Digital Manipulatives

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

 S152:   SATURDAY, 2:15-3:05 PM, CORONADO EF       Hi. The session begins at 2:15.       Feel free to work/play before that.       Copies of the 5 spreadsheets are available on thumb drives in the room.

First We'll "Play," Then We'll Work

Please introduce yourself to those around you.

Manipulative theory says: "Begin with free play & unstructured time before setting the stage for work" so we will do something like that.

Open the spread sheet just below and using the notes pictured on the spread sheet, see what you can do. Then we can better judge how to continue.

Session Purpose and Objectives

 This session and page is built for both those who know how to use concrete manipulatives and those who do not.  If you do not know how to use a concrete manipulative, a digital manipulative is only a play thing. So we will consider a bit of theory first. This page is also written for those who have experience in cutting/selecting/pasteing and those who do not.     The time it takes to complete this work depends on one's skill set.

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

Digital Manipulatives Purpose

 Digital manipulatives were created to: Introduce in the concrete and debrief in the abstract.  Increase the number of graphics used in class - speak pictorial more often.  Increase visualization as a form of presentation, summary, debriefing.  Create math experts, those who have enough facility in multiple languages to choose the language in which to work and communicate.  Restate a mathematical idea in as many math class languages as possible for increased understanding on the part of both the speaker and the listener.   Bring a cart load of manipulatives to class without having to bring a cart load of manipulatives to class.

More Work and Play

Solve, & Create a Cartouche, & Add Vectors, & Write Digital Algebra Problems

Use multiple strips & fraction bars, & Add & Subtract on a Nomograph, & Assemble a jig saw puzzle, & Use Napier's Bones to Multiply, & Demonstrate that 2/9 + 1/3 is 5/9.

Compute & Play on the 100s Boards

Calculi and Boards, & Egyptian Multiplication, & Slide Rules, & The Sine Law
 Chinese suan pan: 2/5, 2 over 5 (biquinary) Japanese soroban: 1/4, 1 over 4 (decimal)

Material Used Today

 Sheet Contents select copy paste Intro to Digit ManipulativesThis work from "Term Tiles & Tokens" @ www.mathnstuff.com/math/algebra/tttoc.htm and @ www.termtiles.com problems 2 - 4 Using Term Tiles to complete manipulative work.This work from "Term Tiles & Tokens" @ www.mathnstuff.com/math/algebra/tttoc.htm game for two players The best middle school mental computation and vocabulary game ever.This work from "A Game for Two Players" @ www.mathnstuff.com/math/papers/games/42game.htm and @ www.mathnstuff.com/papers/games/42.xls extra tiles & tokens Storage. Because sometimes you need extra pieces. answers Answers to some problems.

 Sheet Contents solve Solve 3 + 2x = 4x - 1This material is found @ www.mathnstuff.com/math/algebra/tt22.htm and www.mathnstuff.com/math/algebra/tttoc.htm hyro Create your own cartouche or write ancient Egyptian numbers or glyphs.This is page: www.mathnstuff.com/papers/langu/hyrogl/hyro.xls. vectors Add 4 @ 45° and 6 @ 135° by building the resultant vector on the rectangular plane.This stuff is found @ www.mathnstuff.com/math/xls/clocks.xls and @ www.mathnstuff.com/math/spoken/here/2class/330/polrect.xls write problems Spread sheet completes polynomial computation and solves linear and quadratic equations.This material is found @ www.mathnstuff.com/math/algebra/tttoc.htm

 Sheet Contents multiple strips/fraction bars Write equivalent fractions. Add or subtract fractions.See www.mathnstuff.com/math/spoken/here/2class/60/mult.htm nomograph To add & subtract wholes, integers, fractions, decimals.See www.mathnstuff.com/math/spoken/here/2class/130/nomogrf/nomo.htm and www.mathnstuff.com/math/spoken/here/2class/130/nomogrf/nomogrf.xls for more info. unit circle Assemble a unit circle jig saw puzzle.Unit circle spread sheet found @ www.mathnstuff.com/math/spoken/here/2class/330/gif/unit1.xlsAnimated unit circle found at www.mathnstuff.com/math/spoken/here/2class/330/unit.htmManipulative master found at www.mathnstuff.com/math/spoken/here/2class/330/gif/unitc.gif napier's bones Napier's Bones for multiplication, division, and taking roots. Problem 4: Multiply 2467 by 8.Stored @ www.mathnstuff.com/math/spoken/here/2class/60/napierb.xls Multiplication with Napier's Bones is @ www.mathnstuff.com/math/spoken/here/2class/60/nbonesm.htm#mult Division with Napier's Bones is @ www.mathnstuff.com/math/spoken/here/2class/60/nbonesd.htm#divide Root Extraction with Napier's Bones is @ www.mathnstuff.com/math/spoken/here/2class/60/nbonesr.htm#sqrt thirds, sixths, ninths Problem 5: Demonstrate that 2/9 + 1/3 is 5/9.Found @ www.mathnstuff.com/math/spoken/here/2class/70/frtiles/fract.xlswith many other fraction bars.

 Sheet Contents 100s regular 100s board negs positive, negative board multiples 12 copies of the 100s board colored with multiples of 2 to 13 uncolored multiples 12 copies of the 100s board