July 2010 Archives

7th Grade Math - Simple Interest

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If you learn one thing about percents this week, make sure it's this: Simple Interest. If you are looking for an example of applicable math, this is it. Let's say you have a large purchase and you need to borrow money for it. Or maybe you have money and want to invest it and get some interest back, such as put it into a savings account or buy a bond. You start out with a principle amount, you add in a rate of interest and a set amount of time to complete this transaction. Using these numbers, it is possible to determine exactly how much interest will accrue during the set time period.

This can be very important when you have a long-term loan as over time, the interest could add up to more than you want to spend. Or if you are investing, you may want to know how much money you'll earn after the set time period.

Watch today's 7th grade math video on Simple Interest and let Edward Burger teach you the basics before using several examples to reinforce the lesson. Today's video has 4 lectures on it today, so make sure you click the forward button directly to the left of the timestamp to move to the next lecture and watch them all!

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7th Grade Math - Percent Increase and Decrease

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Computing the percent increase or the percent decrease can give you a good sense of how things are changing. This is definitely one of those math concepts that get used frequently in the real world. Companies are always comparing numbers and percentages in order to determine if business is improving . Or maybe you are at a sale and need to calculate the exact price of something based upon a percentage discount.

I absolutely love percents. Not only are they fun when things are marked down in a store, but it's always nice when you get a percentage increase on your salary. They are important when you are looking into financing a car or a house and need to determine your interest rate. And even people can be categorized by percentage. For example, I was in the top 10% of my class in high school. How about you?

In today's free 7th grade math video, Percent increase and Decrease, Edward Burger teaches you these concepts. Today's video has a total of three lessons, so be sure you click on the forward button directly to the left of the time stamp to watch all three!


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There's so much hype surrounding technology in education that it can be hard to distinguish between fact and fiction. Is modern technology giving your child unparalleled educational resources, or is it distracting her and ruining her attention span?

Peter Grunwald's insightful new report on technology in the classroom examines the connection between teachers' use of technology and students' development of "21st-century skills" like critical thinking, problem solving, creativity, adaptability, and productivity. In doing so, it busts five prevalent myths about how we can take advantage of technology in schools to help students acquire these skills.

  • 1. The myth: New teachers and teachers with more access to technology use technology more often.
    The truth: Although restricted access to technology does discourage some teachers from using it, the main reason teachers elect not to use technology is because they don't feel it's necessary for a particular lesson.
  • 2. The myth: Technology doesn't do much for students who aren't already high achievers.
    The truth: According to teachers, technology seems to benefit all students, including those learning English as a second language and those with behavioral or emotional problems.
  • 3. The myth: Teachers' use of technology doesn't really matter, because students these days are already comfortable with technology.
    The truth:A student may be comfortable with technology, but that doesn't mean he or she is using it to learn.
  • 4. The myth: Teachers and administrators are on the same page when it comes to their feelings about technology and 21st century skills.
    The truth: Administrators tend to have more positive feelings about technology than teachers do. They support its use more strongly and are more enthusiastic about its effects on students.
  • 5. The myth: Teachers feel well prepared to use technology in the classroom to cultivate 21st century skills in students.
    The truth: Teachers often feel that their initial (undergraduate) training in this area is insufficient. They believe they're better prepared by advanced training like postgraduate studies and certification programs.


In the end, the report concludes:

The survey findings demonstrate strong connections between technology and 21st century skills. This suggests that it is important to focus on both technology and 21st century skills to achieve critical education outcomes....we need to better prepare and train teachers in technology competencies and 21st century skills so teachers can lead their students to better outcomes.


To read this and other reports about the intersection of education and technology, click here.

Percentages are really valuable in trying to figure out numbers when we only know part of the story. It turns out that if we use some algebra we can figure out the entire story. Percentages are used to express how large/small one quantity is, relative to another quantity. Calculating percent is a fairly simple math calculation. Calculating the reverse where you have the percentage and the final result and must determine the original number may seem daunting. However, by carefully translating the problem into a mathematical equation, you can easily solve the problem.

Finding a number when the percent is known is very useful skill to have. In today's free 7th grade video, Prof. Burger not only shows you how easy it is to convert these problems into equations and solve them, but he gives you a couple of real world examples to demonstrate how you can use this in your day to day life.

Today's video has a total of 3 lectures. Make certain you click on the forward button directly to the left of the time stamp to move to the next lecture in order to watch the entire lesson.

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7th Grade Math - Factors and Multiples Worksheet

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It's Friday and time for a free 7th grade math worksheet! Today's worksheet covers the entire Factors and Multiples subchapter. 4 pages of questions encompassing the topics of Prime Factorization, Greatest Common Factor, and Least Common Multiple.

This week we covered some really important, fundamental concepts of Math. You will use these ideas over and over when working in other areas of Math like fractions and functions. Of course, if you missed any of the previous videos, check them out first and then check your knowledge with our worksheet.

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7th Grade Math - Least Common Multiple

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Least Common Multiple is the smallest positive number that is a multiple of any list of numbers you are given. Often, it refers to two numbers, but as Professor Burger demonstrates in today's free 7th grade math video, it can also be applied to as many numbers as you want.

There are several ways to find the least common multiple of a group of numbers. You can compute all the multiples of each number and then determine the lowest multiple they have in common. You can also utilize prime factorization to figure the least common multiple. Believe it or not, you will use this concept often in other math concepts. In fact, it is most useful when working with adding, subtracting, or comparing fractions with different denominators. Professor Burger also demonstrates a real world application in the last lecture to help show how useful this idea is in your everyday life.

Today's video contains a total of 3 lectures to give you a strong understanding of least common multiples. Make certain you click on the forward button directly to the left of the time stamp to move to the next lecture.

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7th Grade Math - Prime Factorization

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Prime numbers are always a mathematician favorite. In some sense they are the fundamental building blocks upon which all other whole numbers can be built. Basically, a prime number is a number that can't be factored into two numbers that are each smaller than the original. Otherwise, if a number can be factored into two smaller pieces, then it is called a composite number. Every single composite number can be written as a product of prime numbers. Prime Factorization is the process of finding what prime numbers you need to multiply together to get the original number.

Prime numbers come up often in Cryptography, the study of secret codes. The people who make or break secret codes often utilize prime factorization. Because very large numbers are very hard to factor, it can take a computer a long time to compute. This makes them very useful for security purposes. In fact, in 2009 several researchers factored a 232-digit number utilizing hundreds of machines over a span of 2 years. That's a long time for one number!

We are jumping into our 7th grade math curriculum with today's free video on Prime Factorization. Edward Burger takes you through the basics and then several examples to ensure your full understanding of today's subject. There happens to be a total of three lectures on the video, so make certain you click on the forward button directly to the left of the time stamp to move to the next lecture.

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Pre-Algebra - The Coordinate Plane

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Are you ready for the weekend? How about a little math first?

In today's free Pre-Algebra video Professor Burger discusses The Coordinate Plane. The coordinate plane is a plane containing a horizontal number line, the x-axis, and a vertical number line, the y-axis. This particular plane is called The Cartesian Plane, due to the use of Cartesian coordinates. The name Cartesian comes from its inventor, the French mathematician and philosopher René Descartes. Interestingly enough, many people speculate that Descartes was inspired by Renaissance painters who used a grid, in the form of a wire mesh, as a tool for breaking up the component parts of their subjects they painted. We may never know the truth, but we do know that the Cartesian coordinate system aided in the development of calculus by Isaac Newton and Gottfried Wilhelm Leibniz.

Learning about the coordinate plane is the first step in graphing numbers and equations, and is used extensively throughout math and math related subjects. You will use graphs for many future math subjects as graphs can tell you much about a series of numbers.

Today's video has a total of 3 lectures covering everything from the quadrants of the coordinate plane to how to plot points on the coordinate plane given the coordinates. Don't forget to click the forward button directly to the left of the time stamp to move to the next lecture.

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Pre-Algebra - Square Roots and the Pythagorean Theorem

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Finding square roots is one of those math ideas that is fairly simple. Basically, to square a number, you just multiply it by itself. The square root is the number you multiplied by itself. Sometimes it's an easy calculation: the square root of 25 is 5. Other times, as Prof. Burger demonstrates, it's a bit trickier as with the square root of 30 since there is no whole number that equals 30 when squared.

Once you've got the basics of square roots, Prof. Burger moves on to the Pythagorean Theorem, one of the most important theorems in math. Not only will you learn the theorem, but also why it is true! Then it's on to applying the theorem as it is demonstrated in several examples, including how to reverse it to prove a triangle is a right triangle!

Today's free Pre-Algebra video has a total of 4 lectures in it covering Square Roots and the Pythagorean Theorem. This will be plenty to help you thoroughly understand the subject. Just make sure you click on the forward button directly to the left of the time stamp to move to the next lecture.

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Pre-Algebra - Factoring with the GCF

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The Greatest Common Factor is the largest positive integer that divides two or more numbers without a remainder. This concept can be applied to factoring polynomials, which makes things a bit trickier, but very important as this is often the first step in solving more difficult math problems. In today's free Pre-Algebra video, Edward Burger gives you several examples to run through to get you used to factoring polynomials using the greatest common factor.

Get ready to dive deep into factoring polynomials. You'll start with the basics and work your way to the last lecture where you'll learn how to handle the ever-exotic binomial factors. Sounds tough, right? But, with our Factoring with the GCF video, you'll quickly learn the basics and have no problem handling complex factoring problems.

Today's free video has a whopping 4 lectures on it! So, don't forget to click on the forward button directly left of the time stamp to move to the next lecture. Each lecture builds on the previous to give you a solid foundation in factoring polynomials using the greatest common factor.

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Pre-Algebra - Multiplying Binomials

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Today we're learning how to multiply binomials. FOIL is one of the best known ways to do this. It is a great mnemonic to help you remember the standard method of multiplying two binomials. It is literally:
First
Outer
Inner
Last

It works only for the specific and special case of a two binomials. FOIL tells you to multiply the first terms in each parentheses, then multiply the two terms that are on the "outer" (furthest from each other), then the two terms that are on the "inner" (closest to each other), then the two terms that are on the "inner" (closest to each together), and finally the last terms in each of the parenthesis.

If your head is spinning with all these spiffy math terms, worry no longer because Edward Burger will clear everything up in today's free Pre-Algebra video on Multiplying Binomials. He'll explain the meaning of FOIL, how to use it and give you several examples to put it into use. This is a basic, but very important concept that you will use often in your Algebra studies. It is not too difficult to learn once you remember what it stands for, just follow the steps and the method will work!

Today's video has a total of 3 lectures. Make certain you click on the forward button directly to the left of the time stamp to view them all.

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Congratulations Professor Burger!

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Thinkwell is very proud to share the news that our math professor, Edward Burger, was awarded and endowed chair by Williams College! As of July 1st, he will be the Lissack Professor for Social Responsibility and Personal Ethics.

Congratulations Professor Burger on this prestigious and well-deserved award!

6th Grade Math - Functions Worksheet

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Are you tired of functions yet? We've been covering them all week in our free 6th grade math videos with Edward Burger. At this point, if you have followed us this week, you should be well prepared to show your grasp of the concept with today's free worksheet on Functions! Today's worksheet is 4 pages of questions covering the topics of Tables and Functions, Graphing Functions, and Slope and Rate of Change. If you're not ready for the worksheet, go back and visit our previous blog posts to view the videos first.

Next week we'll be moving away from 6th grade math and covering some of our other course offerings. If you have been wanting to sample some of the courses we have, feel free to browse through the blog archives, visit our YouTube channel (we love comments) or check out our Demo page!

Hope everyone has a great weekend and comes back Monday ready to learn some more.

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Great Virtual Tours to Keep Kids Busy

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With the summer heat finally taking hold of everyone, field trips are a nice change of pace for many. Unfortunately, some of the best places to visit and actually receive some form of educational value are not the most convenient for everyone. I spent that past few weeks surfing the internet looking for some really great virtual field trips. These virtual field trips are rather nicely done and provide good learning opportunities without having to pack up the family truckster and listen to "Are we there yet?" for long periods of time.

Plant Hunters
Tour the New York Botanical Garden and learn about the variety of plants they have. Great educational information!
http://www.nybg.org/planthunters/

Acropolis
Incredible 360 views. Pictures are outstanding and look great even full screen!
http://www.acropolis360.com/

Panoramic Virtual Tour of Smithsonian National Museum of Natural History
Room-by-room walking tour of the whole museum.
http://www.mnh.si.edu/panoramas/

The Louvre

It could take days to see all the Louvre has to offer, so do it from the comfort of your own home!
http://www.louvre.fr/llv/musee/visite_virtuelle.jsp?bmLocale=en

Grand Canyon Virtual Tour
You can even take a virtual raft trip through the Grand Canyon!
http://www.nps.gov/grca/photosmultimedia/virtualtour.htm

Taj Mahal
360 panorama photos and information about this beautiful building.
http://www.taj-mahal.net/index.htm

St. Paul's Cathedral

Beautiful tour with great panoramas and min-movies.
http://www.explore-stpauls.net/

Nautilus Live
Follow deep sea divers as they explore ancient history on the sea floor! Live cams let you experience expeditions as they happen!
http://www.nautiluslive.org/

National Geographic Virtual Rain Forest at Night

This is a shorter tour, but has some great information about the plants and animals in a rain forest.
http://www.nationalgeographic.com/features/00/earthpulse/rainforest/index_flash.html

Statue of Liberty
Really great photos and information about the Statues of Liberty.
http://www.nps.gov/stli/photosmultimedia/virtualtour.htm

Do you have any favorite virtual tours besides the ones above? Post them in the comments section as we'd love to see what else is out there!

6th Grade Math - Slope and Rate of Change

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We've been working with functions in tables. Thankfully, tables make our next subject much easier to determine. Today's free 6th grade math video is covering Slope and Rate of Change. In order to determine rate of change, we compare how the y's are changing to the x's in order to see how that relationship, or quotient, is changing as we go through data. Rate of change is either constant or variable. A constant rate of change means that each x,y quotient is the same throughout the values. Whereas a variable rate of change is the opposite with the quotient changing each time. In the first lecture, Edward Burger makes this an easily understood concept by running through a couple of examples to make the difference between constant and variable rates of change clear.

Today's video has two lectures in it, and in the second lecture Prof. Burger uses a real-world application of this to further your understanding. Using evaporation of water as the example, he shows how a science class would graph the data and connect the points with line segments. The slope of the line will correspond to the rate of change.

Don't forget to click on the forward button directly to the left of the timestamp to move to the second lecture in today's video!

Are you currently looking for curriculum other than 6th grade math? Check out our other offerings on our demo page!

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6th Grade Math - Graphing Functions

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One of the most powerful and greatest things we can do with functions is to look at them. By looking at them, namely their graphs in the coordinate plane, we can begin to extract information. How do we build these beautiful, graphical visualizations of functions? With today's free 6th grade math video, Prof. Burger shows how to do just that. He starts with a simple function in a table in the first lecture. He then shows us that by looking at the points that are generated when we plug in x's and get out y's we end up with ordered pairs that become the coordinates for points on a graph. Once created, it becomes apparent the power of looking at a graph associated with a function. It allows us to see the overall structure of the function. A table only gives us a few points, but the graph gives us all the points at once.

Today's video on Graphing Functions includes a whopping 4 lectures! Make certain you click on the forward button directly to the left of the time stamp to move to the next lecture.

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Professor Edward Burger on Maine's NBC-TV

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We're excited here at Thinkwell to share that Edward Burger was on station WCSH-6 in Portland Maine! He was interviewed on 207, a news magazine show, by host Rob Caldwell. Learn more about one of our favorite professors as he talks about the teachers who inspired him, why he isn't a lawyer and why quality of failure is so important to him.

Check out the video of his interview here.

6th Grade Math - Tables and Functions

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Functions allow us to see how changes in one thing result in changes in something else. A function is a rule that relates two quantities so that each input value corresponds exactly to one output value. How do we go about finding functions? It turns out that to find a function we have one input and then that results in some kind of output. To figure out a rule that will allow us to predict future outputs given inputs is really what's at the heart of trying to find a function.

Today's free 6th grade math video covers Tables and Functions. Learn with Prof. Burger as he teaches you to utilize data in a table to write an equation for a function and then use the equation to find a missing value. He even gives a real-world example where functions can come in handy! There are three separate lectures in today's video, so don't forget to click on the forward button directly to the left of the timestamp to move to the next lecture.

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6th Grade Math - Volume and Surface Area Worksheet

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This week we learned how to calculate both the surface area of a three-dimensional object and the volume, or how much it holds inside. I guess you could say we've learned three-dimensional objects inside and out! So, now that we understand these concepts and have seen the possible real world uses of them, it's time to test our knowledge.

Today's free worksheet covers the entire Volume and Surface Area subchapter from our 6th grade math course. Three-dimensional figures, volume of prisms, volume of cylinders, and surface area are all covered in this 4-page worksheet. If you followed the videos all week, this worksheet should be a cinch.

We'll be back next week with more videos. Until then enjoy the worksheet and have a safe and happy July 4th!

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6th Grade Math - Surface Area

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Now when we have three-dimensional objects, we can talk about more than just the volume, which is the amount of content inside. We've covered how to do that all week so far. Now let's talk about how much area there is along its surface. That is called the surface area.

Surface area is the sum of all the areas of all the shapes that cover the surface of an object. Some shapes, such as a cube, are fairly simple to calculate the surface area of versus a shape like a cylinder that involves a little more math to solve.

Thankfully, Professor Burger makes this easier with his demonstrations in today's free 6th grade math video. You'll get some great visuals that will not only help you understand the concept but be able to easily apply this knowledge whenever you need. Whether it's planning for how much paint you need to cover a wall or how much tile to buy before laying a new floor, there is a great deal of real world uses for surface area!

Today's video has 3 separate lectures that will provide a good foundation in surface area. Make sure you click on the forward button directly to the left of the time stamp to move to the next lecture. And don't forget to come back tomorrow for the worksheet covering all the videos we've watched this week!

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About this Archive

This page is an archive of entries from July 2010 listed from newest to oldest.

June 2010 is the previous archive.

August 2010 is the next archive.

Find recent content on the main index or look in the archives to find all content.