News/Events

March 3 – World Math Day. Be part of this international competition. Get the details online or here at BEST Tutoring.

March 4 – March Forth with Math.  It’s Robot Day. Learn the Math that drives technology. March 1 thru 7 is METS week in Missouri, so watch your email for what’s happening; you won’t want to miss out.  The M is for Math because “Math Rocks!”

March 16, 17, 18 – Spring Break Chess Camp.  Join us at Planet Fun to learn some good moves for ages 6 to 14.  Each camper gets pizza, snack, a chess scorebook  and a FULL day of play!

March 27 – 28 – RC Race Across St. Peters at the Home & Garden Show.  Stop in for more details and a registration form.

Happy March Birthday to Heidi and Prachi!

5 Part Series: Myths That Can Cause Math Anxiety
Myth #4: IN MATH, WHAT’S IMPORTANT IS GETTING THE RIGHT ANSWER.

If you are building a bridge, getting the right answer counts for a lot, no doubt. Nobody wants a bridge that tumbles down during rush hour because someone forgot to carry the 2 in the 10’s place! But are you building bridges, or studying mathematics? Even if you are studying math so that you can build bridges, what matters right now is understanding the concepts that allow bridges to hang magically in the air – not whether you always remember to carry the 2.
That you be methodical and complete in your work is important to your math instructor, and it should be important to you as well. This is just a matter of doing what you are doing as well as you can do it – good mental and moral hygiene for any activity. But if any instructor has given you the notion that “the right answer” is what counts most, put it out of your head at once. Nobody overly fussy about how his or her bootlace is tied will ever stroll at ease through Platonic Realms.

For more information, please visit http://www.mathacademy.com/pr/minitext/anxiety

Tips and Techniques: One Major Math Tip Per Grade Level

Use these tips to check your child’s progress in the math classroom.  Students should be comfortable handling these grade-level and below grade-level questions by the end of the year.

If your child has finished: [Ask the following questions for your child’s grade-level and below]

Kindergarten: Find half (1/2) of even and odd numbers.

First Grade: Know combinations of numbers that make 10.

Second Grade: Be “fluid” with single-digit addition.

Third Grade: Mentally and visually add 1/2s and 1/4s.

Fourth Grade: Know times tables “by heart.”

Fifth Grade: Order Fractions using benchmark numbers.

Sixth Grade: Be able to mentally calculate percents by using “friendly” numbers.

Seventh Grade: Be able to convert fractions to decimals to percents.

Pre-Algebra: Effortlessly add and subtract positive and negative numbers.

Algebra: Be able to solve simple equations “by inspection.”

News/Events

February 15 – President’s Day.  Find out about some big numbers that you wish Congress would understand.

March 4 – March Forth with Math.  Learn how to make Math fun and interesting. Workshop details are at www.nlightening.com or send an email to Sarah at BEST.StPeters@gmail.com for a complete program.

March 1 thru 7 is METS week in Missouri, so stay tuned for email with what’s happening; you won’t want to miss out.  The M is for Math because “Math Rocks!”

Happy February Birthday to Cameron, Silvia, Ellyse, Diamond, Paul, Wesley, and Lauren!

5 Part Series: Myths That Can Cause Math Anxiety
Myth #3: MATH CREATES LOGIC, NOT CREATIVITY.

The grain of truth in this myth is that, of course, math does require logic. But what does this mean? It means that we want things to make sense. We don’t want our equations to assert that 1 is equal to 2. This is no different from any other field of human endeavor, in which we want our results and propositions to be meaningful – and they can’t be meaningful if they do not jive with the principles of logic that are common to all mankind. Mathematics is somewhat unique in that it has elevated ordinary logic almost to the level of an art form, but this is because logic itself is a kind of structure – an idea – and mathematics is concerned with precisely that sort of thing.

But it is simply a mistake to suppose that logic is what mathematics is about, or that being a mathematician means being uncreative or unintuitive, for exactly the opposite is the case. The great mathematicians, indeed, are poets in their soul.
How can we best illustrate this? Consider the ancient Greeks, such as Pythagoras, who first brought mathematics to the level of an abstract study of ideas. They noticed something truly astounding: that the musical tones most pleasing to the ear are those achieved by dividing a plucked string into ratios of integers. For instance, the musical interval of a “fifth” is achieved by plucking a taut string whilst pressing the finger against it at a distance exactly four-fifths along its total length. From such insights, the Pythagoreans developed an elaborate and beautiful theory of the nature of physical reality, one based on number. And to them we owe an immense debt, for to whom does not music bring joy? Yet no one could argue that music is a cold, unfeeling enterprise of mere logic and calculation.

For more information, please visit http://www.mathacademy.com/pr/minitext/anxiety

Tips and Techniques: Think Before You Speak

All too often students blurt out the first thing that comes to mind. While we want to encourage a certain amount of “risk taking” by our students, we also want them to be thoughtful in their responses. In the words of John Wooden, “Be quick, but don’t hurry” – in Latin, festina lente, “hasten slowly”.

What is the most common wrong answer for each of these questions

• “How far is it from 67 up to 100?” [43]
• 7 – 2 ½ = ______ [5 ½]
• 3 x 5 ½ = ______ [15 ½]
• 6 ÷ ½ = ______ [3]
• A student bought three pencils for 10 cents each and two erasers for 5 cents each. Find the total cost of all of the pencils and erasers. [15 cents]
• A 100 pound watermelon is 95% water and 5% melon. How much water must be removed to make it 50% water and 50% melon? [45% or 45 pounds]
• A fish tank is three-fourths full. Two-thirds of the water leaks out. How much of the tank still contains water? [1 ½]
• (x + y)² = ______ [x² + y²]

When we see our students making these kinds of mistakes, it is worthwhile to put down our pencils and spend some time discussing the fact that while many math questions are as straightforward as they may seem, many are not. Most important of all, we always have to be thinking when doing math.

News/Events

December 23 – January 4, 2010 – Open by appointment. Have a great Holiday!

Happy January Birthday to Scott, Elijah, Jordan, Camille, Andrew, Maya, Peter & Brendan!

Spin and Win Bonus! Students who complete 3 or more pages in December or January get to spin the wheel for an extra prize like hot cocoa, a game or funny putty. And, kids who  answer the “Question of the Day” also get a chance to spin for a bonus.

5 Part Series: Myths That Can Cause Math Anxiety
Myth #2: TO BE GOOD AT MATH YOU HAVE TO BE GOOD AT CALCULATING

Some people count on their fingers. Invariably, they feel somewhat ashamed about it, and try to do it furtively. But this is ridiculous. Why shouldn’t you count on your fingers? What else is a Chinese abacus, but a sophisticated version of counting on your fingers? Yet people accomplished at using the abacus can out-perform anyone who calculates figures mentally.

Modern mathematics is a science of ideas, not an exercise in calculation. It is a standing joke that mathematicians can’t do arithmetic reliably, and I often admonish my students to check my calculations on the chalkboard because I’m sure to get them wrong if they don’t. There is a serious message in this: being a wiz at figures is not the mark of success in mathematics.

This bears emphasis: a pocket calculator has no knowledge, no insight, no understanding – yet it is better at addition and subtraction than any human will ever be. And who would prefer being a pocket calculator to being human?

This myth is largely due to the methods of teaching discussed above, which emphasize finding solutions by rote. Indeed, many people suppose that a professional mathematician’s research involves something like doing long division to more and more decimal places, an image that makes mathematicians smile sadly. New mathematical ideas – the object of research – are precisely that. Ideas. And ideas are something we can all relate to. That’s what makes us people to begin with.

Tips & Techniques: Travel Math for the Holidays

You and your family are going on a 300-mile automobile trip. You can count mile markers, trucks, or wheels that you pass, or see who can spot the largest license plate number, then ask yourself:

1)  At an average speed of 60 miles per hour, how long will the whole trip take?

2)  If you car gets 25 miles per gallon, how many gallons of gas will be used on the trip?

3)  If gasoline costs $3.25 per gallon, estimate the cost of gas for the trip.

4)  After you have traveled 60 miles:

• a)  How much farther do you have to go?
• b)  What fractional part of the trip have you traveled?
• c)  What percent of the trip is left to go?

5)  After you have traveled 60% of the trip:

• a)  How much farther do you have to go?
• b)  What fractional part of the trip have you traveled?
• c)  What percent of the trip is left to go?

6)  When you have 1/10 of the trip left to go:

• a)  How far have you traveled?
• b)  How many gallons of gas have been used so far?
• c)  What percent of the trip have you completed?

7)  If you increase your average speed from 60mph to 75 mph:

• a)  How much faster will you get there?
• b)  By what percent did your time for the whole trip improve?

Student of the Month

Michael GreenLee

News/Events

December 12, 1:00pm – 10:00pm – Holiday Christmas Card Crop

December 23 – January 4, 2010 – Closed for the Holidays. Have a great Holiday!

Happy December Birthday to Jacob, Scott, Megan, Zach, Tyler, Katherine, Bridget, William, and Ted!

Spin and Win Bonus! Students who complete 3 or more pages in December or January get to spin the wheel for an extra prize like hot cocoa, a game or funny putty. And, kids who  answer the “Question of the Day” also get a chance to spin for a bonus.

5 Part Series: Myths That Can Cause Math Anxiety
Myth #1: Aptitude for Math is Inborn

This belief is the most natural in the world. After all, some people just are more talented at some things (music and athletics come to mind) and to some degree it seems that these talents must be inborn. Indeed, as in any other field of human endeavor, mathematics has had its share of prodigies. Karl Gauss helped his father with bookkeeping as a small child, and the Indian mathematician Ramanujan discovered deep results in mathematics with little formal training. It is easy for students to believe that doing math requires a math brain, one in particular which they have not got.

But consider: to generalize from “three spoons, three rocks, three flowers” – to the number “three” – is an extraordinary feat of abstraction, yet every one of us accomplished this when we were mere toddlers! Mathematics is indeed inborn, but it is inborn in all of us. It is a human trait, shared by the entire race. Reasoning with abstract ideas is the province of every child, every woman, every man. Having a special genetic make-up is no more necessary for success in this activity than being Mozart is necessary to humming a tune.

Ask your math teacher or professor if he or she became a mathematician in consequence of having a special brain. (Be sure to keep a straight face when you do this.) Almost certainly, after the laughter has subsided, it will turn out that a parent or teacher was responsible for helping your instructor discover the beauty in mathematics, and the rewards it holds for the student – and decidedly not a special brain.

Tips & Techniques: Number Sense

Here are a variety of skills that exercise and enhance Number Sense for students at different levels of ability:

Level 1: Sometimes it is faster and easier to solve math problems using Number Sense, as opposed to doing so algorithmically.
For instance, since 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55,
what is 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20?

Level 2: An important thing to understand when developing Number Sense is that mathematical terms have very concrete, specific definitions. While a thesaurus will most likely list the word “probability” as a synonym of the word “odds,” in math, the two concepts, though related, have their own separate definitions. As probability is the ratio of the “number of ways to win” to the “total number of ways things can happen,” odds are defined as the ratio of the “number of ways to win” to the “number of ways to lose.”
With this in mind, if the probability of winning a certain game is 2 to 3,
what are the odds of winning the game?

Level 3: Most of the time, when we consider the concept of absolute value from a geometric perspective, we think of it one-dimensionally, that is, a number’s absolute value is a number’s distance from 0 along a given number line. Absolute value, however, also pertains to points on a two-dimensional plane or even in a three-dimensional space. A single point’s absolute value can thus be defined as the distance of the point from the origin (0,0) on a two-dimensional plane and (0,0,0) on a three-dimensional plane.
Given this, what is the absolute value of the point with coordinates (5,12)?

Math Matters

When we want to know what time it is, reaching for a watch or a clock is second nature. Before the advent of mechanical clocks, however, people relied on other methods, like the sundial, which used the position of the sun in the sky to measure time. The oldest sundials date as far back as 3500 BC, and they have been used throughout ancient and modern times.

The basic principle behind a sundial’s functionality is that the shadow of a fixed object changes throughout the course of the day as the Earth rotates on its axis and the sun appears to move across the sky. The first sundials were essentially tall fixed objects (now referred to as the sundial’s gnomon) such as the Ancient Egyptian obelisks. Later on, the addition of marked dial faces made tracking shadows more accurate by quantifying them.

The Earth is tilted as it both rotates on its axis and revolves around the sun. Because of this, the shadows cast by the gnomon at a given time vary from day-to-day. For a more accurate dundial, gnomons were tilted to align with the Earth’s axis, that is, pointing towards true north (for  those in the northern hemisphere) or true south (for those in the southern hemisphere).

Discrepancies exist between clock time and apparent solar tim (time as measured on sundials). Due to a combination of the elliptical shape of the Earth’s orbit (as opposed to a perfect circle) and the Earth’s tilted position, the sun’s position in the sky is subsequently irregular and affects the time presented on the sundial. The difference between these two times (known as the equation of time) varies throughout the course of the year as the Earth’s position relative to the sun changes.

Student of the Month

Diamond Goodman

News

BEST Tutoring is going Live this month with 24/7 online Homework Help.  Just send an email to Math247@BESTtutoringLive.com.

November 13 – Trivia Night to benefit ABLE in St. Charles County

November 25/26/27 – Closed for Thanksgiving Holiday

November 29, 2pm – 4pm – Makeup Session from Thanksgiving Holiday

Writing Eight Exercise – By Diane Craft

A large 8, laying on its side, is drawn on a large piece of paper. A long, vertical line is drawn down the middle of the writing eight. Mark the left side of the paper as side 1, and the right side as side 2. Place an arrow going up towards side one. Draw a place for the student’s non-writing hand at the bottom of the middle line. Place a dot, or “parking place” in the middle of the vertical line. The student positions himself so that he sits right in the middle of the paper, by the vertical line. He traces the eight, always going up the middle and counterclockwise (towards side 1) for three complete circuits. He then superimposes the letters of the alphabet (lower case) on the proper side of the eight, saying the name of the letter out loud as he makes it. The letter is made just as large as the circles on the paper. In between each letter he makes he will make three full circuits of the eight before doing the next letter. Continue until the entire alphabet is done. The paper should look messy.
In this exercise, the left brain is stimulated by writing the letters, while the right brain is stimulated by going around the track. By superimposing the letters directly upon the eight, the left and right brain hemispheres learn to communicate more effectively, removing writing blocks that may have been there for years. Remember: The student goes three times around the track between each letter. The letter is made only once.
As the student begins this exercise, you may find that he might have trouble keeping his body lined up in the middle, and keeping his non-writing hand on the paper. Put your hand on his hand to remind him to keep it in place, if necessary. Keep a copy of the alphabet letters in front of the student for as long as he needs them. To effectively rehabilitate the visual/motor system, you must do the exercise four times a week for 6 months at least. The rewards of an open writing gate are great! The child’s thoughts will flow so much more easily when writing!

For tips and a video, please visit http://lifeattheevans.blogspot.com/2009/05/writing-eight-exercise.html

Tips & Techniques: Mental Math: Division

Many times, mental math is a better way to solve math problems than using an algorithm. Here are two approaches to division using mental math.

Example 1: 75/6
6 is the same is 2 x 3, so instead of dividing by 6, we can divide 75 by 3 and then divide that quotient by 2. So, 75/3 = 25, and 25/2 = 12 ½. Done!
Try these:
1) 99/6 = ______________
2) 75/15 = _____________
3) 150/12 = ____________
4) 430/20 = ____________

Example 2: 200/15
Another way to look at division is to ask yourself, “How man of these are inside of that?” For 200/25, ask yourself how many 25s are there inside of 100. There are 4 25s in 100, so inside of 200 there must be twice as any; 8. So, 200/25 = 8.
Try these:
1) 300/25 = ___________
2) 90/15 = ____________
3) 1000/125 = _________
4) 6/1 ½ = ____________

Math Matters

It is hard at first to imagine a strip of paper with only one side and only one edge, but in 1858, mathematicians discovered the Möbius strip. The Möbius strip has the interesting mathematical property of being non-orientable – unlike most surfaces we see in daily life, it has just one side! It is not possible to paint it with two colors, and an ant walking along it could go indefinitely without every coming to an edge.

To help imagine a Möbius strip, make a model at home. Take a long strip of paper, form a half-twist by turning one end over, then glue the ends together. Now start drawing a line down the center of your strip. When your line is as long as the strip, there is still blank paper in front of you! When you get back to your starting point, your line is twice as long. You drew on what we normally think of as “both sides” of the paper, but you never met an edge. This is because there is only one side! Now try other experiments like marking along the edge or cutting along your first line – you will get interesting results!

The Möbius strip was interesting to mathematicians (and magicians) in the 1800’s and has practical applications today. It has been used for long-lasting conveyor belts (that wear evenly because there is only one side), and for recording tape with twice the play time! In mathematics, the Möbius strip is of interest in the fields of geometry and topology.

Student of the Month

T. J. Klosterhoff is making great progress through Algebra II, since he’s been coming to BEST Tutoring!

News/Events

October 3 (11:00am – 4:00pm) – Scholastic Chess Tournament.  Chess builds each student’s confidence, learning that problem solving and thinking can be FUN.  Signup today to save $2.

October 17 (1:00pm – 11:00pm) – Christmas Card CropFest.  Get your cards done early, impress your friends, and trim away some holiday stress.  Yes, there will be chocolate.

October 24 – Kid City Expo at the St. Louis Science Center.  An all day event your family is sure to enjoy with special “treats” at 2pm.

November 13 – Music, Movies and Cars Trivia Night to support ABLE in St. Charles County.

Dysgraphia – Visual/Motor Processing Dysfunction Characteristics

The processing glitch that affects children the most is an interference in the writing system (spatial, visual/motor system). The process of writing has not been taken over by the child’s automatic brain, which is the right brain hemisphere. This causes the child to have to use much more energy to write. This can make a child look lazy, uncooperative and unmotivated because writing is involved in so many learning activities. See if your child has many of the following symptoms of stress in the writing system:

• Reversals in written letters both laterally and vertically, six months after being taught to write them correctly if written daily.
• Reversals in written numbers.
• Poor spacing in writing.
• Difficulty copying from book or board.
• Resistance to learning or writing cursive.
• Displaying awkward writing posture, with eye and hand very close together.
• No “helping hand” used when writing despite being instructed to do so.
• Failure to complete written assignments despite performing well on tests.
• Spaces math papers poorly.
• Tells great stories orally, but writes very little.
• Leaves out letters in a spelling test, but could spell the word orally correctly.
• Wants to do all math “in his head,” no matter how long the problem is.

Tips & Techniques: Half

Pencil-and-paper, symbolic computations with fractions should wait until a student has a firm grasp of the concepts involved from a verbal-reasoning point of view. The following exercises should be done orally with students (so we’ve written, for example, “one-half” instead of ½”.)

Addition with Half:

“One-half plus one-half equals a whole” is the basic notion for adding fractions.
Then, “two and one-half plus three and one-half” can be thought of as:
”two plus three is five” (add the whole numbers),
”one-half plus one-half equals a whole” (add the fractions), and
”five and one are six” (combine the results).

Subtraction with Half:

“Seven take-away two and one-half” is often answered by kids as “five and one-half” because they subtract the whole numbers and just “bring down” the half. They don’t realize that they must “break-into” the whole to get the answer. Here’s how to show them the right way to think about this question.

Hold up seven fingers, five on the left hand and two on the right, and say, “Here are seven.”
Next, put down the two fingers on the right hand and say, “I’ve taken away two, so how many are left?” (five)
Then say, “I have five left. Now I’ll take away half, so how much is left?” Now, fold down the first joint on the thumb of the left hand. (Four and one-half).

This demonstration will help students realize that they must “break-into” the whole.

The Science of Stars

Math is the language of science. It’s also the language of the stars – at least, the way NASA sees them. You might guess that the math used in space exploration is very advanced, and you’d be partly right; but there are also many aspects of space science that you can understand with math that you learn in high school!

One of the most basic math problems involved in any space launch is describing the space shuttle’s motion. This requires a good understanding of coordinate systems, which we use to figure out the spacecraft’s position and orientation, and also describe any changes during flight!

If we want to understand how solar radiation is absorbed into the Earth’s atmosphere, we learn about logarithms. Simple algebra helsp us compare how much farther the Hubble Space Telescope can see into the universe, than a regular telescope on the ground. By finding the Least Common Multiple of the number of years it taks Jupter (12 yrs) and Saturn (30 yrs) to revolve around the Sun, we calcuate how often we on Earth see them close together in the night sky (every 60 years!)

Over the years, space exploration has stimulated the growth of many of the concepts you learn in your math classroom today, so it’s not surprising that much of the math you learn can still be applied to understand space! So, the next time you look at the night sky, keep those lessons in mind, and soon you’ll be seeing the stars in a whole new way.

News/Events

Congratulations to Zeke, Haley, Satya, Sarvesh, Sean, Sachin and Mitul for advancing to the next level at the St. Peters Chess Club.

Happy September Birthday to Joseph, Katie, William, Alexandria, Matt and everyone we might have missed! Also Happy Birthday to the owners of BEST Tutoring, Molly & Tim!

Sept. 3: FLL Smart Move Kickoff

Sept. 7: Closed for Labor Day

Sept. 13: Molly’s Math Birthday Blast! – 2pm
Build an ice cream sundae and learn dollar tricks!

Oct. 3:  Scholastic Chess Tournament 11:30am

Ever wonder what the numbers on a dollar bill symbolize?

The bill’s serial number is the most prominently displayed set of digits on the dollar, but they’re not alone. If you take out a dollar, you’ll notice there are four large numbers in the corners of the bill’s open space. Like the encircled letter to the left of Washington’s portrait, these numbers tell which Federal Reserve Bank issued the note. (Each Fed’s number corresponds the letter of the alphabet assigned to the bank, with A=1, B=2, and so on.)

The tiny letters and numbers that appear on the top left and bottom right of the bill’s obverse indicate the position of the note on the Treasury’s printing plates. If your dollar bill has a tiny “FW” before this code, those letters indicate that it was printed at the Treasury’s facility in Fort Worth, Texas, rather than in Washington, D.C.

-Excerpt from an article by Ethan Trex: http://blogs.static.mentalfloss.com/blogs/archives/32057.html

Tips & Techniques: per CENT

Percent is an appropriate topic for first and second grade students if it is presented as an outgrowth of Counting, Wholes and Parts, and Proportional Thinking.

Percent means “parts per hundred,” “how many for each hundred”:
per – (for each) + cent (hundred, as in century, cents …).

First and second graders learn quickly that 100% is the “whole thing,” “all of it,”:

• “100% orange juice” means “made only of oranges.”
• “100% right” means “all right, none wrong.”

Kids who have learned to mentally compute half of various quantities have no trouble learning that 50% means “half of it.” After all, 50 is half of 100!

• “50% off” means “half price.”
• “50% right” means “half right, half wrong.”

Similarly, 25% means “a quarter,” since it is “half of a half” and 25 is half of 50.

Second and third grade students who have learned to count in groups and know that percent means “how many for each 100” can apply that knowledge to solve problems like:

• “How much is 15% of 300?” (Count 15 for each hundred … 3 hundreds … 15 + 15 + 15 = 45.)
• “How much is 12% of 250?” (Count 12 for each hundred … 2 whole hundreds (12 +12) and half of a hundred (6) … 12 + 12 + 6 = 30.)

Not that all these questions can be done orally, without ever using pencil and paper!

The History of the Dollar

Money plays an important role in our everyday lives. Most of us know that the word cent refers to 1/100 of a dollar, just as the word century means 100 years and the word centipede refers to an insect with 100 legs. But what do you know about the word dollar?

The word dollar is much older than the American unit of currency, and is used to refer to currency in many other countries as well. In 1519, coins were first minted in a town in Bohemia called Joachimsthal (known today as Jachymov in the Czech Republic). The word thaler was a shortened version of the original word for the coins, which were known as Joachimsthaler. The English version of thaler became dollar, and the name was applied to similar coins in Central Europe, including the Spanish peso. Pesos, or dollars, were widely circulated in Britain’s North American colonies due to a shortage of official British coins. That’s why, after the United States gained its independence, the new station chose “dollar” as the name of its currency instead of keeping the British pound.

Celebrate Math on September 13

Please join us from 2pm to 4pm for a real Math celebration to get your school year moving in the right direction.  See what’s NEW at BEST Tutoring.

Build your own sundae, play chess and learn some Dollar tricks and origami.