Van De Walle suggests, "For students to really understand fractions, they must experience fractions across many constructs, including part of a whole, ratios and divisions".  He also stresses the necessity of students being aware of equivalent fractions. (Van De Walle, 2010, p286)

The concept of fractions is that a fraction is part of a whole or a fraction is less than one. It is with the use of familiar concrete materials that educators can introduce the concept of fractions to their student s. Students need to visualize and experience fractions using real-world resources and experiences. In prep most students can develop the basic understanding of a half, for example, A cake and be cut into equal parts, a A4 paper can be folded in half and quarters, (4 parts). For students to understand the primary concepts of fractions, they need time and practice to reinforce the concept that a fraction is part of a whole, or less than one. Students also need to have the knowledge that as the denominator increases the portion size decreases which is in contradiction to working in whole numbers where the portion is bigger as the number increases.

Common Fractions

A skill linked to common fractions is recognizing the parts and the whole of a fraction. By the end of year one, students should be able to create an image in their mind about one fraction, and how it is different to anther fraction. For example, by comparing the size of ½ an apple to the size of ¼ of an apple. Students would need to be able to visualize the smaller the denominator the larger the parts of the apple will be, or the larger the denominator, the smaller the part of the apple will be. A real-world resource, such as an apple is a great resource to use to demonstrate to students how to recognize the size of fractions during the student language stage of the Language Model (Jameson-Proctor, R 2011).

Further on, the same concept can be demonstrated with resources such as a fraction pizza. Students can build their own fractions by creating equal parts of the pizza and stating what the fraction is, for example, a student cuts the pizza in half, holds up one half and states “this is one part of two’”.  This moves students from the student language to the materials language stage as they begin to move away from familiar object to substituted objects.

The image below shows how a student may represent their ability to process their concept of fractions, at the materials stage of the language model.

Equivalent Fractions have the same value, even though they may look different. For equivalent fractions students need to build upon their understanding that the same fractional amount can be written in different ways, for example 2/4 is the same as 4/8.

When you multiply or divide both the top and bottom by the same number, the fraction keeps its value. A rule that student would need to remember and to demonstrate is ‘What you do to the top of the fraction you must also do to the bottom of the fraction’.

A thinking strategy that a student could use to demonstrate this is by using multiplication.

The picture below demonstrate how a student might demonstrate the different ways that 1/3 can be written at the symbolic stage of the language model. The strategy involves multiplying the top and bottom number by two to get the next equivalent fraction.

This strategy would be used during step 6 of the Teaching Sequence for Common Fractions (Jamieson-Proctor, EDX1280 Foundations of Numeracy Wk7.ppt 2011). 

BBC (2011). BBC Skill Wise + Maths. Dolphin Racing . Retrieved August 27 2011. From: http://www.bbc.co.uk/skillswise/game/ma17frac-game-dolphin-racing-fractions

Jameson-Proctor, R (2011). Topic 7- Fraction Concepts, Common fractions and Operations on CF’s. [Lecture recording].  University of Southern Queensland, Toowoomba. Recoding retrieved from:    https://mediarep-prd-vip.usq.edu.au/b-repository/2011/2/EDX/EDX1280/Lecture_7_Common_Fraction_Part_1/Lecture_7_Common_Fraction_Part_1_-_Flash_(Original_Size)_-_20110829_11.16.22AM.html

IXL (2011). Fractions: Halves, thirds, and fourths. Retrieved August 27 2011, from: http://www.ixl.com/math/grade-2/halves-thirds-and-fourths

National curriculum, (2011). Mathematics foundations years. From:  http://www.australiancurriculum.edu.au/Foundation 

Queensland Studies Authority, (2010). Mathematics essential learnings by the end of year three. Retrieved August 16 2011from http://www.qsa.qld.edu.au/downloads/early_middle/qcar_el_all_yr3.pdf

[YouTube] (2009). Beginning Fractions and Decimals Sample Clip. Created by: Rock And Learn. Retrieved August 28 2011 from: http://www.youtube.com/watch?v=FEh02-2XZoQ&feature=related

Van De Well, J. Karp, K. and ay williams, J (2010). Elementary & Middle School Mathematics Teaching Development. (7th Ed.). Pearson Education, Inc.