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    Math Tokens

Tokens Designed for Use in a Digital Age

    5 spread sheets
    Insert Gif
    & Math History
    & Algebra
    & Pictures
    HS, HS+
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        Open a spreadsheet.  Right-click then copy then paste each image on the left into the spread sheet.  You've created digital manipulatives, math tokens, things that can move on a spread sheet as one might move tokens on a board.
      Your tokens are a set of negative and positive tiles for signed number computation. The spread sheet is required. The images are required. The possibilities are vast in number and may be profound in impact. See instructions and then you might wish to experiment with 5 spread sheets to give you a sample of some of the possibilites.  Save a copy of the spreadsheet where you can find it and edit the format to fit your screen.
      Use different pictures or tokens for different jobs -- Term Tiles and Tokens for algebra & prealgebra, Napier's Bones for multiplicity, to multiplying, or to take roots, coins for teaching money, and more specialized spread sheets & tokens for more specialized tasks like introducing the unit circle, "proving" area formulas, faction /decimal addition / subtraction, finding the resultant vector.
      Write a birthday card in hyroglyphics or using Morse Code or nautical flags. Represent and compute as the ancients did in Egypt and Greece and through the Middle Ages using calculi and counting boards. Multiply and divide by Mediation and Duplation - halving and doubling.
      Save and edit a math token spreadsheet for yourself (for not-for-profit purposes), but keep the original copy right, author and source page on the table of contents where you also might add notes.  Use the resources on the left to assit you in your work.

Math Tokens Sorted by Math Standards
With Notes on Prefered Format & Use, Proficiencies, Resources
      The catagories of "represent," "operate," and "create" might be unfamiliar to the reader.
      They are stages of language and math acquisition which inspired math tokens. The most sophisticated stages are "create" and "interpret" and the goal of education is to have each individual have mastery of math at these levels.
      Where available, manipulative masters, [m], for concrete work and other resources, [s], are listed after the math token spreadsheet. Spreadsheets open in their own window. Resources generally just link from this page.
      Tokens are sorted below by the NJ Math Standards or placed in Other (non-math stuff). Since some are useful in more than one area, they are listed in each area. The Term Tiles & Tokens -- create.xls, hot.xls, and tiles.xls -- have many uses and are similar.
N: Number Sense and Numerical Operations
G: Geometry and Measurement
P: Patterns, Algebra, Functions
D: Data Analysis, Probability, and Discrete Mathematics
M: Mathematical Processes -
  Problem Solving, Communication, Connections, Reasoning, Representations, Technology
O: Other, Non-Math Stuff
N: Number Sense and Numerical Operations
9times [s], 42 [m,m,s], 100s [m,m,s], abacus, bases, board, coins, create [m,s],
fract, hands [s], hot [m, s], napierb [m, m, s], nomogrf [m, m, m, s], nosystm, slide [s],
strips [m,s], sumelse [s], tiles [m,s],
G: Geometry and Measurement
areaf [s,m,s,m], nomogrf [m, m, m, s], slide [s], strips m, s],
P: Patterns, Algebra, Functions
areaf [s,m,s,m], create, [m,s], hot [m,s], jig1 [m,s], polrect [s], sinelaw [m,s], tiles [m, s],
D: Data Analysis, Probability, and Discrete Mathematics
deck, dice
M: Mathematical Processes -
Problem Solving, Communication, Connections, Reasoning, Representations, Technology
42 [m,m, s], create [m, s], hot [m, s], tiles [m, s],
O: No Math
hyro, signalf, trans [s,s] [vanish, The Vanishing Math Teacher]

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