Monday, May 31, 2010

Why Study Math?

Why Study Math?
Math is often referred to as a universal language. Discover reasons for studying math with tips from a mathematics tutor in this free video on math lessons.

Expert: Fernando Millan
Filmmaker: Paul Muller

 

Mathematic Skills for Grades 3-6


NUMBER OPERATIONS AND CONCEPTS
  1. A+ Math  Play exciting games like Matho and Hidden Picture (+ -x /)  Also has great flashcards
  2. Builder Ted In this interactive game, students must order decimals
  3. Comparing Big Numbers
  4. Comparing fractions and decimals - Practice converting one to the other in this interactive game.
  5. Concentration Games from Harcourt Brace: Fractions/Decimal Equivalents, Fractions/Decimal Equivalents II, Fractions/Decimal Equivalents III, Equivalent fractions, Decimals, and Percents.
  6. Cash Out You're the cashier at this crazy store. You need to give change to the customers buying things. Try to sell as many items as possible before the time runs out.
  7. Change Maker Get as much money in your piggy bank as possible, by figuring out the correct change. From FunBrain
  8. Count the Goodies - This multiplication activity from Harcourt School’s Mighty Math Calculating Crew asks you to multiply using regrouping. Three problems at a time are presented.
  9. Decimal Squares Add, subtract and multiply decimals in a multitude of games. New!
  10. Divisibility Rules Simplify your math!
  11. Division Machine This activity has three levels of division for students to practice. New!
  12. Disaster Math - Six sets of interactive word problems: Earthquake Math, Hurricane Math, Tornado Math, Wild Fire Math, Winter Storm Math, and Flood Math.
  13. Fraction Shapes Explore geometric models of fractions and discover relations among them.
  14. Fractions, Decimals or Percent - two are given, you supply the third
  15. Fresh Baked Fractions Click on the fraction that is not equal to the others. From FunBrain. Easy to Super Brain
  16. Game Bone Can you find the 10 hidden bones on the 1 - 100 number square in less than a minute ? (Grade 3)
  17. Genius Boxing Punch your genius opponent by completing the number sentence using <, >, or =. (Grade 3) New!
  18. Guess the Number Developing skills in halving and estimation
  19. Interactive Activities Number and Operations
  20. I Know That!  Online Multimedia Fraction Games, Registration is free!
  21. Hooda Math Hooda Math is all about making math fun and making math easy. Teacher and Student Recommended
  22. Johnnie's Math Page Multiplication Activities
  23. Magic Math Market Discover the magic of two important mathematical concepts: fractions and decimals. (Grades 3-5)
  24. Math 5 Live Lessons> Place Value, Multiples, Factors, Primes, Fractions, Decimals, Multiplication and Division (Grade 5)
  25. Math Baseball Math practice from FunBrain (+ - x /)
  26. Math Run How fast is your brain? A simple brain training game for everyone. Begins with simple addition facts and gets progressively more difficult. New!
  27. Maths: Fractions - Revisewise-Interactive guide to fractions
  28. Maths: Number Patterns - Revisewise-Interactive guide to patterns
  29. Multiplying Fractions Practice multiplying fractions. (Grades 4-6)
  30. Number Cop Choose your game mode: select a number to practice multiples of that number, or select 'Primes' or 'Perfect Squares'. In each game type you will have a total of 50 numbers to test.
  31. National Library of Virtual Manipulatives Number & Operations (Grades 3-5)
  32. National Library of Virtual Manipulatives Number & Operations (Grades 6-8)
  33. One False Move Step into the wrong room and you'll be doomed. You are given a table of numbers.
    Click on the numbers in order from lowest to highest (or highest to lowest). (Easy-Medium-Hard)
  34. Penguin Waiter Game Figure out the tip from FunBrain
  35. Percent Problems - a one-player, or two-player Jeopardy style game from Quia
  36. Place Value Darts Use known number facts and place value to multiply and divide integers, including by 10 and then 100 (whole- number answers). (Grades 5-6)
  37. The Place Value Game -A math game requiring logic, strategy and a little luck!
  38. Place Value Puzzler Choose Place Value. Easy · Medium · Hard · Super Brain.
  39. Place Value Up to 1000 Can you put your knowledge to the test to beat Robbie the Robot? (Grade 3)
  40. Power Football   All operations with decimals. From FunBrain
  41. QUIA Math Journey  An online math activity. (+ - x /,rounding)
  42. Rounding-Fun Brain gives games (Easy, Medium, Hard, Super Brain)
  43. Rounding Off Round off numbers to significant figures, decimal places or the nearest 10, 100 or 1000. From BBC
  44. Snork's Long Division Game A step by step long division game that allows students to practice their long division skills
  45. Soccer Shootout - Multiplying Fractions from FunBrain
  46. Solving Percent Problems Using a Pyramid Grid - an interactive lesson
  47. Spy Guys Interactive Lessons>Decimals, Percents, Integers, Prime Factorization, Fractions, Problem Solving Bank (Grade 6)
  48. Tic Tac Toe Squares Get three X's in a row before the computer gets three O's in a row. From FunBrain (+ - x /) Easy to Super Brain
  49. Visual Fractions This Fractions is a collection of activities that use pie charts, number lines, and other graphics to illustrate fraction operations.
  50. Wicked Interactive Play these exciting mathematic games to improve your basic fact recall
  51. www.multiplication.com Interactive games to help teach the multiplication facts.
MEASUREMENT
  1. Beat the Clock Interactive time game
  2. Gamequarium: Math Games-Measurement
  3. Math 5 Live - Lessons> Area, Perimeter, Volume (Grade 5)
  4. Measurement Equivalents - Match game with standard equivalent measurements, such as pounds, ounces, pints, cups, etc.
  5. Measurement Game - Practice using a ruler, in inches and centimeters. FunBrain
  6. National Library of Virtual Manipulatives Measurement Manipulatives (Grades 3-5)
  7. National Library of Virtual Manipulatives Measurement Manipulatives (Grades 6-8)
  8. Spy Guys Interactive - Lessons>Area, Perimeter, Volume
  9. What Time Will It Be?
ALGEBRA
  1. Algebra Planet Blaster - Practice your math and defend your planet!
  2. Angles - Interactive game to help recognize and label acute, obtuse, and right angles.
  3. Catch the Fly - [all 4 quadrants are used] Use the keyboard to enter the x and y values of an ordered pair to help the fly catch a bug. No score is kept, each question is essentially a one question game
  4. Cool Math - Pre Algebra has a ton of really easy to follow lessons and examples that will make you a successful pre-algebra student.active game
  5. Create your own pattern - Drag shapes to create a pattern. Instructions on how to use this page in your classroom.
  6. Elapsed Time on a Clock - From Harcourt School Publishers
  7. Gamequarium: Math Games-Algebra
  8. Interactive Activities Algebra
  9. Maths: Shapes - Revisewise-Recognize properties and names of shapes
  10. Measuring Angles - Use a virtual protractor for making measurements.
  11. Measuring Angles - Investigating angles and the use of a protractor
  12. National Library of Virtual Manipulatives Algebra Manipulatives (Grades 3-5)
  13. National Library of Virtual Manipulatives Algebra Manipulatives (Grades 6-8)
  14. Number Cracker - guess what number comes next in the pattern
  15. Spy Guys Interactive - Lessons>Summarizing and Extending Patterns
  16. What's the Point - Find the x-y point on the grid.  Funbrain
DATA ANALYSIS AND PROBABILITY
  1. Data Interpretation Games - Numerous activities on using and interpreting data - Activities include bar, pie and line graphs, data collecting and much more
  2. Data Picking - While Class 8H pose for a photo, click on each student to collect data to produce a frequency table.  Next, select a chart or graph that matches your data.
  3. Graphing-Grapher - interactive column graph maker, students can change values and labels
  4. Graphing-Creating your own Graph It's easy to create and even print your own graphs.
  5. Graphing - Virtual Manipulatives Bar Chart, Histogram, Pie Chart, Venn Diagrams
  6. Interactive Activities Probability
  7. Math 5 Live - Lessons> Displaying Data, Probability (Grade 5)
  8. Mode, Mean, Median - Interactive lesson followed by activities - (UK measurements)
  9. National Library of Virtual Manipulatives Data Analysis & Probability Manipulatives (Grades 3-5)
  10. National Library of Virtual Manipulatives Data Analysis & Probability Manipulatives (Grades 6-8)
  11. Pattern Quest By using clues, and eliminating wrong guesses, the player attempts to deduce a pattern in the fewest number of guesses.
  12. Reading Charts and Graphs - students answer questions about various graphs
  13. Train Race This game can be used to extend a basic understanding of the median, mean and range. From BBC
  14. Spy Guys Interactive - Lessons>Graphs, Probability
  15. What Are Your Chances? Gain a little knowledge about probability.
  16. Bar Chart create your own bar graph using your data.
General Math Resources
A+ MATH This Web site has flashcards, math problems, and games -- all with the intent of increasing mathematical knowledge.
BBC Education Maths File   ReviseWise
Beacon Learning Center The resources posted in the Beacon database are products of professional development activities teaching a standards-based planning model.
Brainchild - twenty-four questions, followed by practice on any incorrect responses
Brain Teasers Solve these weekly brain teaser math puzzles. Brain teasers are arranged by grade level and include hints in case you need some help. From Houghton Mifflin's Education Place
Cool Math Cool Math is "designed for the pure enjoyment of mathematics." This interactive site features games, puzzles, calculators, and lesson plans.
Cyberchase Based on the award-winning TV show, this site teaches kids that math is everywhere, everyone can be good at it, and it's fun! The site includes more than 40 interactive games; as well as printable activities, Web adventures, e-cards; and much more.
Dosity.com  Provides numerous online language arts and math activities for students in grades K-8. In addition, the site provides printable work sheets.
Edustock A ThinkQuest page designed to teach what the stock market is. It includes: tutorials on the stock market, how to pick good stocks, information on a select group of companies, and it provides a FREE 20 minute delayed Stock market simulation on the World Wide Web.
FunBrain-Numbers A variety of games related to numbers and mathematics
Hooda Math Hooda Math is all about making math fun and making math easy. New and Recommended!!
I Know That-Math Online Multimedia Educational Math Games.  Registration is free!
Internet4Classrooms  Math Standards for 3rd Grade  4th Grade  5th Grade  6th Grade
Interactive Websites: Math  Provides standards-based cross curricular web resources designed to enhance online learning opportunities. These sites interact with the user usually through either a text-based or graphical user interface.
Math Advantage The activities at this site were created to accompany the Harcourt’s Math Advantage textbook series. The activities, however, relate to basic math concepts and can be used successfully with any Math program.  Kids will enjoy practicing math skills with these fun activities.
Maths File Game Show Topics covered: Algebra, Numbers, Percentages and Fractions From BBC
Maths: ReviseWise Number, Data Handling, Shape, Space & Measure, Mental Maths. From BBC
Math Playground  Features games, puzzles and hundreds of interactive word problems for elementary school students includes Math Word Problems
NCTM Illuminations  From the National Council of Teachers of Mathematics includes lesson plans, video vignettes of teaching and learning, interactive lessons for students, and an interactive version of NCTM math standards.. From Marco Polo.
NumberNut.com A free math activity site that has a huge variety of flash-based math games. Beyond the games, they also have very good descriptions of mathematical concepts 
Think Math from Harcourt School Publishers New
Visual Math This site features a free online interactive tutorial for pre-algebra students that includes games, puzzles, and animations that emphasize learning concepts by visualization.
Woodlands Math Zone Several fun online interactive activities here to help improve your mental maths skills. These pages are aimed at 7 -11 year olds. You must have Java and Flash installed to play these games.

Sunday, May 30, 2010

Double Division with 3 Digit Divisors 612416/983


Method of Vietnamese Diagram: Double the Divisor 3 Times


Method of International Diagram: Double the Divisor 3 Times

Method of Vietnamese Diagram:  Double the Divisor 5 Times
It's Easy!
Step 1 - Double, double, double.
Step 2 - Subtract off multiples.
Step 3 - Add up your answer."

Photos source: Nguyen Thi Lan Phuong, http://321math.blogspot.com

9th Vietnam Mathematical Olympiad 1970


A1.  ABC is a triangle. Show that sin A/2 sin B/2 sin C/2 < 1/4.  

A2.  Find all positive integers which divide 1890·1930·1970 and are not divisible by 45. 

A3.  The function f(x, y) is defined for all real numbers x, y. It satisfies f(x,0) = ax (where a is a non-zero constant) and if (c, d) and (h, k) are distinct points such that f(c, d) = f(h, k), then f(x, y) is constant on the line through (c, d) and (h, k). Show that for any real b, the set of points such that f(x, y) = b is a straight line and that all such lines are parallel. Show that f(x, y) = ax + by, for some constant b.  

B1.  AB and CD are perpendicular diameters of a circle. L is the tangent to the circle at A. M is a variable point on the minor arc AC. The ray BM, DM meet the line L at P and Q respectively. Show that AP·AQ = AB·PQ. Show how to construct the point M which gives BQ parallel to DP. If the lines OP and BQ meet at N find the locus of N. The lines BP and BQ meet the tangent at D at P' and Q' respectively. Find the relation between P' and Q'. The lines DP and DQ meet the line BC at P" and Q" respectively. Find the relation between P" and Q". 

B2.  A plane p passes through a vertex of a cube so that the three edges at the vertex make equal angles with p. Find the cosine of this angle. Find the positions of the feet of the perpendiculars from the vertices of the cube onto p. There are 28 lines through two vertices of the cube and 20 planes through three vertices of the cube. Find some relationship between these lines and planes and the plane p. 

Solutions

A1.
Put x = A/2, y = B/2. We have sin C/2 = sin(90o-x-y) = cos(x+y). So we need to show that sin x sin y cos(x+y) < 1/4, or (cos(x-y) - cos(x+y) )cos(x+y) < 1/2, or 2 cos(x-y) cos(x+y) < 1 + 2 cos2(x+y). But 2 cos(x-y) cos(x+y) ≤ cos2(x+y) + cos2(x-y) ≤ 1 + cos2(x+y) < 1 + 2 cos2(x+y) (since 0 < x,y < 90o

A2. Answer: k·2a7b193c197d, where k = 1, 3, 32, 33, 5, 3·5, a = 0, 1, 2, or 3, b = 0 or 1, c = 0 or 1, d = 0 or 1 (192 solutions in all) 

Solution
1890 = 2·335·7, 1930 = 2·5·193, 1970 = 2·5·197 (and 193 and 197 are prime). So 1890·1930·1970 = 2333537·193·197.

Saturday, May 29, 2010

8th Vietnam Mathematical Olympiad 1969


1.  A graph G has n + k points. A is a subset of n points and B is the subset of the other k points. Each point of A is joined to at least k - m points of B where nm < k. Show that there is a point in B which is joined every point in A. 

2.  Find all real x such that 0 < x < π and 8/(3 sin x - sin 3x) + 3 sin2x ≤ 5.  

3.  The real numbers x1, x4, y1, y2 are positive and the real numbers x2, x3, y3, y4 are negative. We have (xi - a)2 + (yi - b)2 ≤ c2 for i = 1, 2, 3, 4. Show that a2 + b2 ≤ c2. State the result in geometric language. 

4.  Two circles centers O and O', radii R and R', meet at two points. A variable line L meets the circles at A, C, B, D in that order and AC/AD = CB/BD. The perpendiculars from O and O' to L have feet H and H'. Find the locus of H and H'. If OO'2 < R2 + R'2, find a point P on L such that PO + PO' has the smallest possible value. Show that this value does not depend on the position of L. Comment on the case OO'2 > R2 + R'2.  

Solutions

2. Answer: π/2
We have 3 sin x - sin 3x = 4 sin3x. Put s = sin x. Then we want 2/s3 + 3s2 ≤ 5. Note that since 0 < x < π we have s positive. But by AM/GM we have 1/s3 + 1/s3 + s2 + s2 + s2 > 5 with equality iff s = 1, so we must have sin x = 1 and hence x = π/2. 

3. Stated geometrically, the result is: if a disk includes a point in each quadrant, then it must also include the origin. We use the fact that a disk is convex. Let Pi be the point (xi,yi). The segment P1P2 must intersect the positive x-axis. By convexity, the point of intersection, call it X, must lie in the disk. Similarly, P3P4 must intersect the negative x-axis at some point Y, which must be in the disk. Then all points of the segment XY are in the disk and hence, in particular, the origin. 

Source: http://321math.blogspot.com

Find the value of 'x' in the expression

If  a = xy / (x + y) and b = yz / (y + z) and c = zx / (z + x). Know that a, b and c are not equal to zero, find the value of x in terms of a, b and c.

Adding Fractions with Different Denominators


Adding Fractions with Different Denominators

How to Add Fractions with different denominators:
  • Find the Least Common Denominator (LCD) of the fractions
  • Rename the fractions to have the LCD
  • Add the numerators of the fractions
  • Simplify the Fraction

Adding Fractions with Unlike Denominators


Adding Fractions with Different Denominators (No LCD)

Wednesday, May 26, 2010

4th Vietnam Mathematical Olympiad 1965

1.  At time t = 0, a lion L is standing at point O and a horse H is at point A running with speed v perpendicular to OA. The speed and direction of the horse does not change. The lion's strategy is to run with constant speed u at an angle 0 < φ < π/2 to the line LH. What is the condition on u and v for this strategy to result in the lion catching the horse? If the lion does not catch the horse, how close does he get? What is the choice of φ required to minimise this distance?
2.  AB and CD are two fixed parallel chords of the circle S. M is a variable point on the circle. Q is the intersection of the lines MD and AB. X is the circumcenter of the triangle MCQ. Find the locus of X. What happens to X as M tends to (1) D, (2) C? Find a point E outside the plane of S such that the circumcenter of the tetrahedron MCQE has the same locus as X.
3.  m an n are fixed positive integers and k is a fixed positive real. Show that the minimum value of x1m + x2m + x3m + ... + xnm for real xi satisfying x1 + x2 + ... + xn = k occurs at x1 = x2 = ... = xn.

Source: Nguyễn Thị Lan Phương, http://321math.blogspot.com

3rd Vietnam Mathematical Olympiad 1964


1.  Find cos x + cos(x + 2π/3) + cos(x + 4π/3) and sin x + sin(x + 2π/3) + sin(x + 4π/3).
2.  Draw the graph of the functions y = | x2 - 1 | and y = x + | x2 - 1 |. Find the number of roots of the equation x + | x2 - 1 | = k, where k is a real constant.
3.  Let O be a point not in the plane p and A a point in p. For each line in p through A, let H be the foot of the perpendicular from O to the line. Find the locus of H.
4.  Define the sequence of positive integers fn by f0 = 1, f1 = 1, fn+2 = fn+1 + fn. Show that fn = (an+1 - bn+1)/√5, where a, b are real numbers such that a + b = 1, ab = -1 and a > b. 



Solutions


1. Using cos(A+B) = cos A cos B - sin A sin B, we have cos(x + 2π/3) = -(1/2) cos x + (√3)/2 sin x, cos(x + 4π/3) = -(1/2) cos x - (√3)/2 sin x. Hence cos x + cos(x + 2π/3) + cos(x + 4π/3) = 0. Similarly, sin(x + 2π/3) = -1/2 sin x + (√3)/2 cos x, sin(x + 4π/3) = -1/2 sin x - (√3)/2 cos x, so sin x + sin(x + 2π/3) + sin(x + 4π/3) = 0.

2. Answer
0 for k < -1
1 for k = -1
2 for -1 < k < 1
3 for k = 1
4 for 1 < k < 5/4
3 for k = 5/4
2 for k > 5/4




It is clear from the graph that there are no roots for k < -1, and one root for k = -1 (namely x = -1). Then for k > -1 there are two roots except for a small interval [1, 1+h]. At k = 1, there are 3 roots (x = -2, 0, 1). The upper bound is at the local maximum between 0 and 1. For such x, y = x + 1 - x2 = 5/4 - (x - 1/2)2, so the local maximum is at 5/4. Thus there are 3 roots at k = 5/4 and 4 roots for k ∈ (1, 5/4).


3. Answer: circle diameter AB, where OB is the normal to p


Let B be the foot of the perpendicular from O to p. We claim that the locus is the circle diameter AB. Any line in p through A meets this circle at one other point K (except for the tangent to the circle at A, but in that case A is obviously the foot of the perpendicular from O to the line). Now BK is perpendicular to AK, so OK is also perpendicular to AK, and hence K must be the foot of the perpendicular from O to the line.

4. Put a = (1+√5)/2, b = (1-√5)/2. Then a, b are the roots of x2 - x - 1 = 0 and satisfy a + b = 1, ab = -1. We show by induction that fn = (an+1 - bn+1)/√5. We have f0 = (a-b)/√5 = 1, f1 = (a2-b2)/√5 = (a+1 - b-1)/√5 = 1, so the result is true for n = 0, 1. Finally, suppose fn = (an+1 - bn+1)/√5 and fn+1 = (an+2 - bn+2)/√5. Then fn+2 = fn+1 + fn = (1/√5)(an+1(a+1) - bn+1(b+1) ) = (an+1a2 - bn+1b2)/√5, so the result is true for n+1.

Source: http://321math.blogspot.com

2nd Vietnam Mathematical Olympiad 1963

1.  A conference has 47 people attending. One woman knows 16 of the men who are attending, another knows 17, and so on up to the last woman who knows all the men who are attending. Find the number of men and women attending the conference.
2.  For what values of m does the equation x2 + (2m + 6)x + 4m + 12 = 0 has two real roots, both of them greater than -2.
3.  Solve the equation sin3x cos 3x + cos3x sin 3x = 3/8.
4.  The tetrahedron SABC has the faces SBC and ABC perpendicular. The three angles at S are all 60o and SB = SC = 1. Find its volume.
5.  The triangle ABC has perimeter p. Find the side length AB and the area S in terms of ∠A, ∠B and p. In particular, find S if p = 23.6, A = 52.7 deg, B = 46 4/15 deg.



Solutions

1. Suppose there are m women. Then the last woman knows 15+m men, so 15+2m = 47, so m = 16. Hence there are 31 men and 16 women.

2. Answer: m ≤ -3

For real roots we must have (m+3)2 ≥ 4m+12 or (m-1)(m+3) ≥ 0, so m ≥ 1 or m ≤ -3. If m ≥ 1, then -(2m+6) ≤ -8, so at least one of the roots is < -2. So we must have m ≤ -3.
The roots are -(m+3) ±√(m2+2m-3). Now -(m+3) ≥ 0, so -(m+3) + √(m2+2m-3) ≥ 0 > -2. So we need -(m+3) - √(m2+2m-3) > -2, or √(m2+2m-3) < -m-1 = √(m2+2m+1), which is always true.

3. Answer: 7½o + k90o or 37½o + k90o

We have sin 3x = 3 sin x - 4 sin3x, cos 3x = 4 cos3x - 3 cos x. So we need 4 sin3x cos3x - 3 sin3x cos x + 3 sin x cos3x - 4 sin3x cos3x = 3/8 or 8 sin x cos x(cos2x - sin2x) = 1, or 4 sin 2x cos 2x = 1 or sin 4x = 1/2. Hence 4x = 30o + k360o or 150o + k360o. So x = 7½o + k90o or 37½o + k90o.


Source: Nguyễn Thị Lan Phương, http://321math.blogspot.com

1st Vietnam Mathematical Olympiad 1962

1.  Prove that 1/(1/a + 1/b) + 1/(1/c + 1/d) ≤ 1/(1/(a+c) + 1/(b+d) ) for positive reals a, b, c, d.
2.  f(x) = (1 + x)(2 + x2)1/2(3 + x3)1/3. Find f '(-1).
3.  ABCD is a tetrahedron. A' is the foot of the perpendicular from A to the opposite face, and B' is the foot of the perpendicular from B to the opposite face. Show that AA' and BB' intersect iff AB is perpendicular to CD. Do they intersect if AC = AD = BC = BD?
4.  The tetrahedron ABCD has BCD equilateral and AB = AC = AD. The height is h and the angle between ABC and BCD is α. The point X is taken on AB such that the plane XCD is perpendicular to AB. Find the volume of the tetrahedron XBCD.
5.  Solve the equation sin6x + cos6x = 1/4.




Solutions

1. A straightforward, if inelegant, approach is to multiply out and expand everything. All terms cancel except four and we are left with 2abcd ≤ a2d2 + b2c2, which is obviously true since (ad - bc)2 ≥ 0. 

2. Differentiating gives f '(x) = (2 + x2)1/2(3 + x3)1/3 + terms with factor (1 + x). Hence f '(-1) =31/221/3

3. Let the ray AB' meet CD at X and the ray BA' meet CD at Y. If AB' and A'B intersect, then X = Y. Let L be the line through A' parallel to CD. Then L is perpendicular to AA'. Hence CD is perpendicular to AA'. Similarly, let L' be the line through B' parallel to CD. Then L' is perpendicular to BB', and hence CD is perpendicular to BB'. So CD is perpendicular to two non-parallel lines in the plane ABX. Hence it is perpendicular to all lines in the plane ABX and, in particular, to AB.

Suppose conversely that AB is perpendicular to CD. Consider the plane ABY. CD is perpendicular to AB and to AA', so CD is perpendicular to the plane. Similarly CD is perpendicular to the plane ABX. But it can only be perpendicular to a single plane through AB. Hence X = Y and so AA' and BB' belong to the same plane and therefore meet.

4. Put a = sin2x, b = cos2x. Then a and b are non-negative with sum 1, so we may put a = 1/2 + h, b = 1/2 - h. Then a3 + b3 = 1/4 + 3h2 ≥ 1/4 with equality iff h = 0. Hence x is a solution of the equation given iff sin2x = cos2x = 1/2 or x is an odd multiple of π/4. 

Source: Nguyễn Thị Lan Phương, http://321math.blogspot.com

Why Mathematics is so great?

What's correlation between the structure of the mathematical theory and object structure? My ideas about mathematics:

  •  Sign language of mathematically is a system non-contradiction.
  •  Mathematical language is a language system form of symbolic.
  •  Mathematics is a scientific inference, the type of theoretical knowledge.
  •  System of mathematical objects are determined a priori object class but applied mathematics achievement test pilot first.

Dictionary of Classical and Theoretical Mathematics

Title: Dictionary of Classical and Theoretical Mathematics
Author: Catherine Cavagnaro, William T. Haight, II
Publisher: © 2001 by CRC Press LLC
Price: $58.95
Product Description: http://www.amazon.com/Dictionary-Classical-Theoretical-Mathematics-Comprehensive/dp/1584880503

English Vietnamese Mathematics Dictionary

Title: English Vietnamese Mathematics Dictionary
Authors: Chính Đức Phan, Khanh Minh Lê, Lập Tấn Nguyễn, Thịnh Đình Lê, Thúy Công Nguyễn, Văn Bác Nguyễn.
Size: 1.126 KB

Report on Fundamental Lemma

Title: Report on Fundamental Lemma
Author: Châu Bảo Ngô, School of mathematics, Institute for Advanced Study, Princeton, NJ 08540 USA.
Url: http://www.math.ias.edu/~ngo/cdm.pdf

Monday, May 24, 2010

Class Seminar: Application of Mathematics?

In what ways do mathematics affect our lives? (Consider things like  human-based computing, statistics and probability, applied mathematics). When can information be considered property that can be protected by formal laws?

What do visual elements (pattern, shape, size, proportion, texture, color, and proximity of buildings) contribute to the identity of a city? 

References:
  • http://en.wikipedia.org/wiki/Applied_mathematics
  • http://www.ams.org/notices/200111/rev-blank.pdf

Numbers and Counting through Ten

Counting to ten with numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Counting to ten with words:
one, two, three, four, five, six, seven, eight, nine, ten

Counting to ten with objects:

first ten (10) numbers and the quantities they represent


Counting allows us to know the total number of things or objedts in a group. In order to do so, we separate the items from the group one by one, and we the next larger number to each item removed, till none is left and the total number is discovered.

In other words, counting is answering: how many? Beforehand, in order to count, we must know the unique numbers which identify each quantity of things.


Source: http://321math.blogspot.com

Saturday, May 22, 2010

English - Vietnamese Math Glossary: A

English - Vietnamese Math Glossary: A

aboutkhoảng chừng
above ở trên
asolute valuegiá trị tuyệt đối, trị số tuyệt đối
accuratechính xác
accurately label workcông việc có nhãn hiệu chính xác




act it outlàm
acute anglegóc nhọn
acute triangletam giác nhọn
addcộng, tính cộng
addend phần hay số được cộng thêm vào
additionphép cộng, tính cộng, cộng, toán cộng
addition factcơ sở lập luận của phép cộng
addition sentencemệnh đề phép cộng
addition signdấu cộng
additive inversesphần nghịch đảo tính cộng
after sau, sau khi
afternoon buổi trưa
algebra đại số
algebraic expression biểu thức đại số
algebraic patterns khuôn thức đại số
algebraic relationship mối liên hệ đại số
algebraic relationships các sự liên hệ đại số
algebraically có tính chất đại số
alike giống nhau
all tất cả
all together chung tất cả
almost gần, hầu như
amount số lượng
analog clock đồng hồ có kim chỉ giờ và phút
analyze phân tích
angle (∠) góc
angle adjacent góc kề
answer đáp số, kết quả, trả lời
ante meridian (a.m.) trước giờ ngọ (trước 12 giờ trưa)
application sự áp dụng
apply áp dụng
approach giải (bài toán), đạt tới (kết quả)
appropriate mathematical language từ toán học thích hợp
organize work xếp đặt bài toán, công việc
arc cung
area diện tích
argument lập luận, bàn luận
argument conjecture counterexample dẫn chứng dựa trên lập luận phỏng đoán
arithmetic (numeric) expression biểu thức số học
arithmetic expression biểu thức toán học
arrange xếp đặt, sắp xếp
array mảng, chuỗi số sắp theo thứ tự
as long as miễn là, với điều kiện là
associative property đặc tính liên kết
attribute liên hệ, trực thuộc
autumn (fall) mùa thu
average trung bình
axis (axes)trục

Source: http://321math.blogspot.com

Friday, May 21, 2010

How to Make Addition - Subtraction - Multiplication - Division War?

Game: Addition War

Goal: 1 – The learner will read write, model, and compute with rational numbers

Materials:  directions; a deck of cards with 4 each of the numbers 1 through 10 (available on-site); paper (preferably graph paper); pencil

Procedure
:    In problem solving, it might be helpful to think about solutions and answers as two different things. An answer is the final result to a problem, while a solution presents both the answer and the strategy by which it was found.


- Follow the directions on the worksheet, playing several rounds with the student.
- This activity is excellent for basic practice until student commits the basic facts  to memory.

Materials  1 deck of cards with 4 each of the numbers l through 10

Number of players 2-4

Object of the game To collect the most cards.

Directions Shuffle the cards and place the deck number-side down on the 
playing surface.

Each player turns over 2 cards and calls Out the sum of the 2 numbers. The player with the largest sum wins the round and takes all the cards. In case of a tie for the largest sum. each tied player turns over 2 more cards and calls ouT the sum. The player with the highest sum wins the round and takes all the cards from both plays.

Answers can be checked with an Addition Table or with a calculator.

Play continues until there are too few cards left for each player to have another turn. The player who took the most cards wins. Or, players may toss a penny to determine whether the player with the most or the fewest cards wins.

Variation Each player turns over 3 cards and finds the sum.

Advanced version Players turn over 4 cards, form two 2-digit numbers, and find the sum. Players should consider how they form their numbers since different arrangements have different sums. For example, a player turns over 2, 5, 7, and 4. 74 +  52 has a greater sum than 25 + 47. 
Game: Subtraction War

Goal: 1 – The learner will read write, model, and compute with rational numbers

Materials:    directions; a deck of cards with 4 each of the numbers 1 through 10 (available on-site); paper (preferably graph paper); pencil

Objective(s):     The learner will compute with rational numbers (Goal 7).

Materials:  directions; a deck of cards with 4 each of the numbers 1 through 10 (available on-site); paper (preferably graph paper); pencil

Procedure:    In problem solving, it might be helpful to think about solutions and answers as two different things. An answer is the final result to a problem, while a solution presents both the answer and the strategy by which it was found.
- Follow the directions on the worksheet, playing several rounds with the student.         
- This activity is excellent for basic practice until student commits the basic facts to memory.

Materials  1 deck of cards with 4 each of the numbers l through 10

Number of players 2-4

Object of the game To collect the most cards.

Directions Shuffle the cards and place the deck number-side down on the playing surface.


Each player turns over 3 cards, finds the sum of any two of the numbers, then finds the difference between the sum and the third number. The player with the largest difference takes the cards.

Example:

A 4, 8, and 3 are turned over. There are 3 combinations that will result in a positive number.
              4 +    8 = 12: 12     - 3     = 9
    3 + 8 = 11: 11 - 4 = 7   
    3 + 4 = 7  :   8 - 7 = 1
Advanced version  Players turn over cards, form two 2-digit numbers, and find the difference. Players should consider now they form their numbers. 75 - 24  has a greater difference than 57 - 42.

Game: Multiplication War

Goal: 1 – The learner will read write, model, and compute with rational numbers

Materials:  directions; a deck of cards with 4 each of the numbers 1 through 10 (available on-site); paper (preferably graph paper); pencil

Procedure:    In problem solving, it might be helpful to think about solutions and answers as two different things. An answer is the final result to a problem, while a solution presents both the answer and the strategy by which it was found.
- Follow the directions on the worksheet, playing several rounds with the student.         
- This activity is excellent for basic practice until student commits the basic facts to memory.

Materials  1 deck of cards with 4 each of the numbers l through 10

Number of players 2-4

Object of the game To collect the most cards.

Directions Shuffle the cards and place the deck number-side down on the playing surface.

The game is played the same way as Addition Top-it,  except that players find the product of the numbers instead of the sum. The player with the largest product wins the round and takes all the cards.

Answers can be checked with a Multiplication Table or with a calculator.

Variation:  Players turn over 3 cards. form a 2-digit number and multiply by the remaining number.

Game: Division War

Goal: 1 – The learner will read write, model, and compute with rational numbers

Materials:  directions; a deck of cards with 4 each of the numbers 1 through 10 (available on-site); paper (preferably graph paper); pencil

Procedure:    In problem solving, it might be helpful to think about solutions and answers as two different things. An answer is the final result to a problem, while a solution presents both the answer and the strategy by which it was found.
- Follow the directions on the worksheet, playing several rounds with the student.
- This activity is excellent for basic practice until student commits the basic facts to memory.

Materials  1 deck of cards with 4 each of the numbers l through 10

Number of players 2-4

Object of the game To collect the most cards.

Directions Shuffle the cards and place the deck number-side down on the playing surface.

Each player turns over 3 cards and uses them to generate division problems as follows.

Choose 2 cards to form The dividend. Use the remaining card as the divisor.

Divide and drop the remainder. The player with the largest quotient wins the round and takes all the cards.

Advanced version Turn over 4 cards and choose three of them to form a 3-digit number. Divide it by the remaining number. The arrangement of the numbers may result in a greater quotient. For example: 462/5 is greater than 256/4, but 654/2 is even greater.

Arithmetics Skills Test: Time, Patterns, Multiplication (Basic Facts)

Skills:  Time, Patterns, Multiplication (basic facts)


1. David James and Pitter Pan began watching a movie at 3:30.  The movie ended at 4:45.  How long was the movie? Look at a clock with hands if you need help figuring this out.
______ hours and ______  minutes long



2. Leah’s dog, Belle, buried 5 bones in the backyard on Monday.  On Tuesday, she buried 7 bones in the  backyard.  On Wednesday, she buried 9 bones.  If the pattern continues, how many bones will Belle bury on Saturday?   Make a table to help you find your answer.
Look at a clock with hands if you need help figuring this out.





3. John had two dozen fishing lures.  His father had four dozen lures. How many lures did they have in all? Show your work and label your answer.
Make a table to help you find your answer.


4. There were 8 cars in the parking lot.  Each car had 4 tires.   How many tires were in the parking lot? Show your work and label your answer.
Show your work and label your answer.



5. There were six ice skaters on the ice rink.  Each skater had two skates on.  How many skates were there in all?
Show your work and label your answer.


Sourse: http://321math.blogspot.com 

How to make Long Division with Remainders?

When we are given a long division to do it will not always work out to a whole number.
Sometimes there will be numbers left over. These are known as remainders.

e.g: 435 ÷ 25 

4 ÷ 25 = 0 remainder 4 The first number of the dividend is divided by the divisor.

The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 0 = 0 The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.
4 – 0 = 4 Now we take away the bottom number from the top number.

Bring down the next number of the dividend.
43 ÷ 25 = 1 remainder 18 Divide this number by the divisor.

The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 1 = 25 The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.
43 – 25 = 18 Now we take away the bottom number from the top number.

Bring down the next number of the dividend.
185 ÷ 25 = 7 remainder 10 Divide this number by the divisor.

The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 7 = 175 The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
185 – 175 = 10 Now we take away the bottom number from the top number.


There is still 10 left over but no more numbers to bring down.

With a long division with remainders the answer is expressed as 17 remainder 10
as shown in the diagram

Teaching Long Division and Double Division

"Teaching Double Division can help in teaching long division by reinforcing the principles of division and giving students success with a less frustrating alternative.
 
Double Division does not depend on memorizing the multiplication facts or estimating how many times one number goes into another. It may take 50% longer, but it is far less frustrating and probably easier to understand than Long Division.
 
It's Easy!
Step 1 - Double, double, double.
Step 2 - Subtract off multiples.
Step 3 - Add up your answer."

References:
  • http://www.doubledivision.org
  •  http://en.wikipedia.org/wiki/Long_division

Kids Math Games - Math Fun for Kids

   1. K-6 Math Practice - IXL: www.ixl.com/math
   2. Cool Math: www.coolmath4kids.com
   3. Education resource for K-8 Kids and Teachers: www.funbrain.com
   4. Dr Mike's Math Games for Kids: www.dr-mikes-math-games-for-kids.com


Beginning Math Activities                
  1.   BBC Education's  Number Time Games


    1. Simple Add and Subtract


      1. Test the Toad  ( + and -  problems with numbers 1-15)
      2. Little Animals Activity Center ( interactive number games for addition and subtraction)
    2. Number Recognition/Sequencing


      1. Dart Board Level 1 (recognize numbers 1-9)
      2. Find the Number  (Recognition activity for numbers 1-10)
      3. Mend the Number Square ( Place missing numbers on 1-100 grid)
      4. Count Along to 100
      5. Find One More  (matching game)
      6. Numberjacks Snap (matching game digits 1-5)
    3. Snakes and Ladders  (1 player or 2 player activity.. works like chutes and ladders)
    4. Puzzler Jigsaw  (3 levels of jigsaw puzzles:  4pieces, 9 pieces, 16 pieces)
    5. Shaper Japer Dominoes
    6. Watch Addem (Number Movies)
    7. Number Songs  
  2.  FunBrain Activities


    1. Number Recognition/Sequencing


      1. Bunny Count ( count and match numbers and characters)
      2. One False Move (sequence numbers from lowest to highest)
      3. Guess the Number (guess number with high low clues)
    2. Math Brain Activities (25 Board Games to teach skills)
  3. Funschool: Preschool


    1. Fishin'  Mission (count the number and fish and put them in the net)
    2. Stacker  (stack the blocks in sequence order)
    3. Connect the Numbers (from smallest to largest order)
  4. Learning Planet Activities


    1. Number Recognition/Counting/Sequencing


      1. Count Your Chickens ( counting activity)
      2. 1 2 3 Order  (what comes next... up to 10)
      3. Number Train ( make a train and count the cars)
  5. IXL Math Practice Activities (click on grade school level)
  6. Base 10 Count  (group ones into ten... see what number is made)
  7. Primary Math Games Index
  8. I Know That
  9. Teach R Kids
  10. KidPort Math Activities by Grade:


    1. Kindergarten
    2. First
    3. Second
    4. Third
  11. Count Us In Games
  12. Buzzing with Shapes 
  13. Shaper Japer Dominoes  
  14. Parent Help Sites


    1. At Home with Math
    2. I Know That
    3. Figure This
  15. Britannica Math Learning Activities
  16. Learning about Time

2.  Facts / Whole Numbers / Number Line                                             
  1. Addition and Subtraction Activities


    1. Addition Surprise 
    2. Can You Balance?
    3. Addition Fact Challenge 
    4. Elementary Math Games Addition
    5. 3 Digit Addition Activity 
    6. Addition of 3 Digits (using base ten blocks)
    7. Subtraction Fact Challenge 
    8. Elementary Math Games Subtraction
    9. 3 Digit Subtraction Activity 
    10. Dart Board Game (BBC simple addition.. click on control panel to change levels)
    11. Little Animals Activity Center ( interactive number games for addition and subtraction)
    12. Add It Up ( add up number tiles to get target number)
    13. Primary Math Games Index
  2. Addition or Subtraction or Multiplication or Division


    1. Spacey Math by Planet Learning ( fact [ +, -, *, / ] drill)
    2. Interactive Multiplication Games (14 different games to help with multiplication facts)


      1. Flash Fun (practice on own)
      2. Quick Flash (computer quizzes you on level chosen)
      3. Multiflyer
    3. Math Mayhem by LearningPlanet ( +, -, *, / timed practice)
    4. Math Mastery CyberChallenge (+, -, *, / timed practice)
    5. Mad Math Minute ( +, - *, / online quizzes)
    6. Multiplication Matho (race for time as you practice your facts)  
    7. Basic Multiplication Fact Challenge
    8. Basic Division Fact Challenge
    9. Break the Code (basic fact recall)
    10. Elementary Math Games Multiplication
    11. A+ Math Games  ( basic operation activities)
    12. Coloring Book Math ( color online doing math problems)
    13. Math 4 Kids  
    14. Math Activities at Syvum (Helps build basic skills)
    15. Mighty Math Calculating Crew... Multiplication Practice
    16. A+ Math Flashcards( math flashcards and math games for basic operations)
    17. Schoolhouse Flash (click on green start button bottom right of page to practice math facts... + - * /)
    18. I Know That
    19. MathO
    20. Broken Calculator
    21. Arithmetic Four
    22. Printable Math Drill Sheets  


      1. Free Math Worksheet Generator
      2. Math Worksheet Creator (Super Kids)
      3. Printable Math Fact Drill Sheets (Donna Young)
      4. Math Worksheets (Click on red links on right side of page)
      5. Math Slice
    23. Free Online Math Tests (click on purple banner at top of page)
  3. Funbrain Activities with + - * / and whole numbers


    1. Cookie Dough  ( read and write numbers on a check)
    2. Math Baseball  ( fact [ +, -, *, / ] drill)
    3. Math Baseball for 2 people ( fact [ +, -, *, / ] drill)
    4. Math Car Racing ( fun way for fact +, -, * / drills)
    5. Power Football (DECIMAL  fact [ +, -, *, / ] drill)
    6. Tic-Tac-Toe Squares ( practice with + - * / squares, cubes )
    7. Change Maker ( work with $1 or $100, pick coins / bills for change)
  4. Watch Addem (Number Movies)


3.   Factors/ Multiples/ Primes/ Powers/ Triangular Numbers
  1. Product Game  (ILLUMINATIONS NCTM) [ game of skill with factors and multiples] 
  2. Factor Game  (ILLUMINATIONS NCTM) [ game of skill with factors]
  3. Grid Game by BCC Maths File (find factors, multiples, primes, triangular numbers, and/or powers on a grid)
  4. Multiplication Mystery
  5. Multiple Matrix
4.  Fractions
  1. What is a Fraction?


    1. Who Wants Pizza (a fun way to learn about fractions)
    2. WebMath:  Get a Fraction  (get a visual picture)
    3. Math Matching...  Fractions to Models
    4. Mystery Picture with Fraction Word Problems (by Dositey)
  2. Equivalent Fractions


    1. Fraction Frenzie Activity by LearningPlanet ( match equivalent fractions before time runs out)
    2. Fraction Game Tool (Illuminations NCTM)[ move game pieces to other side of board) 
    3. Mighty Math Matching... Equivalent Fractions
    4. Fresh Baked Fractions Activity by Funbrain( find fraction that is not equivalent to the rest)
    5. Soccer Shootout  Activity  by Funbrain( addition and subtraction of fractions)
  3.  Fraction/Decimal Relationships


    1. Math Matching... Fractions and Decimal Equivalents
    2. Math Matching... MORE Fractions and Decimal Equivalents
    3. Math Matching... MORE Fractions and Decimal Equivalents
    4. Math Matching... Fractions, Decimal, % Equivalents
    5. Salon Snap Activity by BBC Maths Files ( match fractions to decimals and %)
    6. Double Fun Match Activity (Click on Fraction/Decimal)  by Funbrain (Match Fractions to Decimal Equivalent)
    7. Fraction Decimal Conversion ( JAVA games matching fractions to equivalent decimals)
  4. Finding a Least Common Multiple (LCM)
  5. Fractions
  6. All About Fractions by AAA Math (Explanation, interactive practice and challenge games about fractions)
  7. Visual Fractions  
  8. I Know That: Fractions Workshop  
  9. I Know That:  Fishy Fractions

5.  Geometry/ Area / Perimeter
  1. General Geometrical Terms


    1. Geometry Flashcards by APlusMath ( match picture to name)
    2. Geometric Terms (JAVA games with common geometric terms)
    3. Online Activities for Geometrical Terms  (from Thinkquest.. Nuts about Geometry)
    4. All About Geometry  by AAA Math ( Explanation, interactive practice and challenge games about geometry)
  2. Polygons/ Shapes /Nets


    1. Shape Database by Ambleweb
    2. Online Pattern Blocks 


      1. Designer Fractions Activity
    3. Interactives: 3 D Shapes 
    4. Nets


      1. Mighty Math.....Nets
      2. Patterns for Solids Figures (Nets)
  3. Angles


    1. Angles (WiseUp from BBC) 
    2. Angles and Terms
    3. What's My Angle (protractor activities by Ambleweb)
    4. Angle Activities by Ambleweb
    5. Measuring Angles by KidPort
    6. Banana Hunt
    7. Introduction to Angles ( JAVA games with common terms related to angles)
  4. Area/ Perimeter


    1. Math Playground: Area and Perimeter


      1. Area and Perimeter Problems to solve
    2. Shape Surveyor  Activity  by Funbrain( solve simple area/perimeter problems)
    3. Mrs Glosser's lessons on Area and Perimeter of Polygons (lessons and activity)


      1. Perimeter of Polygon (Lesson with activity)
      2. Area of Rectangles and Squares (Lesson with activity)
      3. Area of Parallelogram (Lesson with activity)
      4. Area of Triangle (Lesson with activity)
      5. Area of Trapezoid (Lesson with activity)
  5. Symmetry/ Rotations/ Reflections/ Transformations


    1. Symmetry Online Activity
    2. Perfectly Symmetrical.... Rotations
    3. Bathroom Tiles by BBC Maths File ( move bathroom tiles by rotating, reflecting, and translating the patterns) Challenging!!
  6. About Space Activities (from the Annenberg Teacher Project)


    1. I Took a Trip on a Train
    2. Plot Plans and Silhouette
    3. Shadows
  7. About Shape Activities (from the Annenberg Teacher Project)


    1. Quilts
    2. Taxicab Treasure Hunt
  8. Tangrams


    1. Tangrams by KidsCom
    2. Tangrams
    3. Tangrams (Online Tangram activities)
  9. Tessellations 


    1. What are Tessellations by Cool Math
    2. What is a Tessellation?
    3. Totally Tessellated
    4. Tessellation Tool
  10. Challenge of the 7 Cups Activity (Geometry of the Ancients) Challenging!!

6.  Graphing/ Data Collections/ Coordinate Points
  1. Create a Graph Activity (online activity... create bar graph, pie chart, line graph)
  2. Data Picking Activity by BBC Maths File ( make frequency chart and graph data)
  3. Make a BAR Graph
  4. Flash Demos for Understanding Statistics 
  5. Planet Hop Activity by BBC Maths File ( find coordinates of object & graph equation) Challenging!!
  6. What's the Point? Activity by Funbrain (graphing with coordinate points)
  7. Funbased Learning Graphing Games


    1. Easy Version Graph Game
    2. Medium Version Graph Game
    3. Hard Version Graph Game
  8. Looking for the Top Quark Game  (graphing game)
  9. Lunar Adventure Activity by LearningPlanet (graph coordinates to capture asteroids) Challenging!!
7.  Integers
  1. Line Jumper Activity by Funbrain (solve + and - INTEGER problems using the NUMBER LINE)
  2. Builder Ted Activity by BBC Maths File (activity that paces integers in numerical order)
  3. Mystery Picture with Integers (by Dositey)

8.    Online Logic Puzzles/Games
  1. Add It Up
  2. Battleship
  3. Peg Solitare
  4. Cut The Knot
  5. Cryptogram Game (decode messages... letters have been replace with other letters of the alphabet)
  6. Figure This (NCTM)
  7. Interactive Fun Puzzles (many logic puzzles for both younger and older children)
  8. Marbles and Row Puzzle
  9. Mahjongg Puzzle
  10. Math Puzzles (from Discovery School)
  11. Triple Quintzee (like yahtzee)
  12. Math Games (by Math Playground)
  13. Logic Games (by Math Playground)

9.  Mean, Mode, Median
  1. Weather Today by BBC Education (Activity, Fact Sheet, ONLINE test)
  2. Mrs Glosser's lesson on Statistics....Range, Mean, Mode, Median (online lesson and activity)


  3. Train Race Activity  by BBC Maths File ( need to use own calculator with this)
  4. AAA Statistics

10.  Measurement/ Weight
  1. Matching Customary Measures
  2. Measure It Activity by Funbrain ( read a ruler in centimeters or inches)
  3. Animal Weigh In Activity by BBC Maths File ( activity that balances weights on a scale)
11.  Missing number in the series / Patterns
  1. Patterns (BBC Wisenut) 
  2. Number Cracker   Activity by Funbrain (guess  next number in the SERIES)
  3. Geometry Pattern  Activity
  4. Number Pattern  Activity
  5. Crazy Pattern Machine
  6. Pattern Games Activity ( find missing band member to complete the pattern)

12.   PreAlgebra/ Algebra Activities
  1. Late Delivery Activity by BBC Maths File ( find value of an expression )
  2. Equation Match Activity by BBC Maths File ( matching game with = equations)
  3. Evaluating an Equation with 1 variable  by AAA Math (Explanation, interactive practice and challenge games about equations)
  4. Function Machines:


    1. Function Machine
    2. Whole Number Cruncher Machine
    3. Number Cruncher Machine
  5. Order of Operations


    1. Matho 2
    2. Order of Operations (division and addition.. by Dosity)
    3. Order of Operations Activity
    4. Math Frog Activity
    5. Order of Operations  (Mrs Glosser's online lesson and activity)
    6. Operation Order Activity by Funbrain (complete equations using 3 numbers)
  6. Solving Equations:


    1. Webwise... CLICK ON....Solving Equations with BALANCE STRATEGY
    2. Webwise... CLICK ON....Solving Equations with BALANCE STRATEGY Game  (keeps points)
    3.  Virtual Manipulative's Balance Scale ( to help solve equations)
    4. Algebra Four
  7. Guess the Number(s)


    1. Weigh the Wangdoodle  (by Math Playground)


      1. Weigh the Wangdoodle Level 1 (addition)
      2. Weigh the Wangdoodle Level 2 (multiplication)
      3. Weigh the Wangdoodle Level 3 (multiplication)
    2. Funbrain Magician  Activity
  8. Virtual Manipulative's  Algebra Tiles 
  9. Mrs Glosser's lesson...Topics in PreAlgebra (online lesson and activity)


    1. Writing Algebraic Equations for word sentences 
  10. Solving An Equation  by AAA Math (Explanation, interactive practice and challenge games about equations)
  11. Patterns, Functions, and Algebra (Learner.org)
  12. Algebra Webquests


    1. Algebra Quest
    2. March Madness
  13. Absurd Math.. Interactive pre-algebra problem solving games Challenging


    1. Nomean City  Activity
    2. Dr. Plenobius Activity
    3. The 7th Floor Activity
    4. Airtight College Activity

13.  Place Value
  1. Place Value Pirates
  2. Wise Up... Our Number System ( BBC)
  3. Me and My Math... click on Numbers and Place Value
  4. Frog Palace ( PLACE VALUE activity for ones, tens, hundreds place)
  5. WebMath: Placevalue
  6. Place Value Game
  7. All About Place Value  by AAA Math ( Explanation, interactive practice and challenge games about place value)
14.  Probability
  1. Fish Tank Activity by BBC Maths File ( guess probability of catching fish in the tank)
  2. Mrs Glosser's lesson on Probability (online lessons and activity)
  3. What Are Your Chances?  (National Center for Education Statistics) 

15.  Rounding
  1. Rounding Off Numbers Activity by BBC Maths File
  2. Estimation by Rounding Activity
  3. Place Value Puzzler Activity by Funbrain (type in rounded version of number)
  4. Rounding Flashcards
  5. Rounding Decimals to Whole Numbers Game
  6. Hangman Rounding
16.  Games and Mind Bender Puzzles
  1. Battleship
  2. Cryptogram Game (decode messages... letters have been replace with other letters of the alphabet)
  3. Enchanted Mind Java Puzzles


    1. Pentominos
    2. Tangrams
    3. Pyramid Puzzle
    4. Peg Solitaire
    5. Mastermind
    6. Knight's Tour
  4. Flash Games
  5. FunBrain Number Games
  6. Fun Math Memory Game
  7. Marbles and Row Puzzle
  8. Mahjongg Puzzle
  9. Math Brain Games
  10. Mega-Math Activities   
  11. Mental Math Tricks
  12. Peg Solitare
  13. Puzzle Picnic
  14. Reversi  
  15. Simon Says Puzzle (Click on color sequence. See how long you can go )
  16. Soma Cube Fun ( active Soma Cube puzzles)
  17. Su Doku puzzles
  18. Who wants to be a Mathionaire? 
  19. Yahtzee Game 


17.  Metric
  1. Math Matching... Metric Equivalents  
  2. Math Matching... MORE Metric Equivalents  
  3. Metric Matters (Thinkquest tutorial about metric system)
  4. Measure It Activity by Funbrain ( read a ruler in centimeters)
  5. Metrics:  British and English conversions
18 Money
  1. Learning to Use Money
  2. WebMath: Help Me Count U.S. Coins
  3. Change Maker Activity by Funbrain ( work with $1 or $100, pick coins / bills for change)
  4. Counting Change Game
  5. H.I.P Pocket Change ( by US Mint Dept)  GREAT SITE!!!


    1. Games
    2. Cartoons
    3. Time Machine
    4. Coin News
    5. Teacher Help
  6. Money by AAA Math 
  7. Fleet Kids ( Activities about money management, investing, etc.)
  8. Moneyopolis ( financial planning game )

19.  Math in Daily Life
  1. Math in Daily Life
20Math Problems of the Week/ Word Problems
  1. Word Problems for Kids
  2. Word Problems (by Math Playground))
  3. Open Ended Math Problems  
  4. Brain Teasers ( Grades 3,4,5,6,7+)
  5. Math Statistics Teaser Challenges
  6. Aunty Math Problems
  7. Figure This  ( Math index by National Science Foundation & US Dept. of Ed)
  8. Figure This (problems for Middle School students )

21.  Math questions and answers
  1. Ask Dr. Math
23.  Vocabulary
  1. Math Dictionary for Kids
  2. Harcourt Math Vocabulary
24.  Everyday Math Resources
  1. Everyday Math SAMPLE Online Games 

  1. AAA Teacher Resource Page
  2. Algebra Help
  3. Blue Webn Math
  4. Digital Math Filing Cabinet
  5. Education Planet Math Lesson Links
  6. Illuminations  by NCTM  


    1. Interactive Math Tools
    2. Selected Web Resources
    3. Internet-Based Lessons
  7. Math.com 


    1. Math.com for Teachers 
    2. Math.com for Parents
  8. Math Forum  (Math Web Units and lesson plans and more)


  9. Printable Math Drill Sheets  


    1. Math Worksheet Creator (Super Kids)
    2. Printable Math Fact Drill Sheets (Donna Young)
    3. Math Slice
  10. Math Libs
  11. Mrs. Glosser's Math Goodies
  12. Math Ideas (Math ideas/lessons for a variety of topics)
  13. Math Playground
  14. NCTM
  15. NZ Maths Home Page (lesson plan help from New Zealand)
  16. Plane Math Lesson Help  
  17. Principles and Standards for School Mathematics (NCTM)
  18. National Library of Virtual  Manipulatives 
  19. Scholastic Math Activities indexed by topics
  20. Shape and Space in Geometry (from the Annenberg Teacher Project)
  21. Teach R Kids 
  22. Online Activities by Shodor
  23. Free Online Math Tests (click on purple banner at top of page)
  24. Online Worksheets (click on red links of right side of page)