Geometry seems to be one of those topics that some students easily understand, while others struggle with even basic Geometry concepts. This is because Geometry is an area of mathematics that can feel very abstract and strange for many students. It is one of the first subjects that integrate numbers and calculations with the real world, and that's not always an easy concept to understand.
Thankfully, there are online resources that can help any math teacher better explain Geometry concepts. One of those sites is a relatively new website called the Math Open Reference.
While the website may eventually include other mathematics topics and information, it currently is limited to different areas of Geometry, including Plane Geometry, Coordinate Geometry and Solid Geometry. The website even includes interactive graphics and valuable tools for solving complex problems.
Math Open Reference Main Page
The main page of the Math Open Reference lists every area of the website organized by the Geometry area of study, as well as a section devoted to interactive tools that Geometry students can use to better understand different Geometry principles.
While a Geometry book may be enough for some students, other students require this extra instruction and material to better comprehend many of the more advanced concepts found in this field. While the site name is a bit of a misnomer (it isn't quite a "full" math reference site), it does at least serve as a valuable reference site for students that are studying Geometry.
Principles Explained with Clear Graphics
Just about every page that you find on this website features not only well-written, simple explanations, but you'll also notice that those explanations are well supported by imagery and illustrations. Illustrations are important for students that are more visual in how they learn complicated information. Clear definitions are good, but as the saying goes, "A picture is worth a thousand words." That is especially true in the field of geometry.
If you spend time in a classroom with an especially effective, experienced teacher, you'll notice that many of the activities and lessons that the teacher provides to students offer an element of "hands-on" learning.
Experienced teachers recognize that in order for students to truly appreciate a concept, you need to get them involved in a way that goes beyond just reading words. Math Open Reference takes the same approach in a majority of the educational articles you'll find on this site, such as the article above on Congruent Triangles, where students can manipulate both triangles to see what makes two triangles congruent.
You'll find this to be the case in a majority of the articles at this site - the majority of them features useful interactive graphics that do an excellent job conveying important concepts, such as the article on Coordinate Geometry.
In this interactive tool, the student can move either point on the line, and the coordinates are displayed at that specific point. This helps students that are new to coordinate geometry better understand how coordinate numbers relate to actual locations within the real world. Many of these tools can also be expanded to fill the whole screen, and you can also print them for your own use, or to use as handouts for students.
Some articles include much larger and more complex Geometry tools, such as the lesson about calculating volume within a cube.
Volume of a Cube
With this particular interactive tool, the student can adjust the overall size of the cube, and then observe how and to what degree changing the overall dimensions of the cube also changes the total volume within the cube as well. For the larger interactive tools like this one, you may notice that it takes a little longer for the java application to load, but as long as you have java installed in your browser, they should all work fine.
In addition to the interactive geometry tools that you'll find on this site, there's also a useful resource page that provides simple blank graph paper in a printable format. The nice thing about this graph is that you can adjust it for the coordinate placement that you're looking for and then print it out using your printer.
This is useful for students that need graph paper for homework assignments, or for teachers that would like to include blank graph paper along with homework assignments. This is a rare resource where you can customize blank graph paper to suit your needs before sending it to the printer.
At Math Open Reference, you'll also find a section devoted to providing useful tools that students can use to solve Geometry problems. Currently, there isn't a very long list of tools available, but the tools that are on the list are well made and very useful for both students and math teachers. One example is the Graphical Function Explorer (GFE).
General Function Explorer
The General Function Explorer is an impressive graphical utility that looks a lot like a standard oscilloscope that you'd find in just about any science lab. However, in this case instead of measuring an electrical signal, the tool accepts mathematical equations and provides the resulting set of data points for that curve. By modifying the sliders, you can alter the values for each variable and watch to see how those changes affect the shape of the curve.
Another similar tool that's available for charting linear functions (equations that use the form y=mx+b) is the Linear Function Explorer.
Linear Function Explorer
Just like the Graphical Function Explorer, the Linear explorer lets the student alter the variables (a and b) within the standard linear equation. Obviously, this is a bit more limited than the other tool, but since linear functions are so common in mathematics, this is actually a fairly useful too.
Yet another useful tool you'll find in the "Tool" section of the website is the "Quadratic Function Explorer". Similar to the Linear Explorer, this analysis tool lets students study the quadratic equation (y-ax^2+bx+c).
Quadratic Function Explorer
This equation is a core area of study at the first levels of Algebra, so this is an important utility to help students understand each element of the equation.
One of the most versatile tools at this website is the scientific calculator. By today's standards, this calculator is more like a standard desktop calculator, because many of the scientific calculators you purchase today have many more features than this one.
The Scientific Calculator
However, for the purpose of performing more complex calculations involving things like tangent, cosine, square root and natural log, this calculator will do the job well. It's a quick utility that students can use while doing their homework, particularly if the computer they're using only has a simple calculator that doesn't have any of those more advanced functions.
Overall, the Math Open Reference does a good job providing instruction about basic Geometry, but it does an even better job providing high-quality interactive tools that teach both Geometry and basic Algebraic concepts.
Math Open Reference has a long way to go before it becomes a leading portal for Math information, but as a side resource for Geometry teachers and students, it is useful and functional.