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Games and Manipulatives: Digital and Concrete

AMTNJ, 12:00 - 1:30, 12/2017

“Tell me and I forget, teach me and I may remember, involve me and I learn.”
- Benjamin Franklin



Examine these activities and games that help promote conceptual understanding.
Grades: 0-4: "The Hundreds Board - Positives" for addition, subtraction, multiplication, division, vocabulary skills.
Grades: 7-8: "The Hundreds Board - Negatives" for signed number computation.
Grades: 4-8: "Nomograph" for whole number, signed number, decimal, and fraction computation.
Grades: 4-8: "Slide Rule" for whole number, signed number, decimal, and fraction computation.
Grades: 4-8: "Multiple Strips & Fraction Bars" for equivalent fractions, least common denominator.
Grades: 4-11: "Term Tiles & Tokens" for signed number computation, algebraic computation, solving.
Grades: 6-8: "Area Formulas by Paper Folding" for triangle, parallelogram, circle, trapezoid.
Grades: 7-8: Play "A Game for Two Players" for vocabulary skills and mental computation.


Rational


The Languages of the Math Classroom
© '98, '08, '09 Agnes Azzolino
 
MOTHER TONGUE & OTHER TONGUE(S)
Most Sophisticated and also the Most Basic
 
MOSTLY MATH TONGUES
Most Sophisticated, Most Basic
 
VERBAL / Auditory WRITTEN / Symbolic     PICTORIAL / Visual     CONCRETE / Kinesthetic    
  formal spoken mathematics   written word   DIGITAL MANIPULATIVE     object
  informal spoken mathematics       written symbol   moving picture   model
  spoken symbol   semisymbolic   static picture   manipulative/token
  symbol speak   calculator symbol   numeral
  calculatoreze/computereze   graph
  web speak   nonverbal body language


Manipulative and Languages
  • *Features of the Languages of the Math Classroom
  • *manipulative use



Games and Manipulatives


100s 

Addition and Subtraction on the Hundreds Board,
Activities that set the stage for multiplication, division, signed number addition and subtraction


  • ADDITION/SUBTRACTION
    The Book
    Animation
    DIGITAL MANIPULATIVE 100s board
    Blank 100s board
    Blank Negative board

  • SHADE THE MULTIPLES, MULTIPLY, DIVIDE on the 100s board
    Six multiple boards
    Shaded multiples
     
  • Reinforce textbook work GROUP BINGO
    group01.gif
    group02.gif


Multiple Strips, Fraction Bars, Slide Rule and Nomograph for Addition and Subtraction
  • Multiple Strips
    mult.htm -- Multiple Strips & Fraction Bars
    strips.xls -- DIGITAL MANIPULATIVE on a spreadsheet with multiple strips & fraction bars
  • Slide Rule
    Web page on the slide rule
    slide.xls --slide rule DIGITAL MANIPULATIVE
    nomogrf.xls -- Nomographs to add/subtract whole numbers, decimals, fractions
  • Nomograph
    nomo.htm -- Web page on nomographs
    nomogrf.xls -- nomograph DIGITAL MANIPULATIVE


Fractions and Algebra
  • EQUIVALENT FRACTIONS
    Times Table & Multiple Strips Template
    Multiple Strips & Fraction Bars Web Page
    Multiple Strips & Fraction Bars Digital Manipulative
     


  • INTEGER AND ALGEBRAIC MULTIPLICATION & DIVISION
    Integer multiplication
    Algebraic multiplication:
                      2(x+3)       (x+2)(x+3)             (x-2)(x+3)
                      2x(x2+2x+4)       (x-y)3

    Algebraic division     Divide (x² - x - 6) by (x - 3)

    • Solve Equations and Inequalities     Solve: x - 3 = 6


Just Primes
Primes on the 100s board
Primes sheet (Check "prime" in the book MATH SPOKEN HERE!)
Primes blank sheet
Spreadsheet Support

Web Drill and Practice
Who Has Game Web Page
Who Has Game Presentation page


"Prove" Area Formulas

Area of Parallelogram, Triangle, Trapezoid Formulas by Paper Folding
Area Cirlce Formulas by Paper Folding
areaf.xls --DIGITAL MANIPULATIVE on a spreadsheet with area formulas for a rectangle, parallelogram, triangle, trapezoid, circle.
math.htm computes areas, distances, perimeters
area.xls -- computes the areas and perimeters of rectangles, parallelograms, triangles, trapezoids, circles.


Play a few games

"A Game for Two Players"
 
Place playing pieces just off the board near square 1.
Move as indicated.
The winner is the first person to get to 60.
DO NOT MOVE IF:
      you are told to go to a SQUARE ALREADY OCCUPIED or OFF THE BOARD.
WHEN DIVIDING, DISREGARD THE REMAINDER.

"A Game for Two Players" DIGITAL MANIPULATIVE


Leave singing

      GRACE BURTON's "The Three Times Tables"


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  © 10/2017, A. Azzolino