DK+&+PK+for+fractions+and+decimals+-+Year+3


 * **Year Level** || **Content Descriptor.** || **Declarative Knowledge & Procedural Knowledge** || **Progression from the Previous Year Level** ||
 * Year 3 || __Model and represent unit fractions including__ __1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole__

**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. || 'Model and Represent' - partitioning area and length to represent 1/2, 1/4, 1/3 and 1/5 - use multiples of 1/2, 1/3, 1/4, 1/5 to create a complete whole - numerator and denominator - complete whole - compare the number of parts with size of the fraction || - Language goes from 'recognise and interpret' to 'model and represent'

- From halves, quarters & eighths to now also include thirds and fifths

- Fractions are part of a set from visual recognition and interpretation to modelling, representing and comparing. ||

__Content Descriptor/s __
 * __Year Three __**

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058)

__Analysis of Declarative and Procedural Knowledge __ In Year 3 students continue to build on their basic mathematical understanding of fractions. Partitioning is revisited, although this is done using a larger range of fractions. ACARA (2012) states, that although repetition of content descriptors is avoided, concepts and skills can be revisited in order to strengthen and extend students future declarative and procedural knowledge. Students still require active experiences using models, pictures and concrete materials as they model and represent mathematical ideas about fractions (ACARA, 2012). The metalanguage ‘model, represent and compare’ is a key indicator that critical and creative thinking is prevalent in this year level. ACARA (2012) believes that students are engaged in critical and creative thinking throughout the proficiency strands of **Understanding, Reasoning and Problem Solving.** Declarative knowledge is achieved as students develop an **understanding** of partitioning, unit fractions and the metalanguage of numerator and denominator. Procedural knowledge is achieved as students use **reasoning** and **problem solving** when they model, represent and compare fraction multiples to a complete whole.