. Count any edges that are not adjacent to another similar coin (i.e. count all nickel-penny interfaces, and any edge where a nickel or penny is adjacent to an open space. Do not count the external edges on the outer border of the chessboard).
Make 10 moves of the coins (always moving into an adjacent open space either right, left, up, down, or on a diagonal) and again determine the bounding surface areas. Record these surface area values for pennies and nickels. Repeat after 20, 30, 40, 50, and 100 moves.
After each set of moves, report your surface area measurements for both pennies and nickels to your instructor; record these values on a spread sheet for later plotting and analysis.
This part of the exercise should take about 45 minutes to complete the sets of movements and measurement of the surface areas.

Here is an example experiment showing the progressive ordering of pennies (potassium) and nickels (sodium). Show pictures of the 2-D distribution of pennies and nickels after 10,20, 30, 40, 50 and 100 successive moves
Hide

Original random distribution of coins.

Distribution of coins after 10 moves.

Distribution of coins after 20 moves.

Distribution of coins after 30 moves.

Distribution of coins after 40 moves.

Distribution of coins after 50 moves.

Distribution of coins after 100 moves; perfect order.

Plot your results. Assume that each move requires 1 unit of time.

Plot your data on a X-Y plot with surface area on the Y axis and time on the X-axis. What is the distribution of your data? (Try plotting data for pennies, nickels, their sum, and their averages). Create a "best fit" curve through the data as plotted on this X-Y diagram (easily done with functions programmed into Excel). . What type of mathematical function is represented by a curve that has a steep slope to begin (left side of the plot), and becomes asymptotic to the X-axis away from the origin? Did you notice that the first set of coin moves produced the largest change in surface area, and that subsequent sets of moves produced smaller and smaller changes to the surface area?
Have you seen other plots with similar profiles from your other studies in Earth Science?
Show Answer:
Hide radioactive decay; longitudinal profile of rivers.... It appears that many processes in Earth Science may follow the same mathematical laws.
Now plot your data on a log-log plot with surface area on the ordinate (Y-axis) and time on the abscissa (X-axis). Create a "best fit" curve through these data (easily done with functions programmed into Excel). What is the shape of this curve? Does this relationship demonstrate a) an exponential function? b) a power law?
Here is an example dataset (Excel 74kB Dec1 10) for 12 experiments completed by the spring 2010 Mineralogy class at Montana State University. Raw data and corresponding graphs are presented in the attached spreadsheet file. Compare your results with those shown in this example exercise.

Intracrystalline Diffusion and Fick's Law
The rate of transport of mass (and energy) through a fixed medium can be described mathematically by Fick's Law of Diffusion. Show details about Fick's Law of Diffusion
Hide.
The fundamental expression of Fick's First Law of Diffusion can be written as:

J = -D( -- c/ -- x)

Jis the flux of a material along a compositional gradient (e.g. mol / length2time1 ), the amount of material (e.g. atoms or moles) that will flow through a small area during a fixed time interval.
Dis the diffusion coefficient (length2 time -1);
c is the concentration (amount of material per volume, mol/m3), and
x is the length (m)
Fick's Law shows that the flux of an ion diffusing through a stationary medium (like the crystalline lattice in our example) is proportional to the concentration gradient ( -- c/ -- x). As diffusion proceeds, the concentration is always changing, and thus, the flux is always changing. Can you see why this process exhibits non-linear behavior and must be represented as a power law?
Note that The diffusivity, D, scales with temperature:

D ~ (kT/h) exp(-Q*/RT)

where k is Boltzmann's constant, h is Planck's constant, and Q* is an activation energy. This means that the rate of diffusion decreases with temperature. Consequently, exsolution will ultimately grind to a halt as temperature decreases. This is why we can observe perthite development in alkali feldspars in a wide variety of igneous and metamorphic rocks...the perthite texture gives us information about the cooling history of the mineral up to a point, but then exsolution will slow to a stop and the perthite will continue to exist in a metastable state at the surface of the earth.
Different types of diffusion pathways include: intragranular (volume) diffusion, grain boundary diffusion, diffusion in a bulk fluid, and diffusion related to crystal defects. In our example of perthite exsolution, intragranular (volume) diffusion is the operative process. This process is most effective at high temperatures.

Note that generally material tends to move in a direction from high to low concentrations, and thus, compositional gradients tend to be minimized by diffusion. However, in the case of exsolution and perthite development during cooling of a high-temperature, homogeneous alkali feldspar (anorthite), just the opposite effect happens--segregated domains of albite and microcline become more stable at lower temperatures. Why is this the case? The answer lies in the overall energetics of the system. It turns out that lattice strain that is induced upon cooling of anorthite results in large excess energy in the system. To minimize this excess energy, a single homogeneous grain of anorthite (stable at high temperature), will undergo "spinodal" decomposition upon cooling. This results in two energy minima, one for each phase, as illustrated in Figure 2. Upon further cooling, these energy minima continue to separate, thus resulting in two stable phases whose compositions increasingly approach the end member compositions of albite and microcline. A more complete description of this process can be found in Chapters 5 and 7 of Putnis A. and McConnell J.D.C. Principles of Mineral Behaviour 258pp. Blackwell Scientific Publications. Oxford. 1980.
Part III: Computer Simulation

Model output from the NetLogo "segregation"program; 2000 objects achieved 70% similarity.The computer program NetLogo can be used to model complex system behavior. This computer program was developed by Uri Wilensky (1999) at the Center for Connected Learning and Computer-Based Modeling, Northwestern University. Evanston, IL. For this exercise, we will use the pre-programmed function for Segregation

Experiment with this program by changing the input parameters to try to reproduce a) the pattern you developed in the puzzle model above, and b) perthite patterns observed in the natural microcline crystals.

Part IV: Visualization of the Development of Exsolution

The binary solvus phase diagram for the alkali feldspar system at low pressure. Figure provided by Dexter Perkins, used with permission.The binary "solvus" phase diagram (showing the relation of temperature to composition) is typically used to show the phase relations for alkali feldspars. A single homogeneous alkali feldspar occurs at high temperatures (Figure 1a), but as the system cools eventually the phase boundary (solvus) is intersected and the exsolution (unmixing) process begins. "Underneath" the solvus a single feldspar is no longer thermodynamically stable, and the system begins to separate into two phases that become increasingly Na-rich or K-rich upon further cooling. This visualization demonstrates the cooling history of an alkali feldspar, including use of the "lever rule" to calculate phase composition (mineral) and relative proportions. Examine the accompanying illustrations and track the "state" of the system as temperature changes. Binary Solvus for the Alkali Feldspar System. The accompanying illustrations on the right show the "state of the system" in terms of the relative proportions of the phases present for each assigned temperature.
Relate these products and processes to natural occurrences of perthite, and think about the changes that have to take place on the atomic scale to produce the mesoscopic features that are visible in hand samples.

Part V: Thought Questions

Driving forces: in equilibrium thermodynamics, the system always drives towards the lowest Gibbs Free Energy. At equilibrium, chemical potential is zero. This typically means there are no compositional gradients. Why does this system drive towards segregated domains that are rich in Na and K?
Consider entropy "in the system". What do we mean by "the system"?
Refer to Ilya Prigogine's (winner of the 1977 Nobel Prize for Chemistry) classic work on this subject: Order out of Chaos, Man's New Dialogue with Nature (1984, Bantam Books, 394 pp.)

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