## SMILE PROGRAM MATHEMATICS INDEX

The SMILE website is hosted by the Illinois Institute of Technology

The following is a collection of
almost 200 single concept lessons. These lessons may be freely
copied and used in a classroom but they remain the copyright
property of the author.

The Mathematics lessons are divided into the following categories: Geometry and Measurement, Patterns
and Logic, Probability and Statistics, Recreational and Creative Math, Practical
and Applied Math, Arithmetic, Graphs and Visuals, Algebra and
Trigonometry, and Miscellaneous.

**Geometry and Measurement**

The Pythagorean Puzzle by Earl Zwicker
- Illinois Institute of Technology - Dedicated to Prof. Harald
Jensen, Lake Forest College

Areas of States -
Estimation by Janice C. Harvey - Carver Middle School

Liquid Volume by
Robert Foote - Disney Magnet

Spherical Geometry: A Global Perspective
by William R. Colson - Morgan Park High School

Geometry Distance of Triangles using a
Protractor by Eileen Lally - A. Philip Randolph Magnet
School

Circles - Diameter, Circumference, Radius
and the Discovery of Pi by Kathleen Ryan - Randolph Magnet
School

How To Measure Area by Levi Johnson -
James Otis

An Introduction to Pi and the Area of a
Circle by Edwina R. Justice - Gunsaulus Scholastic Academy

Area and Perimeter by Monica Starks -
John Fiske Elementary

Shapes (Geometric) (Lesson 2) by
Violet M. Nash - Spencer Math and Science Academy

Shapes (Geometric) (Lesson 1) by
Violet M. Nash - Spencer Math and Science Academy

Measurements: Inches by Joyce McCoy -
Spencer Math & Science Academy

Getting To Know You by Kathy Koval -
Randolph School

Inch by Inch and Centimeter by Centimeter
Extravaganza by Pamela J. Bates-Hines - Ninos Heroes Academy

Interior Design by Sally Hill -
Horatio May Community Academy

Maximizing & Minimizing the Area of
Rectangles Given a Fixed Perimeter by Tim Amrein - Franklin
Fine Arts Center

Phenomenological Pizza by Robert Foote
- Disney Magnet School

An Introduction To Volume by Linda
James Woods - Harold Washington Elementary School

Measurement of Volume by Richard
Murray - Gage Park High School

Volume and Surface Area by Charlotte
Goldwater - Kenwood Academy

An Introduction to Area and Perimeter
by Edwina R. Justice - Gunsaulus Scholastic Academy

An Introduction to Estimation and
Measurements by Christeen Brown - Robert Fulton Elementary

Circumferences, Diameters, and Radii
by Dwayne Belle - Fuller School

Measuring in Inches and Centimeters by
Debra Thomas - Douglass Math and Science Academy

Estimation by Iona Greenfield -
Carnegie Elementary School

Measurement of Objects Using Similar
Triangles in The Plane by John Gabrielson - Chicago H.S. for
Agri. Science

Travel Triangles by Sarah Barrett -
Mars Hill School

Measurement-What is it? by Claudy E.
Chapman - Hartigan School

Finding the Sum of the Exterior and
Interior Angles of a Polygon by David Drymiller - Morgan
Park High School

Forming, Measuring and Labeling Angles
by Essie Lee May - May Community Academy

What's My Area? by Karen L. Mickel -
William Carter Elementary School

Geometry and the Geoboard by
Jacqueline Darling - Simmye Anderson Community Academy

An Introduction to Angles by Samuel A.
Anoma - Hyde Park Career Academy

Use A Chair To Teach Math by Laura B.
Reed - Rosa L. Parks

Measurement (cup, pt, qt, gal) by
JoAnn Campbell - Leslie Lewis School

Measurements In The Metric System by
Christine Fair - Farragut Career Academy

The Area of a Circle (Version 2.0) by
Edwina R. Justice - Gunsaulus Academy

The Surface Area of a Cylinder (Version
2.0) by Justice, Edwina - Gunsaulus Academy

Similarity by Kee, Natalia - Harlan
Community Academy H.S.

Polygons Made To Order by Malone,
Loretta - Washington High School

Properties Of Quadrilaterals by Olson,
Margaret A. - Morgan Park High School

Parallel lines and Angles by
Singleton, Earl M. III - Daniel Hale Williams

The Surface Area of a Cylinder by
Justice, Edwina - Gunsaulus Academy

Soap Film Models by Pintozzi, Joan -
Curie Metro. H.S.

Primary Geometry by Pitra, Barbara -
Marconi Community Academy

Proving Pi by Williams, Gwendolyn D. -
Paul Robeson High School

The Solar System by Fred J. Schaal -
Lane Tech High School

How Many Regular Polyhedrons Are There In
This or Any Universe? by Lawrence E Freeman - Kenwood
Academy

The Area Of A Circle by Edwina R.
Justice - Gunsaulus Academy

**Patterns and Logic**

M&M MATH by Barbara P. Lorde -
Crispus Attucks Academy

Using Symmetry to Create A Community Quilt
by Beverly Brown - Hedges West

Sorting and Analyzing by Vickie
Townsend - Crown Fine Arts Community Academy

Sorting Through Life! by Barbette
Flennoy - Joseph Stockton

Number Patterns in Pascal's Triangle
by Ulysses Harrison - Dunbar Vocational High School

Visuals Patterns in Pascal's Triangle
by Ulysses Harrison - Dunbar Vocational High School

To Classify Beans And Peas by
Gwendolyn Williams - Adam Clayton Powell

Chess Math by Louis C. Jackson -
Lincoln Elementary School

TESSELLATIONS: An Application Of Simple
Regular Polygons by Mary Racky - Kenwood

Logic and Reasoning by Pearline Scott
- Greeley School

Tower of Hanoi by Paul Eubanks -
Washington High School

Logic by M. Elaine Granger - Irvin C.
Mollison

Counting Triangles by Mamie P. Scott -
Coles School

Using Diagrams in Problem Solutions by
Angel L. Torres - Peabody School

Formula Determination by Odom, Clark -
Collins H.S.

Classification by Wilburn, Delores B.
- Shakespeare School

Learning by Logic - Total Surface Area
by Boyd, Carolyne - Bennett Elementary

**Probability and Statistics**

Laws of Probability:
Mutually Exclusive-vs-Mutually Inclusive Draws by Mikail A.
Siddiq - Raymond School

Probability by Ana Timbers - Stockton

Probability of Childhood Games by
Robert Foote - Disney Magnet School

Probability by Sandy Reed - Robert
Fulton School

Phenomenological Probability by Robert
Foote - Disney Magnet School

Mean, Median, Mode, etc. by Charlotte
Goldwater - Kenwood Academy

Paper Toss Shootout by Edwina R.
Justice - Gunsaulus Scholastic Academy

Statistics of Mars* by Wilhelm L.
Lilly - Kenwood Academy

Averaging by Sharon Thomas - Emmanuel
Christian School

Probability by Turner, Emily - Joplin
Elementary School

Probability by Moss, Laura Willis -
South Shore Community Academy

Modeling Permutation Group by Mary
Margaret Nee - Von Stueben Science Center

**Recreational and Creative Math**

Boomerang by Wilhelm L. Lilly -
Kenwood Academy High School

How Much is a Million? by Sharon
Simmons - Joseph Stockton Elementary

Rocket High by Elizabeth Kelly -
Pilsen Community Academy

Making Ice Cream by Vickie Townsend -
Crown Fine Arts Community Academy

Games Using Multiplication by Amaechi
Onyeali - Carter Elementary

Napier's Rods by Irene Santos -
Alexander Graham School

The Golden Rectangle by Edwina R.
Justice - Gunsaulus Academy

Paper Folding to Make Cubes by Koshy
Kanicherilnalil - Chicago Public Schools

Integer: Tic-Tac-Toe Four In A Row! by
Conchita A. Little - Terrell School

Fractions and Paper Folding by Bill
Wagner - Hyde Park Career Academy

Number Up by Ernestine Bickham - Maria
Saucedo Magnet School

Math Game Using A Tic-Tac-Toe Board by
Gertrude Franklin - William Penn

The Moebius Strip by Arnita Newton -
Kenwood Academy

Fraperdec^{*} by Connie Taylor
- Holy Angels School

How To Use An Abacus by William Gordon
- John Hope Academy

A Fibonacci Primer by Freeman, Larry -
Kenwood Academy

Geometric designs in the game of "Life".
by Byrne, Willaim - Martin Luther King H.S.

Paper Pool by Williams, Barbara - Cook
Elementary School

Graphing Game by Lalagos, Thomas -
Hyde Park Career Academy

Geometric Bingo by Lawrence, Anne -
Wells Community Academy

**Practical and Applied Math**

What Does Greatest
Common Factor Mean to Me? by Stephen Ha - Lloyd Elementary
School

Learning with Links by Winnie Koo -
Ravenswood School

Data Collection - Primary Poster by
Amelia Witherspoon - New Concept School

How do You Stack Up? Revisited by
Robert Foote - Walt Disney Magnet School

Measuring for Cookies by Sally J Hill -
Roberto Clemente Community Academy

Ratio, Percent & Proportions by
Rosalyn Winston - Walt Disney Magnet School

MISSION: POSSIBLE by Mary Terhune -
Rachel Carson School

Dream Home Mathematics by Dennis W.
Montgomery - Lyman Trumbull Academy

Temperature by Patricia A. Calloway -
Spencer Math and Science Academy

Sales Tax by Allen Batts, Jr. - Jane
A. Neil School

Money Matters by Barbette Flennoy -
Joseph Stockton

Budgeting Money by Yolanda Smith -
Douglass Math and Science Academy

Converting Celsius To Fahrenheit by
Amaechi Onyeali - Carter Elementary

Percents by Albert Michael - Robert
Fulton Elementary School

Uncorking Work Problems by David
Drymiller - Marie Sklodowska Curie Metro H.S.

Mass and Weight in the Metric System
by Janet L. Powe - Harold Washington Elem.

Uniform-Motion Problems: Just Playing With
Cars by David Drymiller - Morgan Park High School

Estimating and Counting Money by Omega
L. Minor-Clark - R. Nathaniel Dett Elementary School

Estimation by Theresa W. Akpan - Wells
Community Academy

Using A Round-O-Meter To Estimate by
Kathleen M.K. Pidrak - Edward H. White

Flight Angles Of Inclination by Marie
C. Smith - Anthony Overton Elementary School

Money Sense by Marie Bijou Wong -
Joseph Warren Elementary School

Percents: (An application to real life
problems) by Lucille H. Chambers - Trumbull School

Real Numbers in the Real World by
Ulysses Harrison - Dunbar Vocational High School

Manipulating Formulae...Using Recipes To
Understand by Nancy Ressler - Oakton

Problem Solving Using Percentages by
Thelma A. Rex - Rosa L. Parks Middle School

Whole Language Approach in Solving Word
Problems by Barbara Thomas - Langston Hughes School

Effective Use of Living Space by
William L. Brown - Parkside Community Academy

Making Predictions by Lucille Chambers
- Lyman Trumbull School

Estimation Contest by Sandra A.
King-Bryson - Saucedo Magnet School

Finding area & perimeter in a
miniature house using standardized units by June Muhammad -
Park Manor

Ratios and Proportions by Mamie P.
Scott - Edward Coles Elementary School

Draining the Swimming Pool by William
Byrne - Martin Luther King

Sales Tax and Discounts by Denise Folk
- Richard E. Byrd Academy

Mixture Problems by Alphonso Kennedy -
Lindblom Tech. H. S.

An Introduction to Percent by Kenneth
Surdell - Lewis School

Solving Word Problems by Barbara
Trotter - O.A. Thorp Scholastic Academy

Problem Solving: Steps and Strategies
by Barrett, Sarah G. - Mars Hill School

Time by Davenport, Gracie - Spalding
School

Problem Solving by McCree, Marilyn -
District 12

Ratios by Murray, Richard - Gage Park
High School

Learning ratios and proportions through
scale drawings. by Laskey, Erwin - Eugene Field School

Problem Solving by Rogers, Patricia -
Edward Hartigan

Ratio and Proportions by Trotter,
Barbara - Ole A. Thorp

From Hypothesis To Conclusion...Reading
Maps To Understand Proofs by Blaszak, Maryann - South Shore
Community Academy

Triangulation by Brandon, Ann M. W. -
Oak Forest High School

Cuisenaire Rods And Math by Linda
Easter - Dewitt Clinton Elementary School

**Arithmetic**

Introduction To The
Number Line by Sheila Alexander - Manley School

Extending Our Knowledge of Place Value
by Angie Morris - Burnham School

Filling the Glass (Water, Air, and
Fractions) by William R. Colson - Morgan Park High School

Having Fun working With Fractions by
Brian Cagle - John W. Cook

Number Addition Race by Janice
Schaults - Randolph Magnet School

Lesson for Multiplying and Dividing
Fractions with Post It Notes by Robert Foote - Disney Magnet
School

Adding Mixed Numbers with Unlike
Denominators by Camille Gales - Edward Coles Elementary
School

Multiplication by Virginia Muhammad -
John Hope Community Academy

Putting the Pieces Together (Making a
Fractional Quilt) by Demetria E. McKnight - Bateman
Elementary School

Factors by Edwina R. Justice -
Gunsaulus Scholastic Academy

Place Value by Dwayne Belle - Fuller
School

Percentages by Emma Taylor - Douglass
Math and Science Academy

Counting and Place Value by Carole
Gills - Edward Coles School

Ratio and Proportion by Valesta Cobbs
- John Fiske Elementary School

Introduction to Fractions Using Cuisenaire
Rods by Gwendolyn M. Manson - Benjamin Banneker

Measuring Mixed Numbers by Karen Trout
- Sumner Math and Science Academy

A "New Set of Numbers" (An Introduction of
Integers) by Barbara Barlow - Caldwell School

Primary Understanding and Use of Place
Value by Eleanor Brzozowski - Hanson Park School

Introduction To Equivalent Fractions
by Rose Cartwright - Lyman Trumbull School

Fickled Fractions by Elizabeth
Chambers - Keller Gifted Magnet Center

Addition and Subtraction of Signed Numbers
by David Drymiller - Morgan Park High School

Working with Cuisenaire Rods In
Mathematics by Willis Grace - O. A. Thorp Academy

The Generation Of Fractions by June
Muhammad - Park Manor School

A Method of Front-End Arithmetic by
Eddie Newton - Carver Area High School

Money: Demonstrating Coin Values up to
$1.00 by Camille Gales - Coles Elementary School

How Divine Is My Proportion? by Edwina
R. Justice - Gunsaulus Scholastic Academy

Equivalent Fractions by Gertrude
Lockett - Emmanuel Christian School

Division For Third Graders by Savannah
Walker - Mason School

Prime and Composite Numbers by
Charlotte Goldwater - Kenwood Academy

A Fictional History of Place Value by
Bette B. Jarrow - Goudy Elementary

Fundamentals of Multiplication by Carl
D. Mason - Suder School

Place Value by Ceopal Porter - Dr.
Ralph J. Bunche

Fractions, Simplifying Parts of Shapes --
One-Half, One-Third, One-Fourth by Austin, Sarah - Mary
Bethune

Fraction Message by Harper, Charles -
Goldblatt Elementary School

Identification of Equivalent Fractions
by Jarrow, Bette B. - Gaudy School

Introducing Powers and Models-I by
Barrett, Sarah - Mars Hill School

Math Technique in Multiplication and
Division of Fractions by Garth, Frieda - Farragut Career
Academy

Introduction to Fractions on the
Numberline by Jones, Claudia R. - Crane High School

Equivalent Fractions by Williams,
Flora - O. A. Thorp

Introducing Powers And Models-II by
Barrett, Sarah - Mars Hill School

Understanding Fractions by Bradley,
Florida - Hartigan

Odometers and the Place Value Chart by
Bronson-Cochran, Donna - George B. Swift

Basic Mathematical Operations Using
Mathtiles by Jones, Claudia R. - Farragut Career Academy

Adding Integers by Thomas, John
Charles - N. F. Simeon Voc. H. S.

Locating Rational Numbers On the Number
Line by Winebrenner, William - Dunbar Vocational

Continued Fractions With A Calculator
by Fred J. Schaal - Lane Tech High School

**Graphs and Visuals**

Collecting Data and
Graphing by John Ramsey, Jr. - Morton Career Academy

Environmental Graphing/Eco Graphs by
Chandra E. Price - Burnham Inclusive Academy

The Ups and Downs of Graphing by
Frana Allen - Skinner School

Teaching Arithmetic and Math Concepts To
Headstarters by Jamal Brown - Daniel Hale Williams

Watermelon Graphing by Shirley
Hatcher - Daniel Hale Williams

History Of Our Solar System on a Time Line
by Richard Murray - Gage Park High School

Graphing Speed by Yolanda Smith -
Douglass Math and Science Academy

History Of Our Solar System on a Time Line
by Richard Murray - Gage Park High School

The Statistics of M&Ms by
Charlotte Goldwater - Kenwood Academy

An Introduction to Data Reading and
Computations by Christeen Brown - Robert Fulton Elementary

Counting And Graphing by Vernita Smith
- Mahalia Jackson Elementary School

Locating IIT Using Ordered Pairs by
Diane Yvette Branch - Harold Washington Elementary School

Collecting Data and Graphing by John
Ramsey, Jr. - Teacher's Acad. For Math and Science

Apples A Peel To Me by Olga Moreno -
Horace Greeley School

History Of Our Solar System on a Time Line
by Richard Murray - Gage Park High School

Locating Points Using Cartesian
Coordinates by Mercedes Rodriguez - Clemente Community
Academy H. S.

Getting the Goods on Graphing by Velma
Elois Rouse - DeWitt Clinton

Introduction to Curve Stitching - Line
Designs by Wilhelm L. Lilly - Kenwood Academy

Junk Food Math by Sharon Ross - DeWitt
Clinton School

Rotations by Nash, Susan - Lake View
High School

Graphing Equations From Software by
Webb, James - Harlan H.S.

**Algebra and Trigonometry**

The Cuisenaire Four-Pan
Algebra Balance: Limitations & Suggestions by Bill
Colson - Morgan Park High School

The Pythagorean Puzzle by Earl Zwicker
- Illinois Institute of Technology

Sorting Pennies, A Wagering Activity for
Algebra 1 by David Drymiller - Marie Sklodowska Curie Metro
H.S.

Trigonometric
Functions by Lesia Smith - Michael M. Byrne School

Equalities And Inequalities by Perry
Lemon - Shoop School

Draining The Swimming Pool by Byrne,
William - Martin Luther King H.S.

Inequalities by Butler, Ben Jr. - Gage
Park High School

Linear Equations by Ennis, Beatrix U.
- Senn Academy High School

Algebraic Addition by Junievicz, Alex
- Kelly H.S.

Simplifying Equations of the Form
ax+b=cx+d by Wagner, William F. - Hyde Park Career Academy

Rules of Sign Change by Zuger, Joel P.
- Chicago Metro High School

Using the Balance by Davis, Marie -
Marconi Community Academy

Multiplying and Factoring Polynomials
Using Algebra Tiles by Marshall, Regina - Curie Metro High
School

Vision Props of Signed Numbers by
McMiller, Mable - South Shore High School

Positive and Negative Numbers by
Siegel, Lincoln R. - Cregier High School

Positive-Negative Charge Model For
Integers by Williams, Barbara - J. N. Thorp School

The Sine Function by Ronald G.
Sienkiewicz - Prosser Vocational High School

Visual Structure of Postulates and Axioms
in Algebraic Operations by Sanford Olshan - Roosevelt High
School

Introduction To Solving Equations by
Mary Lynn Bochenek - Central Junior High

Order Of Operations by Bernice E.
Holloway - Bellwood School District #88

Commutative, Associative And Distributive
Properties by James E. Breashears - Robeson High School

**Miscellaneous**

It's About Time by Vernita Smith -
Mahalia Jackson Elementary School

Multiplication and Areas by Albert
Michael - Robert Fulton Elementary School

Zone Out! by Willie Mae Wilson -
Hartigan Elementary School

Elapsed Time by Bernice Joyce Henry -
Edward H. White

Telling Time in Different Time Zone by
Borita Khim - Stockton Elementary School

Area, Arithmetic and Algebra by Larry
Freeman - Kenwood Academy

Area, Arithmetic and Algebra by Larry
Freeman - Kenwood Academy

Tony's Tiger BITES by Maudestine
McLeary - John Hope

Properties of Numbers by Steinfelds,
Leon - King High School

Make-and-Take: Staff Development by
Pintozzi, Joan - Curie Metro. H.S.

An Introduction To
Sets by Belton, John P. - Jones Metro. H. S.

Discovering New Units by Jenkins, Kay
- James Shields Elementary School

Play Ball by Roslyn N. Matthews -
South Shore High School

Using Variables And Ratios To Get You In
The Right Gear by George K. Smith - Dunbar VHS

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