You can get Google to give its assessment of a site’s readability, using a basic-intermediate-advanced scale, but for more granularity, you can use an online utilities like this Readability Calculator.

This recent post, for example, can be comprehended by students somewhere within the 8th and 12th grades.

Citing this post: Urbano, L., 2012. Readability, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in Language Arts, Useful websitesNo Comments » - Tags: online applications, readability

HINT.FM has an amazing animation of winds over the U.S.. A major part of the awesomeness is that it’s updated hourly from the National Weather Service’s weather database, which has an awful lot of excellent data available.

Citing this post: Urbano, L., 2012. Wind Patterns (for the U.S.), Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in Natural World, Useful websitesNo Comments » - Tags: climate, scientific visualizations, visualizations, weather, wind

So that my students could more easily check their answers graphically, I put together a page with a more complete analysis of parabolas (click this link for more details).

Analyzing Parabolas

Standard Form	Vertex Form
y = a x2 + b x + c	y = a (x - h)2 + k
y = x2 + x +	y = ( x - ) 2 +

Intercepts:	Vertex:
Focus:	Directrix:	Axis:

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Solution by Factoring:

y = x² x

Converting the forms

The key relationships are the ones to convert from the standard form of the parabolic equation:

(1)

to the vertex form:

(2)

If you multiply out the vertex equation form you get:

y = a x2 - 2ah x + ah2 + k

(3)

When you compare this equation to the standard form of the equation (Equation 1), if you look at the coefficients and the constants, you can see that:

To convert from the vertex to the standard form use:

		(4)
		(5)
		(6)

Going the other way,

To convert from the standard to the vertex form of parabolic equations use:

		(7)
		(8)
		(9)

Although it is sometimes convenient to let k not depend on coefficients from its own equation:

(10)

The Vertex and the Axis

The nice thing about the vertex form of the equation of the parabola is that if you want the find the coordinates of the vertex of the parabola, they're right there in the equation.

Specifically, the vertex is located at the point:

(11)

The axis of the parabola is the vertical line going through the vertex, so:

The equation for the axis of a parabola is:

(12)

Focus and Directrix

Finally, it's important to note that the distance (d) from the vertex of the parabola to its focus is given by:

(13)

Which you can just add d on to the coordinates of the vertex (Equation 11) to get the location of the focus.

(14)

The directrix is just the opposite, vertical distance away, so the equation for the directrix is the equation of the horizontal line at:

(15)

References

There are already some excellent parabola references out there including:

• Wonderful interactive graphs by Murray Bourne.
• Nice simple explanations of the different forms of the equations.
• More complex explanations from Wolfram Alpha.

Citing this post: Urbano, L., 2012. Everything You (N)ever Wanted to Know About Parabolas, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in Algebra, Mathematics, Technology, Useful websitesNo Comments » - Tags: algebra, graphs, html5, interactive posts, interactive websites, math

I needed a little icon of flames to show the methane from the landfill being burned for heat. So I googled, "svg flames" and ran into the free svg blog. Their svg images are aimed at scrapbookers, but they've got some good ones, and they're free.

Citing this post: Urbano, L., 2011. Free SVGs, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in Useful websitesNo Comments » - Tags: online resources, svg

Cahokia's just one of almost a thousand sites around the world that UNESCO considers to form, "part of the cultural and natural heritage" of the world that has "outstanding universal value." It's a remarkable selection of places, from natural geological wonders like the Grand Canyon, to biological preserves like Peru's Manú National Park, to cultural landscapes like that of Bam, Iran. The long, detailed descriptions of the importance of these sites makes the World Heritage List website is a remarkable resource for cultural and physical geography.

Citing this post: Urbano, L., 2011. Places to Visit, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in Natural World, Social World, Useful websitesNo Comments » - Tags: geography, human geography, online resources, physical geography

Maggie E. has a wonderful eye for spotting small fauna. She found this mason wasp (Monobia quadridens) while we were weeding the Heifer Ranch's herb garden. It had caught this caterpillar and was trying to take off with it. It was a difficult job - the caterpillar probably weighed as much as the wasp - but it finally managed to take it away. According to the Atlas of Vespidae, these wasps prey on small moth caterpillars. Which is probably why they are usually found in open habitats with flowers; hence the herb garden. They also use caterpillars to feed their larvae (Wikipedia, 2011). They'll lay an egg in a cell of their nest and stick a paralyzed beetle larvae, spider or caterpillar in with the egg to feed the wasp larvae when it hatches.

References

Identifying these wasps was not too hard. The first image in the google search for "wasp caterpillar" looked just like the bug we found, carrying almost the same type of caterpillar. The image was from the wonderful "What is that bug?" where you can send in bug pictures and the author (Daniel Marlos) will try to identify them. What's That Bug referenced the BugGuide which gives the full taxonomic classification and a lot of information about habitat, food and life cycle that's in an easily readable form. The BugGuide, in turn, cites some of the more serious resources - books and such. But it turns out that an excellent reference for the wasps (Vespidae) of northern and eastern North America is available online. It's the Identification Atlas of the Vespidae (Hymenoptera, Aculeata) of the northeastern Nearctic region (Buck et al., 2008). The Atlas is hosted on another excellent resource, the Canadian Journal of Arthropod Identification, which is a web-based journal dedicated to documenting Canadian arthropods.

Citing this post: Urbano, L., 2011. A Wasp and its Prey, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in Biology, immersion, Natural World, Useful websitesNo Comments » - Tags: biology, heifer immersion, immersion, insecta, insects, my art photos, photography

Want to find your nearest superfund site? The EPA has an interactive page called, Clean Up My Community, that maps brownfields, hazardous waste, and superfund sites anywhere in the U.S. Note:

• Brownfields are places, usually in cities, that can't be easily re-developed because there's some existing pollution on the site.
• Superfund sites are places where there is hazardous pollution that the government is cleaning up because the companies that caused the pollution have gone out of business, or because the government caused the pollution in the first place. The military is probably the biggest source of government pollution, particularly from fuel leaks and radioactive waste.

Citing this post: Urbano, L., 2011. Superfund Sites in Your Area - And Other Environmental Cleanups in Your Community, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in Chemistry, Natural World, Useful websitesNo Comments » - Tags: environment, epa, pollution, project-based learning, real data, real data source

Molecular models tend to fascinate. As a introduction to the chemistry of elements, students seem to like putting them together, and they tend to enjoy finding out what their molecules are called. You can't beat fitting together molecules by hand as a learning experience, but 3Dchem has a nice collection of interactive, three-dimensional molecules, including molecules of the month. They also have three-dimensional periodic tables showing the sizes of the atoms in the traditional tabular form as well as a spiral.

Citing this post: Urbano, L., 2011. 3d Molecule of the Month, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in Chemistry, Natural World, Useful websitesNo Comments » - Tags: 3d models, interactive websites, molecules, periodic table