March 2011 Archives

Solving an Equation Containing a Radical

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Radical equations have square roots in them and it's that darn square root that can make a simple-seeming equation a real challenge. The key is to remember when you are dealing with radicals, in order to get rid of the radical you must square both sides. Most often, getting rid of the radical leaves you with a much simpler equation that can be factored with few issues. In today's free Pre-calculus lecture, Professor Burger runs through a couple of examples and shows radicals aren't as scary as we might think. He even covers a radical equation that due to its structure contains a binomial. This is Prof. Burger's number one classic mistake many students make in that they square the numbers without using FOIL. Learn how to avoid this mistake and how to properly deal with a variety of radicals within equations in today's video.


Factoring Trinomials Completely

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I absolutely love factoring. There is something about the logic behind it that really gets to me. It's funny because it wasn't something I enjoyed in school; instead I've found a love for it while watching Professor Burger lectures.
Remember FOIL, the technique for multiplying two binomials to form a trinomial? Well, this is the opposite of FOIL, and instead of multiplying 2 binomials; you are undoing that work and factoring a trinomial down to the 2 binomials. What's nice is you can always check your work with FOIL and know you got the correct answer. The key to factoring trinomials is to go through your factoring list. First look to see if there are any common factors or any grouping possibilities. Then, break up the squared term and list possible factors. Watch Professor Burger's lecture on Factoring Trinomials in today's free College Algebra video. You'll find that the best way to solve these is through a little trial and error as he runs through a couple of sample problems.

As an educational company, Thinkwell values literacy highly. That's why we're proud to support the Literacy Coalition of Central Texas, which works to improve literacy rates among people of all ages so they can, for example, fill out job applications or navigate the healthcare system.

On Tuesday night, the LCCT held one of their famous Happy Hour Spelling Bees to raise funds for their organization, and Thinkwell fielded a team of three spelling whizzes, including yours truly. We sailed through the first ten rounds on words like stoic, florid, leprechaun, and propitiate. Our team member Dan flawlessly spelled the word connoisseur--the very word that had lost us the competition last year! (I do not envy French spelling bee participants.)

Our good luck, however, was not fated to last. When ours was one of only three teams left, we struck out on neomenia. Apparently it has nothing to do with mania and everything to do with the lunar cycle; it comes from the Greek words "neo" (new) and "men" (month/moon). Oh well, there's always next year. And now we can name one of the books in the Twilight series in Greek...though the value of that particular skill is, perhaps, somewhat dubious.

In addition to earning money for a great cause, the spelling bee was a reminder that even wordy adults can always improve their vocabularies. I was an English major in college, but I learned more than one new word that night. My favorites were fantods (a state of distress) and flocculent (fluffy). All in all, it was a successful night, and one that will help boost literacy in the Central Texas community.

Chemistry in Action - Pipetting

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As you can easily imagine, precision and accuracy in measuring ingredients for chemistry experiments is incredibly important. Precision being the ability to reproduce a measurement and accuracy meaning how close a measurement is to the true answer. Being off by even a small amount when mixing chemicals can result in some very negative things happening, including an inaccurate result. One of the more precise pieces of glassware utilized when measuring liquids is a volumetric pipette. A volumetric pipette is a long glass tube that is used to transfer a precise amount of liquid from one container to another. Professor Gordon Yee demonstrates how to use a pipette to accurately measure a liquid in today's free Chemistry lecture on Pipetting.


Finding Instantaneous Velocity

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At the beginning of today's free Calculus video on Finding Instantaneous Velocity, Professor Burger uses a graph of the position function for a bicycle trip he took. He's concerned he rode faster than the speed limit and is using Calculus to find out if, in fact, he did. It is possible to find his average velocity using a secant line. A secant line is a straight line that intersects a curve, in this case the graph of his trip, at two or more points. The average rate of change is equal to the slope of the secant line between the two points.  In comparison, a tangent line is a line that touches but does not intersect the curve. Instantaneous rate of change is equal to the slope of the tangent line at the point it touches the curve. Prof. Burger reviews the concept of instantaneous rate, demonstrates setting up the limit and then shows how to find the instantaneous rate in today's lecture. By the end of the video you'll know how to answer the very first and most fundamental question of Calculus: How can we find instantaneous velocity?

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Graphing Exponential Functions: Useful Patterns

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Graphs are a great way to learn more about a function. It's not too difficult to create a graph based upon a function, as you just need to plug in numbers for X and solve the function to determine the points that create the graph. You might notice in the examples, the function never crosses the x-axis; instead it gets closer and closer without ever touching. It's impossible for the function to be negative and this results in graph that has a horizontal asymptote. Professor Edward Burger notes that exponential functions are easily recognized by their graph. No matter how you change the function, as long as it's exponential it'll always result in an asymptote, the big difference being the pitch of the curve and its location on the coordinate plane.

Check out today's free Pre-Calculus video on Graphing Exponential Functions to learn more!


Free Resources for Celebrating St. Patrick's Day

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St. Patrick's Day isn't just about shamrocks, wearing green and drinking green beverages.  What may surprise some of you is that this mostly secular celebration of Irish Culture was begun as a religious holiday. In fact, it's truly about celebrating one of the patron saints of Ireland. As such, it's a good opportunity to learn about the history and culture of Ireland.  And we thought this would be a great time to post a list of resources and activities to get you into the St. Patty's Day spirit.

Learn the history behind the day with the History Channel. They have a ton of videos and information about the holiday and the man behind it.

Homeschool Share has an entire page of resources to help you create a unit study on St. Patrick's Day. There are tons of links that tie the holiday to different subjects from geography and vocabulary to art and math.

EasyFunSchool also has a page to help you build a unit study. Their links will direct you to music, online games, traditional Irish Food and even an online quiz.

All Things Beautiful obviously has their mind on a leprechaun's pot of gold as they focus on rainbows with a couple of easy home experiments with color and food.

If you haven't checked out Free Kids Crafts before, this is a great chance to peruse the list of St. Patrick's Day crafts they have. This list is a wide range of crafts for a variety of ages.

Momtastic has a fun St. Patty's Day treasure hunt idea.

And, of course, don't forget to wear green or you might get pinched!!

Pi Day - Celebrate a Mathematical Constant

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It's Pi Day!! In case you don't know, March 14 is the day we celebrate the mathematical constant π. Why March 14th? Well, look at the date: 3/14. Since 3, 1, and 4 are the three most significant digits of pi, it's the perfect day!

In honor of this day, we have several links to help you celebrate:

- The Joy of Pi - This is a companion to the book of the same name. The site has lots of information about Pi, basic facts, its history, and fun activities.
- Education World created an entire lesson planning article for Pi Day with activities by grade.
- Exploratorium has some great activities and links for kids.
- Listen to the sound of Pi as a violin solo. This piece is based on the numbers of Pi to 220 decimal places. The composer explains how he did it throughout the video.
- Try your hand at this Salted Caramel Apple Pie recipe that is one of my favorites. Pie on Pi Day is much better than cake!

Of course, we can't forget our Calculus lecture on The Music of Math. Professor Edward Burger discusses how he converted Pi to music and gives you a sample of the music he was able to create. If you haven't seen this video before, I highly recommend it. The floating Ed Burger head during the music is definitely worth the download alone.

pi_thumbnail.jpgFinally, several folks from Thinkwell are participating in a great fundraiser/world record attempt: Pie Hard. Pie Hard is attempting to break the world record for most pies thrown in a pie fight. All proceeds go to the Sustainable Food Center of Austin and all pie leftovers are going to slop for Green Gate Farms. We won the world record with 1270 pies thrown! Here's some of the fun:



Dr. Elizabeth Davis, executive vice president and provost at Baylor
University, has announced the one-year appointment of Dr. Edward B.
Burger to the position of vice provost for strategic educational
initiatives. Burger, the 2010 recipient of Baylor's Robert Foster Cherry Award for Great Teaching, had been a visiting professor at Baylor during the fall semester.

Burger is professor of mathematics and The Lissack Professor of Social Responsibility and Personal Ethics at Williams College. During his one-year appointment, which begins in July, he also will hold the title of visiting professor of math.

"I am very pleased that Dr. Burger will return to Baylor to assume this important leadership role," Davis said. "As the Cherry Award winner, Ed Burger came to our campus as one of our nation's most outstanding, passionate and creative professors and immediately made a tremendous impact on faculty and students, both inside and outside the classroom. I am delighted that Ed will return to our campus to help spearhead our efforts to increase our effectiveness educating our students for leadership and service in the 21st century."

"I am delighted and honored to be invited to return to Baylor and serve in this new role," Burger said. "I look forward to collaborating with faculty, students and administrators on imaginative projects that have the promise of inspiring us all collectively to consider the true transformative potential of the modern academy."

Burger earned his bachelor's degree in mathematics from Connecticut College in 1985 and received his doctorate in 1990 from The University of Texas at Austin. In addition to Baylor, he has taught or been a visiting scholar at the University of Waterloo in Canada, The University of Texas at Austin, Westminster College, Texas Christian University, University of Colorado at Boulder and Macquarie University in Australia.

A math professor at Williams College since 1990, Burger has been honored with numerous teaching and writing awards, including the 2007 Award of Excellence from Technology & Learning magazine, the 2006 Reader's Digest "100 Best of America" as Best Math Teacher, and the 2006 Lester R. Ford Award, the 2004 Chauvenet Prize and the 2001 Deborah and Franklin Tepper Haimo Award for Distinguished College Teaching of Mathematics, all from the Mathematical Association of America. He was named the recipient of Baylor's Robert Foster Cherry Award for Great Teaching in January 2010.

Burger is the author or co-author of more than 30 research articles and 21 books and CD-ROM texts, including The Heart of Mathematics: An Invitation to Effective Thinking, which was honored with a 2001 Robert W. Hamilton Book Award; Coincidences, Chaos and All That Math Jazz: Making Light of Weighty Ideas (each co-authored with Michael Starbird from The University of Texas at Austin); and Extending the Frontiers of Mathematics: Inquiries into Proof and Argumentation. He is an associate editor for The American Mathematical Monthly and a member of the editorial board for Math Horizons.

Burger also has written and appeared in hundreds of educational videos, including the 24-lecture video series, "Zero to Infinity: A History of Numbers" and "An Introduction to Number Theory" in "The Great Courses" series through The Teaching Company. Some of his college-level videos can be found at

As the recipient of Baylor's Cherry Award - the only national teaching award presented by a college or university to an individual for exceptional teaching - Burger taught two popular classes during the fall 2010 semester at Baylor, "Ideas in Mathematics" and "Foundations of Combinatorics and Algebra." He also launched the Cherry Faculty Forum, a weekly program well-received by faculty across the disciplines who met regularly to discuss defining and fostering creativity both in the classroom and in their own scholarly pursuits.

"From the moment he arrived, Dr. Burger was warmly received by students and faculty, as he effectively engaged representatives from across the Baylor campus in important dialogue about innovative teaching and learning in the academy," Davis said. "That experience suggested that Ed could provide valuable assistance and perspective as we consider thoughtfully, and on behalf of our students, during the next year, the kinds of educational innovation we want to invest in and focus on in the future."

One of the biggest problems I see reported by teachers is keeping their students engaged. It's common to hear complaints of students not able to focus longer than 10 minutes--and yet put that same kid in front of a video game and they're engaged for hours. Watch a kid playing a video game, and you'll see strong concentration and the ability to ignore external distractions. I've had to actually touch a child who was playing games on the shoulder just to get him to realize I wanted his attention! This alone tells me that kids can focus and be engaged; it's just a matter of presenting information in a way that interests them. I think video games are a great way to teach and keep kids learning in the classroom. The key is how you implement them.

I remember playing Oregon Trail, Lemonade Stand, and Where in the World is Carmen Sandiego? as a child. These games taught me problem-solving, math, financial planning, and even geography, and I loved playing them even though their graphics were sadly low-tech in comparison to today's games. The funny thing is you can find modern versions of all of these games today, probably because of their success in engaging children into the story of the game, teaching without being "teach-y." You quickly learned that many people on the Oregon Trail died of dysentery, and rainy days can kill a lemonade stand. And all of this was before the incredible technology we have today.

Our education system is finally taking the steps to test games to determine if they're effective learning tools. Take, for example, the school Quest to Learn, which as profiled in this New York Times article. The school teaches everything in a gaming environment and instructs students in developing games as well. Just learning to develop games involves using math, writing, art, and critical-thinking skills, which is quite a bit to gain from one activity. I found this comment about Katie Salen, the lead institutional partner for Quest to Learn, very interesting:

A game, as Salen sees it, is really just a "designed experience," in which a
participant is motivated to achieve a goal while operating inside a prescribed
system of boundaries and rules. In this way, school itself is one giant designed
experience. It could be viewed, in fact, as the biggest and most important game
any child will ever play.

It can be a weird thing to consider school a game, but think about it: both involve rules you use to gain knowledge and achieve a goal, whether that's slaying a dragon or passing a test. Grades are like scores you get for successfully completing your mission of learning a particular subject--your report card is your "high score." I can see this increasing competitiveness amongst students as they strive to beat their friends. And the beauty of video games is they can be designed for group play so that students can learn to work successfully in a team in order to win. These are all very desirable skills in today's job market.

We'll see if video games can be one of the solutions to our education crisis. The research is still out, and not enough has been done to show they result in more student engagement and better grades. I do think that a game utilized as an activity to back up a specific lesson can be very successful. We here at Thinkwell have games and interactivities as part our curriculum, and the response has always been positive. In fact, students usually ask for more of them!

Chemistry - Theoretical Yield and Percent Yield

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Theoretical yield is the maximum amount of product that can be made from the reactants given. How much product is made depends on how much reactants you start with. In today's Free Chemistry lecture, Professor Gordon Yee demonstrates first how to calculate theoretical yield for a balanced reaction. When calculating a balanced reaction, things have to be expressed in moles. You then have to calculate a limiting reagent problem to figure out what we will run out of first. Professor Yee gives you two methods of solving this balanced reaction problem. Interestingly, most chemical reactions don't result in as much product as you expect. This is because a lot of reactions don't necessarily go only to one single product. They might give you a couple of products, albeit minor products. Also, when you are purifying your product you lose a little. The actual yield is always going to be less than the theoretical yield. That is where percent yield becomes important, as it is the actual yield expressed as a percentage of the theoretical yield. Watch today's video and learn more about calculating theoretical yield and percent yield.


The Top Ten Algebra Mistakes

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Knowing what to do to in algebra is half the battle. Knowing what NOT to do can be just as important and it's what we explore in today's free video. For many students, this lecture on The Top Ten List of Mistakes is a favorite. I love all of the little songs for each mistake and the lecture is a great example of Professor Ed Burger's sense of humor. This video is one of the first you see in our College Algebra course and as you continue to learn algebra, you'll see why. This is a lecture that all algebra students can appreciate.

While the lecture is fun and entertaining, don't forget to pay attention to the mistakes being noted. These are all simple errors many of us have made while working algebraic problems.  Every time I'm about to make one of these mistakes, I'll suddenly hear one of the songs from this lecture and avoid getting stuck with the wrong answer. By the end of the video you'll be singing, "When in doubt, write it out."



Determining Whether a Trig Function is Odd, Even, or Neither

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We've explored trigonometric functions in the past, but today's video is a bit different. While we can easily determine if a function is odd or even by looking at its graph, Professor Edward Burger also shows how to look at the function to come to the same conclusion.

A function is even if it's symmetric about the Y-axis, so anything done on the right side is mirrored on the left side. In math terms even would be if f(-x) = f(x). A function is odd if it has some symmetry but it's more like a flip-of-a-mirror symmetry. Whatever is done on the right, the same thing is done on the left but sort of in reverse. This can be also be explained in math terms as f(-x) = -f(x).

In today's free Pre-Calculus lecture, you'll learn how to visually determine whether a trigonometric function is odd, even, or neither. It really helps to see the graphs to understand this concept. You'll learn that sine is odd, cosine is even and tangent is odd and how to prove this with both the graph and the function itself. Don't forget that trigonometric functions can also be neither odd nor even if it's not symmetric to either the Y-axis or to the origin. This is one lecture you'll want to see as the visuals really help explain and show the difference between odd and even functions.


American Government: Women and the Struggle for Rights

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With March being Women's History Month, I thought it would be a great time to feature a lecture from our American Government course: Women and the Struggle for Rights. It can be easy to take for granted the rights we enjoy every day and forget that when our country was founded women did not have the right to vote, could not serve on juries and often could not get any education let alone higher education. Women were even barred by law from serving in any profession. It wasn't until the 1920s when women gained the right to vote and despite this gain in freedom, discrimination was still commonplace until 1964 when Congress passed the Civil Rights Act. We've come a long way, and today's lecture describes the struggle that led to the opportunities women enjoy today.

The fight for women's rights is a fascinating bit of history and it's uplifting to see how many changes there have been since the Declaration of Independence was signed. There is still a ways to go as women now have to overcome cultural barriers in order to achieve full participation in our country. Seeing more women as CEOs of large corporations and eventually President or even Vice-President of the country will help this movement truly reach its goal of equality.


In today's free Pre-calculus video, we're going to take a look at vectors that are given to us in standard form and see if we can figure out both the magnitude and in some sense the direction, which is given by what's called the direction angle.  Just in case you don't remember, magnitude is the length of the vector. The direction angle is an angle that starts at the positive x-axis and is measured counterclockwise. You'll be using your Trigonometry skills as you apply the Pythagorean theorem to find the magnitude of vectors. And then, Professor Burger will demonstrate how to figure out the direction angle using any of the trig functions. It's a quick little lecture that will definitely get you comfortable with finding the magnitude and direction of a vector.


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This page is an archive of entries from March 2011 listed from newest to oldest.

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