# Games and Manipulatives: Digital and Concrete

## “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

## Games and Manipulatives

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

• 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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