pdf video

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.

Don't worry about messing up. You can always download another spread sheet.

Digital Manipulative Spread Sheet 1

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

Manipulative and Languages

Features of the Languages of the Math Classroom

Manipulative Use

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

Digital Manipulative Spread Sheet 2

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.

Digital Manipulative Spread Sheet 3

Compute & Play on the 100s Boards

Digital Manipulative Spread Sheet 4

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)

Digital Manipulative Spread Sheet 5

Multiply 25 x 12 by Doubling and Halving

Material Used Today

Digital Manipulative Spread Sheet 1

Sheet	Contents

select copy paste	Intro to Digit Manipulatives This 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.

Digital Manipulative Spread Sheet 2

Sheet	Contents

solve	Solve 3 + 2x = 4x - 1 This 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

Digital Manipulative Spread Sheet 3

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.xls Animated unit circle found at www.mathnstuff.com/math/spoken/here/2class/330/unit.htm Manipulative 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.xls with many other fraction bars.

Digital Manipulative Spread Sheet 4

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

Digital Manipulative Spread Sheet 5

Sheet	Contents

calculi	Abaxes (Sand Tables), Reckoning Boards, Banks (Using Calculi) See: www.mathnstuff.com/math/spoken/here/2class/40/40abacu/abacus.xls See: www.mathnstuff.com/papers/amtnj09.htm for history & use of abacus. See: The "units" worksheet of www.mathnstuff.com/math/xls/hands.xls for a table which does not have powers of the same base.

Egyptian Mult	Egyptian Multiplication See: www.mathnstuff.com/math/spoken/here/2class/40/40abacu/abacus.xls. See: www.mathnstuff.com/math/xls/xls.htm#digitalm. See: www.mathnstuff.com/math/spoken/here/2class/60/egyptm.htm for Egyptian Computation. See: www.mathnstuff.com/math/spoken/here/2class/60/emulti.htm, Multiplication by Doubling and Halving (Mediation & Duplation) w/Calculi

Additional Material Not Used Today

The Languages of the Math Classroom

Digital Manipulatives on the Web Page Entitled Spread Sheets

Math Tokens Home Page Manipulatives Listed by Number Sense, ..., Geometry, ... Non-Math Stuff

Hold a shekel in your hands

Divide the circle to compute its area

Expand (x+y)³

"Roll" a die or pair of dice

Play addition rummy with a deck of cards

Additional Material Not On This Site

The International Slide Rule Museum

Slide Rule History

$[MC,i. Home, site home page]$

$[master list of all MSH! dictionary words]$ $[tutorials & resource material arranged by topic$