When someone mentions the word dilation, what comes to mind? For me, it's what they do to my eyes every time I go to the optometrist. From a math perspective, dilation is a transformation that changes the size of a figure but not the shape. Which explains the eye term. Even more exciting is the connection to art. Like yesterday's video on tessellations, dilation has definite applications in art. For instance, drawing dilations is very similar to perspective in art. All you artists out there check out today's free Geometry video on Dilations. The real world application problem even focuses on enlarging an photo to create a very large painting! With four great lectures on today's video, Professor Burger will walk you through understanding and applying the concept of dilation. Just make sure to click the forward button to the left of the time stamp to move to the next lecture!

# December 2010 Archives

You might not think that math has artistic applications, but you would be wrong. Yesterday we posted a video on symmetry, a concept that comes up in art often. Continuing on the same path, today's free Geometry video is on Tessellations. A tessellation is a repeating pattern that completely covers a plane with no gaps or overlaps. Many of us have seen tessellations in art when viewing work by M.C. Escher. They are also very common in nature, from honeycombs to artichokes. But did you know there are different types of tessellations? There are regular tessellations, which are formed by congruent regular polygons, similar to what you might see with tile walls. Then there are semiregular tessellations, which are formed by two or more different regular polygons, with the same number of each polygon occurring in the same order at every vertex. There are even tessellations that are neither regular nor semiregular. Have no fear; however, as Professor Edward Burger will demonstrate the differences between each and how to identify them over the course of the 4 lectures on today's video. Just make sure you click the forward button to the left of the timestamp to move to the next lecture on the video.

We humans are naturally attracted to symmetry. Many folks are drawn to the harmony and balance that is associated with symmetry. There is even evidence that facial symmetry impacts how attractive one person is to another. But did you know there are different types of symmetry? You've got the basic line symmetry where if you place a line over a figure dividing it in half, one side is a mirror of the other. In addition, there is rotational symmetry, where an object can be rotated and still look the same. And finally, when dealing with three-dimensional shapes, there is plane symmetry where a plane divides the figure into two congruent, reflected halves. Learn all this and more with today's free Geometry video with Professor Edward Burger on Symmetry.

Today's video has 4 lectures on it, so make certain you click the forward button to the left of the time stamp to move to the next lecture.

Spheres are shapes we encounter daily, whether it's kicking a soccer ball or checking a location on a globe. A sphere is a perfectly round, three-dimensional object. Due to its lack of flat sides, we can't compute length times width times height to determine the volume of a sphere. Instead, the formula changes to four-thirds pi r cubed. Yes, our good friend pi has made a comeback in today's free Geometry video on Spheres. In addition to learning about the volume of a sphere, you'll learn how to calculate the surface area of a sphere. Professor Burger also touches on how changing dimensions of a sphere impacts the volume. Then, combining our surface area and volume knowledge, he'll demonstrate how to find both measurements in composite figures. A composite figure is made from two or more geometric figures. Sounds complicated, but it's not so hard once you know the basics.

With 5 lectures, this video is a great tutorial on spheres and a good sample of our Geometry curriculum. Don't forget to click the forward button at the end of each lecture to move to the next one!

We learned about measuring the outside of Prisms and Cylinders in last week's video: Surface Area of Prisms and Cylinders. In today's free Geometry video, Volume of Prisms and Cylinder, it is time to think about what's inside. Volume is basically how much three-dimensional space a substance or shape occupies or contains. Finding the volume of an object requires a simple formula that is the length times the width times the height. Of course, while this is easy with a cube, or a rectangular prism, it starts getting tricky when you move to Cylinders. Professor Burger will help you understand the basics and then encourage you to put your brain to it with a real world example. Whether you are determining how much water is needed to fill a pool, or how much soup can fit in a can, volume is an important concept to learn as it has so many day-to-day applications.

As always, make sure you click the forward button to the left of the time stamp at the end of each lecture. Today's video has 5 lectures and you won't want to miss a minute!

I'm a writer, obviously, and I have always loved writing. My parents owned a typesetting company when I was growing up, and one of my odd jobs was to help out with proofreading. As I continued writing in high school, and eventually college, this skill really paid off. After all, one of the most important steps of writing is proofreading your piece at least once or twice before considering it done. Sometimes it's not even about catching the grammatical errors or misspellings; instead it's about reading over what you wrote to ensure it flows and sounds good. Needless to say, I was taken aback this week when I caught an article about Oregon's decision to allow students to use spell check on state writing tests. Spelling is an important part of the proofreading process, and many students may consider spell check as this final step instead of taking the time to read over their papers. It is possible this decision could lead to worse test scores because some kids could overestimate the power of spell check.

I guess what really bothers me about Oregon's decision is that it places less importance on spelling in a time when spelling needs to be focused upon. Part of me feels the decision makers have never received an email from a teenager. Spelling often gets thrown out the window when writing personal messages, and you are lucky if everything is capitalized properly. With the rise of the Internet and social media as platforms for communication, neither kids nor adults can afford to ignore these rules. Spelling is a core skill needed for writing. If you can't spell, you can't communicate. Have you ever received a serious letter, or maybe a rÃ©sumÃ©, with misspellings in it? I know I have, and my first thought was to discount the writer and not take them nearly as seriously as I would if they had taken the time to check the document first. I have seen people not get jobs because of misspellings. And yet, Oregon, in an attempt to "better assess students' writing skills and focus less on typos" has made a decision that I think will have negative results. The article even points out that the spell check doesn't catch everything, but I would be willing to bet many kids hit that button and accept whatever the spell check spits out. And this is another reason where I have to question this decision. After all, spell check is unreliable. I use it, but I also have the benefit of an editor to read over my work and tell me when I have missed something. I guess I just can't see how we can test a student's ability to write and remove spelling from the equation. What do you think?

Did you know that you could make crystal ornaments and sun catchers out of borax? Definitely some science involved, so check out this easy to do project that uses items most of us have at home.

http://www.naturemoms.com/blog/2010/12/05/how-to-make-borax-crystal-ornaments-and-sun-catchers/

If you don't have all your stockings hanging by the chimney with care, check out this free "All the Trimmings Stocking" pattern. You can customize it for the look you want, and it's a pretty simple sewing project.

http://www.dsquilts.com/fabric

*and*patterns.asp?PageID=214

Learn about Hanukkah, the Festival of Lights! With so many traditions, it's a beautiful 8-day celebration.

http://sunflowerschoolhouse.com/2010/hanukkah-2/

Learn about Kwanzaa with the Official Kwanzaa Web Site. From the roots of the holidays to the meaning behind each symbol, there is a wealth of information about the celebration of family, community and culture.

http://www.officialkwanzaawebsite.org/index.shtml

Christmas is celebrated all over the world and each country has its own traditions. Learn more about how they celebrate.

http://www.theholidayspot.com/christmas/worldxmas/

This site covers the gamut of holidays and is full of activities, printables, and descriptions of the different winter holidays across the world.

http://teacher.scholastic.com/activities/holidays/index.htm

I absolutely love journal writing and think kids get quite a bit from the activity. It's a great time to reflect and journal! Here is a list of Christmas journal writing prompts.

http:/homeschoolparent.blogspot.com/2010/12/christmas-journal-writing-prompts.html?spref=tw

If you just need to keep the kids busy, here are some free holiday worksheets for preschool-sixth grade.

http://hellopress.net/free_worksheets.html

And finally, I had to include this blogpost from Daze of Adventure. Lots of great educational toy suggestions and the comic up top will make any homeschooler laugh.

http://www.dazeofadventure.com/2010/12/homeschoolers-christmas.html

Let's say you were going to paint your room. You wouldn't want to just guess about how much paint you needed, instead it would be a perfect time to use those lateral area skills to determine exactly how many cans of paint would be required to paint the whole room. Lateral area is the surface area of a shape minus the bases. It is also an integral component of surface area as it composes a portion of the total surface area.

In today's free Geometry video, Professor Edward Burger explains Surface Area of Prisms and Cylinders so the next time you decide to paint your room; you'll be able to figure out how much paint you need so you don't end up with too little or too much! In addition to prisms and cylinders, you'll also learn how to find the surface area of composite three-dimensional figures. These can be tricky for many students as there are multiple shapes involved, but Professor Burger shows how it can be simple with a little extra thought. Definitely pay close attention to each of the 5 lectures as Surface Area can be used often in your daily life. Make sure you click on the forward button to the left of the time stamp as you won't want to miss a single lecture!

This past Friday, in lieu of having a company holiday party, Thinkwell threw a party for a group of 4-year-olds at Mainspring School. Mainspring is a non-profit early childhood, family-centered education center that caters to the needs of underprivileged families. Mainspring's goal is to help these kids enjoy learning and become self-assured and socially competent in order to excel in school and in life.

We started the party of with a round of snacks for everyone. While the kids munched on grilled cheeses with the crusts cut off, they sang songs and played little kazoos and whistles.

After snack time, we gathered all the kids together for the activities we had planned. We previously took photos of each child, and the project was to decorate a frame for each photo to give to their parents. Once they were done, they worked with one of us to wrap the gift and make a little card for their parents. We also had two wonderful women painting faces throughout the party. Girls with butterflies on their cheeks and boys with bat wings and fake blood on their faces quickly emerged and ran around the play area.

A couple of parents arrived to pick up their kids during our party and the looks on their faces were worth our time throwing this party. They were surprised and grateful that a group of strangers took the time to do something special for their children. Needless to say, we all left Mainspring smiling, happy to have made a fun event for these kids.

Suppose that something is moving and we want to try to understand what that movement is. There are two basic pieces of information that we have to know. We have to know what direction is the object moving, and how fast. Those two pieces of information can be linked together to form what we think of as a vector. A vector is a visual manifestation of movement.

In today's free Geometry video on vectors, you'll learn how to name a vector using component form, which lists the horizontal and vertical change from initial point to terminal point. Then Professor Burger covers finding the Magnitude of a Vector using the Distance Formula and then you'll bring in your knowledge of right triangles to figure the direction of the vector. This video contains plenty of examples to get you comfortable with the concept of vectors. The fourth lecture covers equal vectors, which are two vectors that have the same magnitude and the same direction. It also covers parallel vectors, which are vectors that have the same direction or possibly opposite direction. Unlike equal vectors, though, parallel vectors may have different magnitudes.

Today's video has a total of 5 lectures on it. Don't forget to click the forward button to the left of the time stamp to move to the next lecture on the video.

Bring up the terms sine, cosine, and tangent and most students immediately get intimidated. But it doesn't need to be this way as these are simple trigonometric ratios that anyone can calculate. It's just a matter of remembering what each ratio is and plugging the measurements into the ratio. In today's free Geometry video, Professor Edward Burger explains these Trigonometric Ratios so all students can be fearless when encountering any of these terms. He even walks you through the steps of using a calculator for each, which can be helpful when the ratio is only a portion of a problem you are working. Today's video should help everyone realize that instead of being intimidating, sine, cosine, and tangent are incredibly helpful in determining different unknown measurements of triangles.

With 4 lectures on today's Trigonometric Ratios video, don't forget to click the forward button to the left of the time stamp to move to the next lecture and watch them all.

Triangles can be tricky for some folks, but there are several theorems to make things simpler. For example, the Isosceles Triangle Theorem, which states, if two sides of a triangle are congruent, then the angles opposite the sides are congruent. Half the difficulty can often be in remembering these theorems. Professor Burger comes to the rescue with today's free Geometry video on Isosceles and Equilateral Triangles. Building on some of the concepts we learned in the previous videos on Measuring and Constructing Angles and Congruent Triangles, you'll learn how to prove these theorems and apply them to isosceles and equilateral triangles. After watching the 4 lectures on the video, you will have a solid understanding of the theorems and applying them. Just remember to click the forward button to the left of the timestamp to move to the next lecture so you can watch them all.

Triangles are congruent if both their corresponding angles and their corresponding sides are congruent. Once you know that two triangles are congruent, you can use the knowledge you have about one triangle to calculate parts of the other triangle. You'll learn how to do this and more in today's free Geometry video on Congruent Triangles. Watch as Professor Burger shows you how knowing two triangles are congruent can make it simpler to calculate the different properties of each triangle. You'll learn how to prove the triangles are congruent by using the definition of congruence. With several examples to practice, you'll get a great overview of congruent triangles over the 4 lectures on today's video. Make certain you click on the forward button directly to the left of the time stamp to move to the next lecture so you don't miss a second!

Wikipedia is a great repository of information, but it can also be inaccurate due to its reliance on the public to keep entries accurate and up-to-date. I argued this recently when some friends and I were discussing turtles as pets and the fact they live long lives. You see, my father raises turtles and is constantly teasing me about the fact that I will someday inherit a bunch of turtles from him. Yet, my friends didn't believe that a common box turtle could live 40 years. They decided to jump on the Internet to find the truth. They immediately pulled up Wikipedia only to hear me scream "Just because it's on Wikipedia doesn't mean it's true!" Ironically, Wikipedia agreed with me and I felt vindicated by the site I had just argued against. The next day I found my foot placed firmly in my mouth. Why? Well, I needed the answer to something for work, and my first instinct was to check on Wikipedia. I quickly realized how often I utilize the site to refresh my memory on certain facts.

Once I realized my hypocrisy, I decided it was time to figure out how best to use Wikipedia without worrying about inaccurate information. I think consulting Wikipedia for a quick answer to something is fine and good, but when researching a paper, you can't rely on the resource. Most teachers and parents refuse to allow Wikipedia as a source.

So how do you use Wikipedia without getting in trouble? The key is to remember not to use it as a primary source. Instead, use it to find your primary sources. Most Wikipedia articles end with a list of references. These links often contain the firsthand information you need. However, you should always check the reliability of these links. Like most of the web, they can be inaccurate, biased, or not trustworthy enough to use as a source.

Another way to make Wikipedia work for you is to find other possible key words. Due to the large number of authors that contribute to Wikipedia, it's likely you'll find highly relevant key words within an article. This can help you expand your search if you find different terminology from what you were using in your research.

If in doubt, check the History and Discussion tabs at the top of each Wikipedia entry. The History tab contains a wealth of information about how often and by whom the page has been updated. The Discussion tab, however, may be my favorite. This page allows contributors to discuss and debate issues connected with a particular topic. You can find which facts are in contention and sometimes learn a bit about an author's reliability.

Wikipedia is a truly powerful resource. In a sense, it's comparable to an encyclopedia that is constantly being updated. However, like an encyclopedia, it should be used as a starting point for research, not an ending point.