## Fractions

### Elementary School Lessons & Materials for Teachers

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The lessons and materials available here come from a variety of sites and organizations. Some include offers for video or software, and some are lesson plans. Where the originals are Claris or Acrobat (PDF) documents, we have for the most part converted them to HTML, leaving a link back to the parent page from which you can download the formatted version.

For more on fractions, search or browse the fractions/decimals/percents pages in the Internet Mathematics Library.

#### Introduction to Fractions

What are Fractions? (Neufeld)
Use concrete examples to understand the meaning of fractions, and compare and order them.
Fractions are Cool! (Fraction Vocabulary) (WWMT)
The meaning of 'numerator', denominator', 'proper' and 'improper' fraction, 'greatest common factor' (GCF), fraction in lowest terms', 'least common multiple' (LCM).
Simple Fractions (S.O.S. MATHematics)
Covers Identification, Factoring Integers, Reducing Fractions, Multiplication, Division, Building Fractions, Addition, Subtraction, and Order of Operations.

#### Addition and Subtraction of Fractions

Add fractions with the same and different denominators, and reduce them to simplest form.
Subtracting Fractions (Neufeld)
Subtract fractions with the same and different denominators.
Fraction Shapes (Lanius)
No matter what shape your fractions are in... a geometric approach.
Edible Fractions on Fraction plates (Caniglia)
Practice understanding fractions as part and whole as well as the concept of fractions in real-life situations.
Fractions in the Olympics (Caniglia)
Add unit fractions with the same or different denominators.
Search for Wholes (Caniglia)
Add fractions with like and unlike denominators to find whole units.
Visual Fractions (Rand)
A site with Java programs that provide instruction and practice in identifying and renaming fractions, adding and subtracting fractions, mulitplying and dividing fractions, and comparing fractions.

#### Multiplication and Division of Fractions

Multiplying Fractions (Neufeld)
Learn to multiply fractions.
Multiplying Fractions (Millard)
A lesson that includes a worksheet and an interactive exploration of the concept of 3/5 using The Geometer's Sketchpad.
Dividing Fractions (Neufeld)
Learn to divide fractions.
Common Fractions (Junior Maths, S.M.A.R.D.)
From the Secondary Mathematics Assessment and Resource Database: Two approaches to dividing fractions.
Multiplying Fractions; Mixed Numbers (Explorer)
From a series of 18 15-minute videos. To solve a series of problems that arise when they go into the pizza selling business, students learn how to multiply fractions. A designer of television and movie sets describes how multiplying fractions and mixed numbers helps him measure and build precisely.
Visual Fractions (Rand)
A site with Java programs that provide instruction and practice in identifying and renaming fractions, adding and subtracting fractions, mulitplying and dividing fractions, and comparing fractions.

#### Mixed Numbers

Adding and Subtracting Fractions and Mixed Numbers (WWMT)
Mixed numbers are whole numbers that are mixed with fractions: learn to look at the denominators.
Subtracting Mixed Numbers (Explorer)
From a series of 18 15-minute videos. Using a game show format, students learn how to subtract mixed numbers. The show's host explains the steps involved: common denominators, regrouping, and subtracting only the numerators. Common mistakes are explained . A costume maker explains the importance of understanding subtraction of mixed numbers in his work.
Multiplying Fractions; Mixed Numbers (Explorer)
From a series of 18 15-minute videos. To solve a series of problems that arise when they go into the pizza selling business, students learn how to multiply fractions. A designer of television and movie sets describes how multiplying fractions and mixed numbers helps him measure and build precisely.
Dividing Fractions and Mixed Numbers
What is 1 1/2 divided by 1/2? From the NASA Math Proficiency Test. A detailed answer is provided.
Visual Fractions (Rand)
A site with Java programs that provide instruction and practice in identifying and renaming fractions, adding and subtracting fractions, mulitplying and dividing fractions, and comparing fractions.

#### Equivalent Fractions and Fractions as Parts of Wholes

Edible Fractions on Fraction plates (Caniglia)
Practice understanding fractions as part and whole as well as the concept of fractions in real-life situations.
Equivalent Fractions (Neufeld)
Express fractions as equivalent fractions and reduce them to simplest form.
Equivalent Fractions (Lofties)
An activity designed to show students that the notion of several names for a number is similar to the notion of several names for a person.
Fraction Games (Caniglia)
Games designed to help students see parts of the whole and equivalent fractions.
Mars Fraction Hunt (Williams)
Provides practice in the use of fractions, changing fractions, using equivalent fractions, and paying attention to detail.
Orange Slices (Caniglia)
Investigate oranges to find out if oranges have the same number of slices; investigate the fractional part of an orange.
Search for Wholes (Caniglia)
Add fractions with like and unlike denominators to find whole units.
Seeing Equivalency (Jewell)
Overhead transparencies you can make to show students how equivalent fractions measure up on the number line.

#### Fractions in Real Life Situations

Edible Fractions on Fraction plates (Caniglia)
Practice understanding fractions as part and whole as well as the concept of fractions in real-life situations.
Fractions in the Olympics (Caniglia)
Add unit fractions with the same or different denominators.
Fractions in Recipes (DeSpain-Lyon)
Use a recipe for brownies to practice adjusting quantities in cooking for different numbers of people.
Mighty M&M Math (Judy Conklin)
Fun ways to learn about fractions and percentages using these favorite candies.
Multiplying Fractions; Mixed Numbers (Explorer)
From a series of 18 15-minute videos. To solve a series of problems that arise when they go into the pizza selling business, students learn how to multiply fractions. A designer of television and movie sets describes how multiplying fractions and mixed numbers helps him measure and build precisely.
Share 6 cookies With 7 People (MathMan)
Young children (ages 6-7) learn to add fractions through graphing and partial sums, and about infinite series. A sample problem with answers from Chapter 1 of Don Cohen's worksheet book.

#### Fractions and Decimals

Decimals (WWTF)
A bit about decimals as ratios and how they relate to fractions.
Shooting Percentages (Jewell)
Have fun tossing a ball into a wastebasket while at the same time practicing skills at fraction/decimal conversion and knowledge of percentages.

#### Tangrams and Fractions

Tangrams and Fractions (Caniglia)
Tangram puzzles provide an excellent background for determining fractional parts and wholes.
Constructing Your Own Set of Tangrams (Scavo)
From Tom Scavo's Web Unit on Tangrams
How To Make a Tangram Set (Tobler)
Download Claris Works or Acrobat (PDF) files of lesson plans and directions for making tangrams
Make Tangrams (Zenigami)
Offers insight into how tangram pieces fit together, and stimulates interest in forming shapes and exploring patterns.

#### Review and Enrichment

Chinese Tangram Puzzles (Multicultural Math Fair)
Students solve puzzles using rotation, reflection and translation to fit all the pieces together. Versions in English and Spanish.
Fractions of a Dollar (Taking Stock)
Students convert fractions used in stock quotes into dollar equivalents.
Fractions Review (Triton College)
A review that covers the definition of a fraction, an important property, equality, reduction, addition, multiplication, and division.
Fraction Shapes (Lanius)
No matter what shape your fractions are in... a geometric approach.
Hershey Fractions (Tobler)
Use a Hershey chocolate bar to reinforce fractional concepts.
Learn Fractions with Cuisenaire Rods (Silha)
Pages that teach fractions using manipulatives: Taken in order, these lessons build on each other and reinforce basic knowledge of fractions. What are Cuisenaire Rods? Using Cuisenaire Rods to Name a Fraction; Identify the Numerator and Denominator; Least Common Denominator; Adding and Subtracting Fractions; Equivalent Fractions; Teacher Notes.
Make One (Buckeye)
A card game: review the four basic operations with fractions.
Zero-In (Buckeye)
A card game using fractions: be the first player to lay down all cards in a book or books.
Monster Math (Jewell)
A card game to reinforce any math concept.
A lesson that can be used to review any kind of mathematics material.

#### Reference Materials

Summary of Fractions (S.O.S. MATHematics)
An outstanding summary of rules that concern operations with fractions.
Eric's Treasure Trove of Mathematics (Eric Weisstein)
Select the letter "f" and look for "fraction" and "fractal."
Fibonacci Numbers, Pineapples, Sunflowers and The Golden Mean (Mathman)
Mathematics from a Pineapple: Infinite sequences, limit of a sequence, ratios, fractions,and decimals. Also Looking at a Regular Pentagon. Sample problems from Chapter 7 of Don Cohen's book, Calculus By and For Young People.
Ian's Proof that Infinity = -1 (Mathman)
Young children try writing the sum of an infinite series as a fraction. A sample problem from Chapter 3 of Don Cohen's book, Calculus By and For Young People.
Measuring Fractions & Decimals: Memory Aid (Johnny Hamilton)
Double and halve measuring fractions; halve mixed numbers with an even or odd whole number. Excerpt from the book Math to Build On by Johnny and Margaret Hamilton (1993).
Fractions and Infinite Series (Mathman)
Seven-year-olds add 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ... forever! A sample problem from Chapter 1 of Don Cohen's book, Calculus By and For Young People.
Share Six Cookies with Seven People (Mathman)
Young children (ages 6-7) discover fractions by dividing cookies: 3 cookies between 2 people, 2 cookies among 3 people, etc. A sample problem from Chapter 2 of Don Cohen's book, Calculus By and For Young People.
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Mara Landers