World Explorer Books - Children's Books About Exploration

Follow the Dream: The Story of Christopher Columbuswritten and illustrated by Peter Sis; ages 5 and upOver 500 years ago a little boy was born in the city of Genoa, Italy. His father was a weaver, but Christopher Columbus dreamed of faraway places, adventure, and discovery. He observed the ships that sailed into the harbor and listened to the sailors and merchants as they told tales of their

Exploration Kids Books - American Exploer Books

Who Was First? Discovering the AmericasRussell Freedman; ages 11 and upHistorian Russell Freeman explores the various claims to the "discovery" of the American continents. Every U.S. school child knows the story of Columbus, but what about the Chinese explorer, Zheng He? This lavishly illustrated volume traces explorers' journeys with archival maps, charts, and timelines. Freeman discusses the

Reading Readiness Books: ages 3-4

Get your 3 to 4 year old ready to read and learn with these age-appropriate story recommendations.How can we help our children as they are learning to read?  One of the building blocks of reading competency is phonetic awareness. What are the sounds that make up a written word? Phonemic awareness refers to the ability to hear and tell the difference between words, sounds, and syllables in

Best Music Books For Children

Teach your child all about instruments, melody, and more with these recommended music books for preschoolersKids Go!by They Might Be Giants; illustrated by Pascal CampionHipster rock group They Might Be Giants return after their Grammy-winning CD for kids, Here Come the 123s, with a book and song combination to get kids off the couch and get moving. The song was originally created in 2008 for a

Top 10 Kids Math Web Sites

FunbrainA math arcade and interactive math games are only two of the many features of this site, which offers games in a wide variety of topics. Classic games on this site include math car racing. Check out the teacher's resource page and the curriculum guide. Time4LearningComplete online curriculum for preschool through the eighth grade. 

Middle School Educational Software

QuickStudy English VocabularyTake the quick path to writing success! Quickstudy English Vocabulary provides a solid educational foundation that will raise grades and test scores and improve vocabulary and writing skills in the classroom and beyond. The curriculum-based lessons are designed by educators to help students expand their vocabulary in an engaging, interactive learning

Software For Kids

Millie's Math HouseDevelop a love for math with Millie! In seven fun-filled activities, kids explore fundamental math concepts as they learn about numbers, shapes, sizes, quantities, patterns, sequencing, addition, and subtraction. They count critters, build mouse houses, create crazy-looking bugs, make jellybean cookies for Harley the horse, and find just the right shoes for Little,

Best Books for 10 Year Old Boys

There are many overlaps between books ‘for’ boys and books ‘for’ girls (and the gender divide was really driven by the twitter enquiry that prompted the list of best books for girls), but there are differences too. However much of an old-style Doc-Marten-wearing feminist Kate was (is…), and however much she swore that she would not encourage her own children into gender stereotypes, she’s come to

5th Grade Math Worksheets - 5th Grade Math Test (3)

Question 1: 6.2% written as a decimal is: 0.620.0620.00626.2Question 2: 13/25 may be written as a percent as:13%26%44%52%Question 3: 74 - 73 = 4924013432058Question 4: There are 12 milk containers in a box. Each container weighs 5/6 pounds. How many pounds does the box weigh?12 pounds5 pounds10 pounds8 poundsQuestion 5: m = 15n + 2What is m if n = 3?m = 2m = 15m = 45m = 47Question 6: 2(6x - 1) =

Math 5th Grade Test - 5th Grade Math Test (2)

Question 1: What is the perimeter of the rectangular in the figure below?6.2m6.6m8m8.2mQuestion 2: What is the area of triangle ABC if AD = BC = 6 inches?12 square inches16 square inches18 square inches22 square inchesQuestion 3: Which of the following is not a composite number?13141516Question 4: A group of middle school student has made $46.5 by selling lemonade. They charged $1.5 for a cup of

Math 5th Grade Test - 5th Grade Math Test (1)

Question 1: 4521 × 613 = 1,771,3731,871,3732,871,3732,771,373Question 2: 4/5 - 1/2 =3/102/51/103/5Question 3: How many integers between 1 and 50 contain the digit 3?12141518Question 4: A middle school has 116 students enrolled in four classes. If there is an equal number of students in each class, what is a way to determine the number of students in 5th grade?subtract 4 from 116add 116 to

15th Swedish Mathematical Society Problems 1975

1.  A is the point (1, 0), L is the line y = kx (where k > 0). For which points P (t, 0) can we find a point Q on L such that AQ and QP are perpendicular?2.  Is there a positive integer n such that the fractional part of (3 + √5)n > 0.99? 3.  Show that an + bn + cn ≥ abn-1 + bcn-1 + can-1 for real a, b, c ≥ 0 and n a positive integer. 4.  P1,

14th Swedish Mathematical Society Problems 1974

1.  Let an = 2n-1 for n > 0. Let bn = ∑r+s≤n aras. Find bn - bn-1, bn - 2bn-1 and bn.2.  Show that 1 - 1/k ≤ n(k1/n - 1) ≤ k - 1 for all positive integers n and positive reals k. 3.  Let a1 = 1, a2 = 2a1, a3 = 3a2, a4 = 4a3, ... , a9 = 9a8. Find the last two digits of a9. 4.  Find all polynomials p(x) such that p(x2) = p(x)

13th Swedish Mathematical Society Problems 1973

1.  log82 = 0.2525 in base 8 (to 4 places of decimals). Find log84 in base 8 (to 4 places of decimals). 2.  The Fibonacci sequence f1, f2, f3, ... is defined by f1 = f2 = 1, fn+2 = fn+1 + fn. Find all n such that fn = n2. 3.  ABC is a triangle with ∠A = 90o, ∠B = 60o. The points A1, B1, C1 on BC, CA, AB respectively are such that

12th Swedish Mathematical Society Problems 1972

1.  Find the largest real number a such that x - 4y = 1, ax + 3y = 1 has an integer solution. 2.  A rectangular grid of streets has m north-south streets and n east-west streets. For which m, n > 1 is it possible to start at an intersection and drive through each of the other intersections just once before returning to the start? 3.  A steak

11th Swedish Mathematical Society Problems 1971

1.  Show that (1 + a + a2)2 < 3(1 + a2 + a4) for real a ≠ 1. 2.  An arbitrary number of lines divide the plane into regions. Show that the regions can be colored red and blue so that neighboring regions have different colors. 3.  A table is covered by 15 pieces of paper. Show that we can remove 7 pieces so that the remaining 8 cover at least 8/15 of

10th Swedish Mathematical Society Problems 1970

1.  Show that infinitely many positive integers cannot be written as a sum of three fourth powers of integers. 2.  6 open disks in the plane are such that the center of no disk lies inside another. Show that no point lies inside all 6 disks.3.  A polynomial with integer coefficients takes the value 5 at five distinct integers. Show that it does not take the value 9

9th Swedish Mathematical Society Problems 1969

1.  Find all integers m, n such that m3 = n3 + n. 2.  Show that tan π/3n is irrational for all positive integers n. 3.  a1 ≥ a2 ≥ ... ≥ an is a sequence of reals. b1, b2, b3, ... bn is any rearrangement of the sequence B1 ≥ B2 ≥ ... ≥ Bn. Show that ∑ aibi ≤ &sum aiBi. 4.  Define g(x) as the largest value of |y2 - xy| for

8th Swedish Mathematical Society Problems 1968

1.  Find the maximum and minimum values of x2 + 2y2 + 3z2 for real x, y, z satisfying x2 + y2 + z2 = 1. 2.  How many different ways (up to rotation) are there of labeling the faces of a cube with the numbers 1, 2, ... , 6? 3.  Show that the sum of the squares of the sides of a quadrilateral is at least the sum of the squares of the diagonals. When

7th Swedish Mathematical Society Problems 1967

1.  p parallel lines are drawn in the plane and q lines perpendicular to them are also drawn. How many rectangles are bounded by the lines? 2.  You are given a ruler with two parallel straight edges a distance d apart. It may be used (1) to draw the line through two points, (2) given two points a distance ≥ d apart, to draw two parallel lines, one

6th Swedish Mathematical Society Problems 1966

1.  Let {x} denote the fractional part of x = x - [x]. The sequences x1, x2, x3, ... and y1, y2, y3, ... are such that lim {xn} = lim {yn} = 0. Is it true that lim {xn + yn} = 0? lim {xn - yn} = 0? 2.  a1 + a2 + ... + an = 0, for some k we have aj ≤ 0 for j ≤ k and aj ≥ 0 for j > k. If ai are not all 0, show that a1 + 2a2 + 3a3 + ..

5th Swedish Mathematical Society Problems 1965

1.  The feet of the altitudes in the triangle ABC are A', B', C'. Find the angles of A'B'C' in terms of the angles A, B, C. Show that the largest angle in A'B'C' is at least as big as the largest angle in ABC. When is it equal? 2.  Find all positive integers m, n such that m3 - n3 = 999. 3.  Show that for every real x ≥ ½ there is an integer n such

4th Swedish Mathematical Society Problems 1964

1.  Find the side lengths of the triangle ABC with area S and ∠BAC = x such that the side BC is as short as possible. 2.  Find all positive integers m, n such that n + (n+1) + (n+2) + ... + (n+m) = 1000. 3.  Find a polynomial with integer coefficients which has √2 + √3 and √2 + 31/3 as roots. 4.  Points H1, H2, ... , Hn are arranged in the

3rd Swedish Mathematical Society Problems 1963

1.  How many positive integers have square less than 107? 2.  The squares of a chessboard have side 4. What is the circumference of the largest circle that can be drawn entirely on the black squares of the board? 3.  What is the remainder on dividing 1234567 + 891011 by 12?

Top 10 Maths Books

Lecture Notes on Mathematical Olympiad Courses: For Junior Section (Mathematical Olympiad Series) http://amzn.to/OlympiadCoursesAmazon.com: Lecture Notes on Mathematical Olympiad Courses: For Junior Section (Mathematical Olympiaamzn.toAmazon.com: Lecture Notes on Mathematical Olympiad Courses: For Junior Section (Mathematical Olympiad Series) (9789814293532): Xu Jiagu: Books 15 000 problems

Geography Books

Free world geography quiz & games at http://www.worldgeographyquiz.net

Scientific Method Limitations

ntroduction to Scientific Method Limitations:              This article is showing the limitations for scientific method. Scientific method is otherwise said to be as scientific notation which helps to show the big numbers into simplest form of a number. Scientific method is of positive and negative method. Example for scientific Method:Positive Method: 170000000 this can be expressed as

How to do long division with two digit quotients?

We've learned that we can figure out the single-digit quotient, or answer, for two-digit divisor problems using estimation. This time around, we'll use estimation to determine two-digit quotients for two-digit divisor problems.Let's look at this division problem, which has a two-digit quotient:To start, it's important to determine the first part of 741 that we can divide by 32. That

Two-digit divisor in long division - How to do long division with 2 digit divisor?

When the divisor has two digits, the procedure works the same way but instead of using facts from multiplication tables when dividing, we might have to use pencil and paper to perform helping multiplications on the side, so to speak. 14    7  4  3  4  14 goes into 7 zero times, so we look at 74. To find how many times does 14 go into 74, you probably have to do

How to do long division with 2 digit divisor

Introduction of division with 2 digit divisor:          In mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that is the inverse of multiplication.Specifically, if c time’s b equals a, written:           c x b = aWhere b is not zero, then a divided by b equals c, written:             = c.In the above expression, a is called the dividend. Source: Wikipedia

Long Division of Polynomials Step by Step

Introduction to long division of polynomials:               In arithmetic, long division is the standard procedure suitable for dividing simple or complex multi digit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient.  (Source

Math Games and Activities for kids

Mathematics is said to be the study of the structure, change, quantity and space. Mathematicians, or those who work in this field, tend to study patterns and conjectures using the principles of deduction derived from definitions and axioms. Looking at this definition of mathematics, you will certainly remember those days when you were dreaded by the thought of learning math. Well, your kids

The Free Ride In Public Schools

To protect children's self-esteem or deflect complaints by parents, many public schools today automatically advance failing students to the next grade level. In other schools, some students are left back a maximum of one year, then promoted again regardless of their academic skills.The No Child Left Behind Act tries to solve this problem. The federal government is pressuring public schools to set

Math Homework Help

Are you struggling with mathematics in school or college, TutorsOnnet math tutoring can provide help in a convenient and effective way. Math can be a major struggle for children ' starting in Grade 1 and continuing throughout their high school years and beyond. Children who find the subject less intuitive than others can often face hours of frustrating homework, alongside equally frustrated

49th Eötvös Competition Problems 1945

1.  Knowing that 23 October 1948 was a Saturday, which is more frequent for New Year's Day, Sunday or Monday? 2.  A convex polyhedron has no diagonals (every pair of vertices are connected by an edge). Prove that it is a tetrahedron.

43rd Eötvös Competition Problems 1939

1.  Show that (a + a')(c + c') ≥ (b + b')2 for all real numbers a, a', b, b', c, c' such that aa' > 0, ac ≥ b2, a'c' ≥ b'2. 2.  Find the highest power of 2 dividing 2n! 3.  ABC is

42nd Eötvös Competition Problems 1938

1.  Show that a positive integer n is the sum of two squares iff 2n is the sum of two squares. 2.  Show that 1/n + 1/(n+1) + 1/(n+2) + ... + 1/n2 > 1 for integers n > 1. 3.  Show that for

41st Eötvös Competition Problems 1937

1.  a1, a2, ... , an is any finite sequence of positive integers. Show that a1! a2! ... an! < (S + 1)! where S = a1 + a2 + ... + an. 2.  P, Q, R are three points in space. The circle CP passes through Q and R, the circle CQ passes through R and P, and the circle CR passes through P and Q. The tangents to CQ and CR at P coincide. Similarly, the

40th Eötvös Competition Problems 1936

1.  Show that 1/(1·2) + 1/(3·4) + 1/(5·6) + ... + 1/( (2n-1)·2n) = 1/(n+1) + 1/(n+2) + ... + 1/(2n). 2.  ABC is a triangle. Show that, if the point P inside the triangle is such that the triangles PAB, PBC, PCA have equal area, then P must be the centroid.

36th Eötvös Competition Problems 1932

1.  Show that if m is a multiple of an, then (a + 1)m -1 is a multiple of an+1. 2.  ABC is a triangle with AB and AC unequal. AM, AX, AD are the median, angle bisector and altitude. Show that X always lies between D and M, and that if the triangle is acute-angled, then angle MAX < angle DAX. 3.  Find the

34th Eötvös Competition Problems 1930

1.  How many integers (1) have 5 decimal digits, (2) have last digit 6, and (3) are divisible by 3? 2.  A straight line is drawn on an 8 x 8 chessboard. What is the largest possible number of the unit squares with interior points on the line? 3.  A circle or

29th Eötvös Competition Problems 1925

1.  Given four integers, show that the product of the six differences is divisible by 12. 2.  How many zeros does the the decimal representation of 1000! end with? 3.  Show that the inradius of a right-angled

27th Eötvös Competition Problems 1923

1.  The circles OAB, OBC, OCA have equal radius r. Show that the circle ABC also has radius r. 2.  Let x be a real number and put y = (x + 1)/2. Put an = 1 + x + x2 + ... + xn, and bn = 1 + y + y2 + ... + yn. Show that ∑0n am (n+1)C(m+1) = 2n bn, where aCb is the binomial coefficient a!/( b! (a-b)! ). 3.  Show that an infinite arithmetic progression

26th Eötvös Competition Problems 1922

1.  Show that given four non-coplanar points A, B, P, Q there is a plane with A, B on one side and P, Q on the other, and with all the points the same distance from the plane. 2.  Show that we cannot factorise x4 + 2x2 + 2x + 2 as the product of two quadratics with integer coefficients. 3.  A, B are two points inside a given

23rd Eötvös Competition Problems 1916

1.  a, b are positive reals. Show that 1/x + 1/(x-a) + 1/(x+b) = 0 has two real roots one in [a/3, 2a/3] and the other in [-2b/3, -b/3]. 2.  ABC is a triangle. The bisector of ∠C meets AB at D. Show that CD2 < CA·CB. 3.  If d is the

19th Eötvös Competition Problems 1912

1.  How many n-digit decimal integers have all digits 1, 2 or 3. How many also contain each of 1, 2, 3 at least once? 2.  Prove that 5n + 2 3n-1 + 1 = 0 (mod 8). 3.  ABCD is a quadrilateral with vertices in

18th Eötvös Competition Problems 1911

1.  Real numbers a, b, c, A, B, C satisfy b2 < ac and aC - 2bB + cA = 0. Show that B2 ≥ AC. 2.  L1, L2, L3, L4 are diameters of a circle C radius 1 and the angle between any two is either π/2 or π/4. If P is a point on the circle, show that the sum of the fourth powers of the distances from P to the four diameters is 3/2. 3.  ABC is a triangle with angle C = 120o. Find the

16th Eötvös Competition Problems 1909

1.  Prove that (n + 1)3 ≠ n3 + (n - 1)3 for any positive integer n. 2.  α is acute. Show that α < (sin α + tan α)/2. 3.  ABC is a triangle. The feet of the altitudes from A, B, C are P, Q, R respectively, and P,

15th Eötvös Competition Problems 1908

1.  m and n are odd. Show that 2k divides m3 - n3 iff it divides m - n. 2.  Let a right angled triangle have side lengths a > b > c. Show that for n > 2, an > bn + cn. 3.  Let the vertices of a regular

14th Eötvös Competition Problems 1907

1.  Show that the quadratic x2 + 2mx + 2n has no rational roots for odd integers m, n. 2.  Let r be the radius of a circle through three points of a parallelogram. Show that any point inside the parallelogram is a distance ≤ r from at least one of its vertices. A2.  ABC is a triangle. The incircle has center I and

15th Iberoamerican Mathematical Olympiad Problems 2000

15th Iberoamerican Mathematical Olympiad Problems 2000A1.  Label the vertices of a regular n-gon from 1 to n > 3. Draw all the diagonals. Show that if n is odd then we can label each side and diagonal with a number from 1 to n different from the labels of its endpoints so that at each vertex the sides and diagonals all have different labels.

14th Iberoamerican Mathematical Olympiad Problems 1999

A1.  Find all positive integers n < 1000 such that the cube of the sum of the digits of n equals n2. A2.  Given two circles C and C' we say that C bisects C' if their common chord is a diameter of C'. Show that for any two circles which are not concentric, there are infinitely many circles which bisect them both. Find the locus of the centers of the

13th Iberoamerican Mathematical Olympiad Problems 1998

A1.  There are 98 points on a circle. Two players play alternately as follows. Each player joins two points which are not already joined. The game ends when every point has been joined to at least one other. The winner is the last player to play. Does the first or second player have a winning strategy? A2.  The incircle of the triangle ABC touches BC, CA, AB

12th Iberoamerican Mathematical Olympiad Problems 1997

A1.  k ≥ 1 is a real number such that if m is a multiple of n, then [mk] is a multiple of [nk]. Show that k is an integer. A2.  I is the incenter of the triangle ABC. A circle with center I meets the side BC at D and P, with D nearer to B. Similarly, it meets the side CA at E and Q, with E nearer to C, and it meets AB at F and R, with F nearer to A. The

11th Iberoamerican Mathematical Olympiad Problems 1996

A1.  Find the smallest positive integer n so that a cube with side n can be divided into 1996 cubes each with side a positive integer. A2.  M is the midpoint of the median AD of the triangle ABC. The ray BM meets AC at N. Show that AB is tangent to the circumcircle of NBC iff BM/MN = (BC/BN)2.

Amazing Number Facts No (part 2)

Here is a remarkable formula: f(n) = n2-n+41 f(1) = 12-1+41 = 41 a prime number f(2) = 22-2+41 = 43 a prime number f(3) = 32-3+41 = 47 a prime number f(4) = 42-4+41 = 53 a prime number   How many prime numbers does this formula produce? A formula that always produces prime numbers in this way has never been found. So just how

Amazing Number Facts No (part 1)

Since 32 + 42 = 52 does it follow that 33 + 43 + 53 = 63 ? Check it out ! Does this pattern continue to be true?The factors of 28 (not including itself) are 1, 2, 4, 7 and 14. Astonishingly these

7th Junior Balkan Mathematical Olympiad Problems 2003

1.  Let A = 44...4 (2n digits) and B = 88...8 (n digits). Show that A + 2B + 4 is a square. 2.  A1, A2, ... , An are points in the plane, so that if we take the points in any order B1, B2, ... , Bn, then the broken line B1B2...Bn does not intersect itself. What is the largest possible value of n? 3.  ABC is a triangle. E, F are

3rd Junior Balkan Mathematical Olympiad Problems 1999

1.  a, b, c are distinct reals and there are reals x, y such that a3 + ax + y = 0, b3 + bx + y = 0 and c3 + cx + y = 0. Show that a + b + c = 0. 2.  Let an = 23n + 36n+2 + 56n+2. Find gcd(a0, a1, a2, ... , a1999). 3.

1st Junior Balkan Mathematical Olympiad Problems 1997

1.  Show that given any 9 points inside a square side 1 we can always find three which form a triangle with area < 1/8. 2.  Given reals x, y with (x2 + y2)/(x2 - y2) + (x2 - y2)/(x2 + y2) = k, find (x8 + y8)/(x8 - y8) + (x8 - y8)/(x8 + y8) in terms of k. 2.  A square is divided into n parallel strips (parallel to

13th All Soviet Union Mathematical Olympiad Problems 1979

1.  T is an isosceles triangle. Another isosceles triangle T' has one vertex on each side of T. What is the smallest possible value of area T'/area T? 2.  A grasshopper hops about in the first quadrant (x, y >= 0).

12th All Soviet Union Mathematical Olympiad Problems 1978

1.  an is the nearest integer to √n. Find 1/a1 + 1/a2 + ... + 1/a1980. 2.  ABCD is a quadrilateral. M is a point inside it such that ABMD is a parallelogram. ∠CBM = ∠CDM. Show that ∠ACD = ∠BCM. 3.  Show that there is no

10th All Soviet Union Mathematical Olympiad Problems 1976

1.  50 watches, all keeping perfect time, lie on a table. Show that there is a moment when the sum of the distances from the center of the table to the center of each dial equals the sum of the distances from the center of the table to the tip of each minute hand.

1st All Russian Mathematical Olympiad Problems 1961

1.  Given 12 vertices and 16 edges arranged as follows:Draw any curve which does not pass through any vertex. Prove that the curve cannot intersect each edge just once. Intersection means that the curve crosses the edge from one side to the other. For example, a circle which had one of the edges as tangent would not intersect that edge.

Hatching the Pot

In the last column, I discussed ellipses and how drawing them involves the fluid, fairly fast movement of the hand, letting your reflexes carry out the kind of rounded shape you intend to make. Now we’ll move on to shading the pot that we previously described in simple outline, using curving lines that are like segments of the ellipse.James McMullanThese are what I think of as “cat stroking