## 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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