MathNotations

Thursday, January 4, 2007

Subscribe to: Post Comments (Atom)

I hope you enjoy the math challenges and discussion on this site. If you have any questions, you can contact me using the new contact form in the sidebar.

When using or adapting any of the materials on this site which I have personally developed, please include proper attribution by indicating that "This investigation (activity, problem) was authored by Dave Marain." Please read and adhere to the Creative Commons License below. Thank you.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

Subscribe To MathNotations!

Site Meter

Featured in Alltop Link here to see MathNotations' ranking and other math sites/blogs as well.

Feedjit Live Blog Stats

• Washington Post Link

READ/LEARN ALL OF THE FOLLOWING!

ZERO IS A 'WEIRDO'!
(W)hole
(E)ven
(I)nteger
(R)Rational/Real
(DO) Cannot Divide by O!
BUT Zero is NOT Positive and NOT Negative!

POSITIVE INTEGERS start from 1

PRIMES start from 2 (not 1)

INTEGERS can be NEGative (and zero!) as well as positive

MEMORIZE the formula for the nth term of an arithmetic sequence: a(n) = a(1) + (n-1)d.
Example: Consider the sequence of positive integers which leave a remainder of 3 when divided by 4. What is the 100th term?
Step 1: List the first few terms 3,7,11,15,... to see the pattern and recognize it is an arithmetic sequence.
Step 2: Identify the values which are given
First term or a(1) = 3
Common difference or d = 4
Number of terms or position of desired term or n = 100
Step 3: Substitute into formula and solve
a(100) = a(1) + (100-1)(4) = 3 + (99)(4) = 399

Of course there are other ways to find the 100th term such as 100 x 4 - 1 but the formula is so useful for so many types of questions it is worth learning!

Know the above by heart and you are way ahead of the game! These facts will absolutely be needed on your next SAT or standardized test!

• There are twice as many girls as boys: 2G = B or G = 2B?

  The English language has many confusing phrases but " as many as " IMO has blighted the youth of many an algebra student. Perhap...
• 1,2,2,3,3,3,4,4,4,4,... What is the 2008th term? SAT-type Questions vs. Math Contest Problems

  Don't forget to submit the name of our Mystery Mathematician. Contest ends around 4-15-08. Thus far, only one correct submission (emaile...
• 'Half as many as' vs 'Twice as many as' Revisited

  OVERVIEW Hundreds of math posts over the last 6+ years and my most popular post is still by far "There are twice as many girls as boy...
• Top Ten Lists of Common (Student) Math Errors!

  If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar.  175 problems divided ...
• Inscribed Square in Right Triangle Investigation

  If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar.  175 problems divided ...
• M^2 - N^2 = 12...Prove there is only one solution in positive integers and much more

  Update: (1) See the visualization for the difference of squares posted on 1-9-08. (2) Read the comments in this post for considerable clari...
• The temperature changed from -5 to 5 degrees. The percent increase was (A) 10% (B) 50% (C) 100% (D) 200% (E) 300%

  Many readers of this post objected to the scientific fallacy in asking for per cent change in temperature even if the arithmetic is correct....
• (no title)

  Use new contact form at top of right sidebar to contact me directly. Note: If you'd like detailed solutions and Common Core strategies ...
• Challenging Geometry: Circles Inscribed in Quadrilaterals, Right Triangles

  If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar.  175 problems divided ...
• Video Solution and Discussion of Twitter SAT Probability Question from 8-25-10

  If interested in purchasing my NEW  2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar.  175 problems divided ...

Click on Globe for enlargement.

[フレーム]

• Mathematical Paradoxes

Highly recommended extensive data comparison of academic institutions' libraries. Many other comparisons of all types are available too, including blogs.

Academic Libraries

PostRank Topblogs 2009 - #8 in Math

Math Notations at Blogged

• Prof. Lynn Arthur Steen (2 Parts)
• Alec Klein (3 Part)
• Professor William Schmidt (TIMSS Director)

1/9801 = 0.00010203040506... has to start repeating at some point but how far will the pattern continue? Link here to find out and much more!

• ADP Assessment Overview (Alg I & II)
• Algebra I Test Overview
• ADP Algebra II Overview (Main Site)

RESULTS ARE NOW POSTED! CLICK HERE !

CLICK HERE FOR DETAILS!

Here's the link!

Click here for a weekly update of this fabulous site!

• Ars Mathematica
• Carnival of Mathematics
• Continuities
• Drat These Greeks!
• dy/dan
• e's ponderings
• Geomblog
• Good Math, Bad Math
• Homeschool Math Blog
• jd2718
• Joanne Jacobs
• john kemeny
• kitchen table math
• Let's play math!
• Math Concepts Explained
• Mathematics Weblog
• MathMom
• MathNEXUS
• Meeyauw
• Polymathematics
• squareCircleZ
• Text Savvy
• Unapologetic Mathematician
• Vlorbik on Math Ed
• Wild About Math

• 0.999...=1 (1)
• 1-significant digit estimation (1)
• 3-4-5 triangles (3)
• 3-dimensional geometry (2)
• 3-dimensional graphing (1)
• 30-60-90 (3)
• 6/pi^2 (1)
• A Class Apart (3)
• absolute value (2)
• ac-method of factoring (2)
• achieve (10)
• activities (3)
• activity (1)
• ADP (1)
• ADP Algebra 1/2 questions (1)
• ADP Algebra 2 questions (2)
• advanced algebra (27)
• advice for parents (1)
• age problem (1)
• Alec Klein (4)
• algebra (38)
• Algebra 1 end of course test (2)
• algebra 1 standards (1)
• algebra 2 (33)
• algebra 2 end of course test (6)
• algebra 2 standards (4)
• algebra for all (1)
• Algebra I Standards (1)
• algebra sense (1)
• algebra standards (1)
• algorithms (4)
• alphametic (1)
• altitude on hypotenuse (1)
• AM-GM Inequality (2)
• AMC (1)
• american diploma project (8)
• amortization (2)
• anagram (2)
• AP Calculus (1)
• AP Courses/Policies (1)
• application (1)
• approximation (2)
• archimedes (1)
• area (9)
• arithmetic sequence (5)
• arithmetic-geometric mean inequality (1)
• arrangements (1)
• assessment (3)
• asymptotes (1)
• average rates (2)
• averages (4)
• balanced view (3)
• binary representation (1)
• Bingo (1)
• binomial probability (2)
• book review (4)
• calculus (18)
• careless errors (1)
• Carnegie Report (1)
• carnival of mathematics (14)
• Cauchy (1)
• CCSS (1)
• CCSSM (1)
• chain rule (2)
• Challenge Problem (1)
• chaos (1)
• chess (1)
• children's anecdotes (1)
• circle problems (1)
• circles (19)
• clock problems (2)
• coin problem (1)
• coincidence (1)
• combinatorial math (18)
• Common Core (9)
• common math errors (1)
• completing the square (1)
• complex numbers (3)
• compound interest (4)
• compound probability (2)
• concept (2)
• conceptual understanding (3)
• cone (3)
• cone in sphere (2)
• congruences (1)
• conjecture (1)
• conjugates (1)
• connections (2)
• contest (16)
• coomon core (1)
• coordinate problems (13)
• core curriculum standards (2)
• counting problems (8)
• critical thinking (2)
• cubes (2)
• curriculum (6)
• cylinders (1)
• dedication (2)
• deductive reasoning (2)
• Desmos (3)
• developing thinking skills (1)
• differentiation (1)
• digit problems (5)
• Diophantine equation (2)
• direct instruction (1)
• direct variation (1)
• discovery learning (2)
• discrete math (5)
• dissection (1)
• distribution (1)
• distributive property (1)
• divisibility (4)
• division algorithm (2)
• division concept (1)
• dodecagon (1)
• early years (1)
• education (1)
• educational philosophy (1)
• egyptian fractions (1)
• elections (1)
• ellipse (1)
• Escalante (2)
• estimation (2)
• Euler (1)
• Experimental mathematics (1)
• explain (1)
• Exploration (1)
• explorations (4)
• exponential function (4)
• exponents (10)
• factoring (3)
• factoring by grouping (1)
• factoring quadratic trinomials (1)
• factors (8)
• fallacies (1)
• famous mathematicians (6)
• featured blogs (2)
• financial math (2)
• fractions (7)
• Friday the 13th (1)
• fun problems (1)
• functional notation (1)
• functional relationships (2)
• functions (8)
• games (3)
• Gauss Circle Problem (1)
• gcf (1)
• generalization (2)
• generalized means (1)
• geom (1)
• geometric sequence (7)
• geometry (79)
• gifted education (6)
• Goldbach Conjecture (1)
• golden ratio (1)
• golden triangle (1)
• grandson (1)
• graphing calculator (2)
• graphs (1)
• growth rate (1)
• harmonic series (1)
• hens laying eggs (1)
• heuristics (1)
• higher-order questions (1)
• higher-order thinking (2)
• history of mathematics (15)
• hole in sphere problem (1)
• humor (2)
• hyperreals (1)
• implicit differentiation (2)
• improper fractions (1)
• improper integral (1)
• indirect proof (3)
• inequalities (1)
• infinite geometric series (1)
• infinite repeating decimal (2)
• infinite series (1)
• inscribed (3)
• inscribed rectangle (2)
• inspiration (2)
• instructional strategies (14)
• Instructional Strategy Series (5)
• integers (1)
• integration (1)
• interview (7)
• inverse variation (1)
• Inverses (1)
• Investigation (1)
• investigations (67)
• issues in education (3)
• issues in math education (5)
• iteration (1)
• jokes (1)
• lattice points (2)
• law of cosines (1)
• lcm (1)
• learning (1)
• learning styles (1)
• limitations of technology (1)
• limits (4)
• linear algebra (1)
• linear equation (1)
• linear function (1)
• linear inequality (1)
• linear programming (1)
• lists (1)
• locus (1)
• logic (12)
• Lynn Arthur Steen (2)
• MAA (1)
• mandelbrot (1)
• Martin Gardner (1)
• Math (1)
• math anxiety (1)
• math challenge (23)
• math club (1)
• math contest (3)
• math contest problems (18)
• Math Education (1)
• math humor (7)
• math instruction (1)
• math mnemonics (3)
• math signs (1)
• math software (1)
• math strategies (1)
• math teachers (1)
• math tricks (2)
• math videos (6)
• math wars (5)
• mathanagram (4)
• mathematical practices (2)
• mathematicians (2)
• MathNotations Contest (12)
• mathnotationsvids (4)
• matrices (1)
• maxima/minima problem (4)
• mean (4)
• median (1)
• median (geometry) (1)
• mental math (3)
• method of shells (1)
• middle school (49)
• middle school math (10)
• mixed numerals (2)
• modular arithmetic (1)
• more (28)
• mortgage (3)
• multidigt multiplication (2)
• multiple representation (2)
• multiples (1)
• multiplication concept (1)
• multiplication of probabilities (1)
• multiplication principle (8)
• multiplication tables (1)
• mystery mathematician (19)
• Name that Mathematician (3)
• national math curriculum (4)
• national math curriculum england (1)
• national math panel (8)
• national standards (6)
• nested radicals (1)
• new year (1)
• nine (1)
• NJ Math standards (1)
• number sense (2)
• number theory (14)
• number tricks (1)
• numerical analysis (1)
• odd/even problems (1)
• odds and evens (2)
• online math contest (4)
• open-ended (4)
• optimization (4)
• organized list (1)
• overlapping circles (1)
• packing (1)
• packing problems (1)
• paper-folding (origami) (1)
• parabolas (8)
• paradox (2)
• parallelogram (1)
• parameter (2)
• parametric (2)
• partitions (1)
• patterns (17)
• Paul Cohen (1)
• pearson (2)
• pedagogy (10)
• percent (10)
• percent change (1)
• percent discount (1)
• percent increase problem (3)
• percent word problem (10)
• percent word problems (1)
• performance (1)
• periodic behavior (1)
• perpendicular lines (1)
• personal philosophy (5)
• Philosophy of Mathematics (1)
• pi (10)
• pi day (10)
• pi poem (1)
• pi^2/6 (1)
• Pick's Theorem (1)
• piecewise function (1)
• place value (1)
• placement test (2)
• podcast (1)
• poll (2)
• popularizations of math (1)
• Power function (1)
• power of a point (1)
• power series (1)
• powers of 2 (1)
• prealgebra (3)
• precalculus (12)
• pressure (1)
• prime factorization (1)
• primes (16)
• probability (13)
• problem of the day (1)
• problem-solving (4)
• Problems of the Day (1)
• Prof. Lynn Arthur Steen (1)
• projectile motion (1)
• proof (10)
• proof without words (1)
• proportions (2)
• PSAT (3)
• purpose of blog (1)
• puzzle (8)
• puzzles (1)
• pyramid (2)
• quadratic (3)
• quadratic function (5)
• quadratic systems (1)
• quadratic trinomials (1)
• quadrilaterals (4)
• quotes (1)
• radical equations (2)
• radicals (5)
• random triangle (1)
• rate-time-distance problems (2)
• rational equation (1)
• ratios (15)
• ratios in geometry (1)
• real number system (1)
• real-world applications (1)
• reasoning (9)
• rectangles (1)
• recursion (4)
• recursive functions (4)
• recursively defined sequences (1)
• reflection (1)
• reform (2)
• regular polygons (1)
• related rates (1)
• relatively prime (2)
• released items (1)
• remainders (5)
• research (1)
• rhombus (1)
• riddle (2)
• right triangles (2)
• rotations (1)
• Rule of Four (3)
• SAT strategies (21)
• SAT-type problems (87)
• scientific notation (2)
• secant-tangent power theorem (1)
• sequences (4)
• series (3)
• sieve (1)
• similar (1)
• similar triangles (8)
• similarity (1)
• Singapore Math (4)
• skills practice (1)
• slope (2)
• slopes (1)
• software review (1)
• spatial sense (10)
• sphere (1)
• square dissection (1)
• squares (6)
• standardized assessment (3)
• standardized tests (6)
• standards (1)
• starting the year (1)
• statistics (2)
• Stuyvesant HS (3)
• subtraction (1)
• sum-difference identities (2)
• sums of consecutive positive integers (2)
• Super Bowl (1)
• survey (3)
• susan ohanian (1)
• symmetry (2)
• systematic counting (2)
• systems of equations (1)
• tangent circles (2)
• tangents (11)
• Taylor Mali (1)
• tc'sTotal Challenges (2)
• teaching (3)
• teaching for understanding (1)
• technology (1)
• test construction (1)
• testing (2)
• Texify (1)
• textbooks (1)
• Thanksgiving message (1)
• theory of equations (2)
• TI program (1)
• tiling patterns (1)
• totally clueless challenge (1)
• triangle inequality (1)
• triangles (3)
• triangular numbers (1)
• tribute (2)
• tribute to teachers (1)
• trigonometry (5)
• twitter (2)
• twitter problem of the day (2)
• two trains in the tunnel classic (1)
• u-substitution (1)
• Unions (1)
• unit fractions (1)
• update (40)
• variation (1)
• Vedic Maths (1)
• verbal phrases (1)
• video lesson (8)
• video review (1)
• volume (3)
• warmup (14)
• weighted averages (1)
• winning strategies (2)
• word problems (2)
• work problems (1)
• writing in math (1)
• XMAS problem (1)

Dave Marain

NJ, United States

Recently retired math educator and Supervisor of Mathematics; 30 years experience as an Advanced Placement Calculus (BC) teacher; Former Author of Math Teachers of New Jersey Annual HS Math Contest; Former K-5 Chair of New Jersey Math Content Standards and Curriculum Frameworks; Former member of Math Item Review Committee for New Jersey High School Proficiency Assessment; Experienced SAT Math Instructor and author of SAT materials; speaker at many regional and national math conferences

View my complete profile