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Introduction to Fractions

By Anna Warfield

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Introductory Fractions: Numerator and Denominator


This fraction lesson plan is a mini supplement on fractions to be used for remedial or extension work and information, teacher guidance and inspiration, alternative instruction, integrating writing and mathematics, or for whatever you wish!


Teachers can use Storyboard That to make short storyboards for a concept, discussion springboard, quick visual review before a unit or lesson, word problems, or as a slideshow presentation to accompany a lesson!

Have students use Storyboard That to write math stories, fraction word problems with realistic applications, explain a concept as an assessment, or explain a concept to show another student (student exchange).



Making the switch from whole numbers to parts and wholes can be very difficult for young minds. It is mind-boggling for some to learn that there are numbers between the counting numbers! Fractions is a topic with which many students struggle throughout elementary and middle school, so it is important that students have a thorough understanding of what fractions are, estimating and comparing amounts visually and numerically, and recognizing reasonable answers.

Encourage students to talk about fractions and what they mean. Mathematics is not all about numbers and answers, but also understanding and reasoning. Teacher-led question and answer sessions are very helpful, but it is also very beneficial for building strong foundations if teachers, and eventually students, lead discussions on mathematical concepts. Fractions can be an excellent starting point for such discussions. Pose a question to the class, such as the Jack and Jill arguments below, for the class to ponder on their own and share, or discuss in small groups.



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What's the Story with Fractions?
What's the Story with Fractions?

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Teacher Information

Many students confuse fractions with the whole numbers that they are so used to seeing. The number “1/3” looks like two different numbers rather than a single numerical value. A fraction is a number with an integer numerator and a nonzero denominator that, for our purposes, can represent rational numbers (1/4 or 3 2/5) and whole numbers (4/2 = 2). The “numerator” is the quantity in the top section of the fraction that represents the number of parts, and the “denominator” is the value below the fraction bar indicating the number of partitions or shares, known also as the “whole".

Fraction notation can indicate ratio and proportions, multiplicative relationships, quotient when dividing two numbers, measurement, and parts of wholes or sets. Beginning fraction masters need only worry about parts of wholes or sets and measurement, but astute students will likely notice multiplicative relationships (i.e. the half circle is twice the size of the quarter circle or, inversely, the quarter circle is 1/2 the size of the half circle) and dividing two numbers (sharing 7 cookies among 3 people would be written 7/3, the same as 7 ÷ 3).

Student Prior Knowledge

Students should come into third grade knowing that shapes can often be split into equal shares, such as halves, thirds, and quarters or fourths. The concept of sharing items, such as supplies or food, as well as sharing time fairly, like turn-taking or splitting the day into class periods/subjects, should be well established by this age. Draw on real-life examples whenever possible to strengthen understanding.

While it is not imperative, it is helpful if students are already familiar with multiplication and division. Mastery of basic facts is a separate skill from understanding and manipulating fractions, but understanding one may help the understanding of the other. Consider reviewing the multiplication/division facts as necessary.

Introduce fractions to students by allowing them to investigate and review prior knowledge. This can be done in a myriad of ways, such as asking what they know, a coloring activity, exploring manipulatives like fraction tiles or pattern blocks, a short video, or an adorable comic strip.


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Fractions Aren't That Scary
Fractions Aren't That Scary

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Identify Unit Fractions

Fractions show equal shares. Pictures that show shapes partitioned into sections that are not the same size do not show examples of fractions. Show pictures of shapes that have been equally and unequally divided.

Allow students to identify the total number of parts in a whole, such as a circle, to find the denominator. The bottom of the fraction, represents the number of partitions (equal shares). Each piece of the whole is therefore one of the whole. Have students guess what to call each part (one half, one third, one fourth etc.) and create a chart together to show the first few common unit fractions. Make a template in Storyboard That to print or project onto the board, or have students create their own storyboard as an assessment of understanding.


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Multiple Numerators

Introduce vocabulary of numerator and denominator. The numerator is the number on top of the fraction bar that represents a part of a whole. The denominator is the number below the fraction bar that shows the number of pieces or partitions in a whole. Numerator looks a little like “number” (how many) and denominator may remind some students of “name”, particularly if they are familiar with other languages, such as French or Spanish. The denominator gives the fraction its name (eg. fifths), and the numerator tells you how many parts of the whole there are (three-fifths).

Have students identify the given fractions and fraction pictures by both number and word names. The examples below show a partially filled storyboard for students to start from, and one way the storyboard could be completed. Additionally, students can create their own on Storyboard That to demonstrate understanding.


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Integrate word problems or fraction stories as examples whenever possible. Depending on the knowledge base of your students, continue on to identifying fractions, or allow students time to explore materials and discuss their findings. Show different ways to represent the same fractions.


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Frayer Model for 2/3
Frayer Model for 2/3

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Fractions on a Number Line

Review the number line with whole numbers briefly; have students create their own number lines in a notebook, on chart paper, or by standing in a row evenly spaced apart. Draw attention to the space in between the whole numbers, and ask students about the value of a spot that is not labeled by a whole number. Show a storyboard to introduce fractions on a number line. Use the example below or come up with your own!


Be sure to point out what whole you are using. For a special challenge, encourage students to think carefully by changing the whole: 0 to 2 or 0 to 10. (1/2 of 10 is 5; 2/5 of 10 is 4)



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Fraction Number Line
Fraction Number Line

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Compare Fraction Denominators

Many students will see a larger number in the denominator and think that the bigger number means a bigger value. Fractions are sneaky that way: as the denominator gets bigger, that means that the whole is being divided into more and more smaller pieces.

Have students create a fraction story that shows what happens when a whole is divided into more and more pieces. Some possible wholes for the story might be:



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Bigger Denominator, Smaller Piece
Bigger Denominator, Smaller Piece

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•   (English) Introduction to Fractions   •   (Español) Introducción a las Fracciones   •   (Français) Introduction aux Fractions   •   (Deutsch) Einführung in Fraktionen   •   (Italiana) Introduzione Alle Frazioni   •   (Nederlands) Inleiding tot Fracties   •   (Português) Introdução às Frações   •   (עברית) מבוא שברים   •   (العَرَبِيَّة) مقدمة في الكسور   •   (हिन्दी) भिन्न करने के लिए परिचय   •   (ру́сский язы́к) Введение в Фракциях   •   (Dansk) Introduktion til Brøker   •   (Svenska) Introduktion Till Fraktioner   •   (Suomi) Johdatus Murtoluvut   •   (Norsk) Introduksjon til Brøker   •   (Türkçe) Kesirlere Giriş   •   (Polski) Wprowadzenie do Frakcji   •   (Româna) Introducere în Fracții   •   (Ceština) Úvod do Zlomků   •   (Slovenský) Úvod do Zlomkov   •   (Magyar) Bevezetés a Frakciókat   •   (Hrvatski) Uvod u Frakcije   •   (български) Въведение в Фракциите   •   (Lietuvos) Įvadas į Šratų   •   (Slovenščina) Uvod v Frakcij   •   (Latvijas) Ievads Frakcijas   •   (eesti) Sissejuhatus Fraktsioonid