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Sample digital manipulatives & Sketchpads found at
  web page  
  pdf of the web page  
  local video  

Table of Contents for This Page

Digital Manipulatives  
Geometer's Sketchpads 

Pre-K & Elementary
  • So, What's A Fraction? & Zero(s) In Fractions
  • Make a Hexagon
  • "The Decimal Bakery - A Math Fairy Tale" Web Pages
  • The Books on the Shelf - A Read Aloud Math Book Video
High School & College & School
  • 8.3 Arc Functons (In Precalc)
  • Slope Song
  • Resources for Teaching Functions in Developmental Math, Precalc, & Calc I
  • So, What's A Fraction? & Zero(s) In Fractions
  • Precalc & Calc I Inside Front & Back Cover Quick Reference Material
  • Angles in Standard Position
  • Angle Measure
  • Radians & Sectors Using the radianSector.gsp
  • Take A Derivative by Singing!
  • Statistics I in 2.5 Hours
  • A Guided Tour of The Spreadsheet stat.xls
  • A Video about the HYPOTHESIS TESTS pdf file
  • "The Lecture Version of fX.f'X.f''X.intX.gsp -- Limits, Derivatives, Antiderivatives, FTC I, FTC II Presented Dynamically & Analytically
  • "HHCC - Hand-Held Calculator Calculus" and Support Programs
  • Absement and 'nth Derivatives of Displacement' Presented Dynamically & Analytically
Other Stuff
  • Sate-of-emergency Snow Storm! - Nothing Closes NYC's 6th Boro
  • Does It Fit? Does It Fit? Bridges Over the Hackensack

    Videos may be listed more than once.

digitalm   Digital Manipulatives
- The 21st Century Version of Tokens

            "Tell me and I forget, teach me and I may remember,
                involve me and I learn." - Benjamin Franklin
  • 1st: a rational & show-and-tell of sample digital manipulatives,
    © 7/2009 metz web page, pdf video, local, Key words:
    Click, Drag, Select, Copy, Paste; Digital Manipulatives as a Math Class Language; Sample, Play, Create.
  • 1st. or Last: Math Tokens   © 2010     Tokens web page pdf file NO VIDEO
    Most digital manipulatives, tokens, are sorted by the NJ Math Standards: Number Sense and Numerical Operations; Geometry and Measurement; Patterns, Algebra, Functions; Data Analysis, Probability, and Discrete Mathematics; Mathematical Processes - Problem Solving, Communication, Connections, Reasoning, Representations, Technology; Other, Non-Math Stuff
  • 2nd: or 3rd: Manipulative Practices & Math Class Languages,
    © 2009 metz1 web page, pdf video, local video, Key Words:
    Math Class Language Stages of Acquisition; Useful Strategies
  • 4th: Ancient Computing Devises Used Digitally,
    © 2010 amtnj09 web page, pdf video, local video, Key Words:
    Fingers & Talley Sticks, Tokens & Coins, Shekel to Stater, Creation of Money, Credit before Coin, Writing Numerals, A Bit About Bases, Abaxes (Sand Table), Reckoning Boards, Banks, Abacuses, Napier's Bones, Slide Rules
  • 3rd: (Algebra) Term Tiles & Tokens, © 2010

    term tiles web page, pdf video, local video, Key Words:
    A Number, Zero , The Opposite, "Zero In" and "Zero Out" to Simplify; Represent, Evaluate, Verify; Integer & Polynomial Computation; Solve; Factor; Create; Appendix/Masters
  • 2nd: Digital Manipulatives - A Lab,
    © 12/2017, 11/2018 dmanip1 web page, pdf video, local video, Key Words:
    "A Game for Two Players," "Term Tiles & Tokens," "Solve 3 + 2x = 4x - 1," "Create your own cartouche or write ancient Egyptian numbers or glyphs," "Add vectors 4 @ 45° and 6 @ 135°," and more
  • Last: Index,
    © 2019, 2022 xls web page, pdf video, local video, Key Words:
    "Hundreds Board," abacus, area formula proofs, numerals in Chinese, Japanese, Roman; coins, other number bases, fraction computation, deck of cards, dice, Napier's Bones, etc.
  • A Game for Two Players emphasizes prealgebra vocabulary & mental computation.

    web page, pdf, digital manipulative, video, local video, Key words: multiple, multiply, divisible, divide, prime, composite, add, decrease, square, reciprocal, opposite.


[Words] MATH SPOKEN HERE! Words/Dictionary/Essays
  • So, What's A Fraction? & Zero(s) In Fractions
    web page, pdf of web page, video of web page local video
    key words: ratio, comparison. numerator compared to denominator, "number of pieces" /"number of pieces in one whole," fractions in symbols and pictures, complex fractions, fractions with fractions, division by zero, fractions with zero(s), undefined, indeterminant, Special Limits, f(0) is 0/0.
  • hexagon:   definition web page
    Make a Hexagon Sketchpad, video of Make a Hexagon
    Key words: construct an equilateral triangle or regular hexagon w/string & straight edge or w/Geometer's Sketchpad local video,

-- Precalc Resources
  • Slope Song
    web page
    Sketch Pad
    local video
    Interact with the web page to listen to audio clips of slopes such as 2, 4/3, 1, 3/4, 0, -3/4., ...
    A Geometer's Skechpad of Slope Song is also introduced.
  • Resources for Teaching Functions in Developmental Math, Precalc, & Calc I
    video -- the expanded version of the talk   video-- LOCAL of the expanded version of the talk     pdf - of the STEM '23, paper/web page:
    WHERE ALL MATERIAL IS LINKED ON THE PAGE including:   Choose the best Math Class Language.   Hear a slope.   Go from slope to difference quotient to derivative.   Use termtiles (hot.xls) then sketchpad (compositeFX.gsp or parabola.gsp or compositeFx.poly.ratl.gsp) to compose functions to illustrate (line)(line)= (quadratic).   “Concretely” translate and reflect graphs with parentFX2.gsp   Easily graph functions, composit functions, inverse functions with inverse.gsp   Graph Asin(Bx-C)+D by just changing the variables with sine.xls   Compute compounding, exponential functions and models with exp2.xls  
  • Precalc & Calc I Inside Front & Back Cover Quick Reference Material
    video tour   local video tour
    Key words: "stuff" one needs in precalc and calc to do the homework, recall material a student should understand but has probably just forgotten and wishes to quickly check. Topics include: laws of exponents & logs, trig identities, values of the 6 basic functions of the 30s, 60s, 45s in all 4 quadrants, tables of derivatives and integrals.
  • Angles in Standard Position
    Sketchpad, video   local video,
    Key words: standard position, central angle, negative and positive angles, coterminal angles
  • Angle Measure - A History w/Down-Loadable Resources
    web page, web page pdf file, Sketchpad used in video, video,   local video,  
    key words -- ancient counting and communication of numbers, Egyptian mathematics, Sumerian/Babylonian mathematics, construction of a hexagon, Roman/Greek mathematics, pi, radians, graph papers, other tools sfor teaching radians also included in video: Make a Hexagon and Radians & Sectors Using radianSector
  • Radians & Sectors Using the radianSector.gsp:
    Sketchpad, worksheet, answers, video local video,
    Key words: angle, circle formulas from middle school, special angles, degree measures, radians, radian measures, arc, arc length, sector, angular speed

calc1 -- Calc I Resources

-- Statistics
  • Statistics I in 2.5 Hours --
    Heavy on Vocabulary & Images, Light on Computation, but No Counting Theory, Includes Materials
    Materials include: web page, spreadsheet, pdf file, video of this page, local video
    * Population, Sample, Data, Statistic;
    * Discrete or Continuous;
    * Take a Samples;
    * Look at the Data;
    * Theoretical vs Experimental & Descriptive vs Analytical Statistics;
    * Probability (not really covered);
    * More Vocabulary and Topics that Are Not Included on this Page;
    * The Binomial Distribution;
    * Thank Goodness for Probability Density Functions;
    * Normal and Standard Normal Distributions;
    * Confidence Intervals;
    * Hypothesis Testing;
    * Just the Vocabulary (Sorted Alphabetically)
  • A Guided Tour of The Spreadsheet stat.xls
    Materials include: spreadsheet, video local video
        Personally, I wouldn't write a stat test without it, and, it's the perfect tool for students to verify written homework, create their own problems, or work on a lab.
    * mean of 5, 10, 20, 30 pieces of data;
    * mean and standard deviation of three groups of 10 scores;
    * standard deviation of 10 numbers using the formula displayed in table format.
    * x-score or z-score or mean or standard deviation
    * mean, standard deviation, and z-scores, and stanine for 30 pieces of data;
    * traditional uses of z-scores and probability table;
    * probability given a normal distribution;
    * traditional & cumulative z-scores probability table;
    * P(x<a), P(x>a), P(a<x<b);
    * probability in a binomial distribution
  • A Video about the HYPOTHESIS TESTS pdf file
    Materials include: web page, pdf file, spreadsheet, video , local video,
          I wouldn't teach hypothesis testing without it. It provides the BIG PICTURE, and a superlative summary, of hypothesis testing and tests.
    Tests Presented: All at once and Indivually, Z-Test, T-Test, 2 Sample Z, 2 Sample T for INDEPENDENT means; 2 Sample T for DEPENDENT means; ANOVA; Kruskal-Wallis; 1 Proportion Z; 2 Proportion Z; Two Sample F-Test; Chi Squared for A Single Variance; Chi Squared for Independence of Proportions; Chi Squared for Homogeneity of Proportions; Chi Squared for Goodness of Fit; Chi Squared for Normality; Sign Test; Wilcoxon Rank Sum Test; Wilcoxon Signed-RankTest; Spearman Rank Correlation Coefficient

-- Algebra Resources
sketchpad Exploring Functions Through Manipulatives
    - manipulatives for Algebra I, Algebra II, and Precalc

Term Tiles & Tokens
    - manipulatives for PreAlgebra and Algebra I

spread sheet notes -- MathTokens
    - digital manipulative spreadsheets on all sorts of math stuff

sketchpad -- Geometer's Sketchpads Geometer's Sketchpads

Classes MATH SPOKEN HERE! Grouped Material

papers Pre-K, Elementary, & Other Good Stuff


  • Resources for Teaching Functions in Developmental Math, Precalc, & Calc I
  • "The Lecture Version of fX.f'X.f''X.intX.gsp -- Limits, Derivatives, Antiderivatives, FTC I, FTC II Presented Dynamically & Analytically
    Sketchpad, web page, pdf, Teachers' Manual web page, The Languages of the Math Classroom     video,   local video
    Key words: end behavior, take a limit, as x approaches c, where f(c) is continuous/not continuous, as x approaches infinity, derivative by definition, by secant, as the slope of a tangent, mark c, f(c), f' (c), f ' ' (c), increasing/decreasing, zero, trig derivatives memory trick, partition, differential, Reimann bBoxes, sums, area under a curve, negative areas, use g(x), cumulative distribution, integral, FTC I, FTC II, "plus c"
  • 10/15/2021, Virtually w/Zoom, @ the 3rd Annual C2 Summit for Pedagogical Advancements in STEM, @ Raritan VCC
    "Functions, Derivatives, Antiderivatives with Sketch Pad,"
  • 1/2018, NJECC, Montclair U, "Digital Manipulatives"
  • 11/2010, AMATYC , "30+ Centuries of Computation in a 21st-Century Format"

-- 'N' Stuff

©11/2023, A2,
[MC,i. Home, site home page] [master list of all MSH! dictionary words] [tutorials & resource material arranged by topic [Good Stuff -- free & valuable resources] [this semester's schedule w/links]