Fractions+&+Decimals+Yr+3

Fractions and Decimals Sub Strand of Number and Algebra Year 3 Analysis

**Background**
Students in year three extend their knowledge of fractions and decimals beyond the notion of an eighth can be found through a half, of a half, of a half. Year three students begin to explore thirds and fifths and continue to explore halves and quarters. It is important that the notion of equal parts, number of part names the parts and as the number of parts increase the size of each part decreases (Booker, 2011, P.418). The continuation of making references to these understandings is important in the notion of developing students understanding of fractions and decimals. A solid understanding of halves, quarters and eights is important when beginning to deal with thirds and fifths. Students should be given plenty of opportunities to practice thirding and fifthing strategies exploring rectangular shapes and number lines. The Australian Curriculum - //Mathematics// (2010) outlines that students by the end of Year 3 should be able to use and recognise fraction symbols. Booker (2011, P.420) states a deep understanding of the representations of fractions in early years imparts the knowledge needed to make sense of fractions.

**The Australian Curriculum**
Outlined below are the content description and elaborations for fractions and decimals at a year two level.

** Content description ** Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole

(ACARA, 2010)
 * Elaborations **
 * 1) Partitioning areas, lengths and collections to create halves, thirds, quarters and fifths, such as folding the same sized sheets of paper to illustrate different unit fractions and comparing the number of parts with their sizes
 * 2) Locating unit fractions on a number line
 * 3) Recognising that in English the term ‘one third’ is used (order:numerator, denominator) but that in other languages this concept may be expressed as ‘three parts, one of them’ (order: denominator, numerator) for example Japanese

By the end of Year three students model and represent unit fractions (ACARA, 2010). The following activity has been adapted from ACARA - Worksamples (2011). The goal of the activity is to get students thinking, analysing, recording and using technical vocabulary to represent fractions. The activity is best suited towards the end of a unit on fractions. The aim of the activity is for students to:
 * Activity 1 Fractions – Representing Fractions **
 * Demonstrate their understanding of fractions and terminology used to represent them
 * Exhibit their ability to partition areas, lengths and collections to create a variety of different fractions

The activity is suited to group and individual work. Students start with a piece of cardboard with the word “Fractions” in the centre. The students then rule the cardboard into quarters. Each student/group receives four different fractions (each set is different) which they need to represent. Students receive a variety of resources to assist them in their investigations. Each group (if completed as a group activity) then explains their findings using correct vocabulary to the rest of the class. Encourage whole class discussions around the results.



**References**
Australian Curriculum Assessment and Reporting Authority. (2010). //The Australian Curriculum: Mathematics.// Retrieved April 5, 2012, from Australian Curriculum Assessment and Reporting Authority Web site: [|http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10?layout=2&y=6&y=7&y=8&y=9&s=NA#level=8]

Australian Curriculum Assessment and Reporting Authority. (2011, December). //The Australian Curriculum:Year 3 Mathematics - Student Portfolio Summary.// Retrieved April 3, 2012, from Australian Curriculum Assessment and Reporting Authority Web site: []

Booker, G., Bond, D., Sparrow, L., & Swan, P. (2004). //Teaching primary mathematics (3rd ed.).// Frenchs Forest, New South Wales: Pearson Education.
 * Matt :) **