DK+&+PK+for+fractions+and+decimals+-+Year+1+&+2


 * **Year Level** || **Content Descriptor** || **Declarative Knowledge & Procedural Knowledge** || **Progression from the Previous Year Level** ||
 * Year 1 || ======__Recognise and describe one-half as one of two equal parts of a whole __======

Elaborations
 * 1) sharing a collection of readily available materials into two equal portions
 * 2) splitting an object into two equal pieces and describing how the pieces are equal || ======//'Recognise and Describe'// Key Ideas ======

- "recognise and describe"
||  ||
 * ======Year 2====== || ======__Recognise and interpret common uses of halves, quarters and eighths of shapes and collections __======

Elaborations
 * 1) recognising that sets of objects can be partitioned in different ways to demonstrate fractions
 * 2) relating the number of parts to the size of a fraction || ======//'Recognise and Interpret// 'Key Ideas ======

=
- objects can be partitioned in different ways to demonstrate fractions ======

=
- Identify how many parts there are in 1/4 or 1/8 etc. (how many parts make up halves, quarters and eighths ======

- "recognise and interpret"
|| ======- Language went from "recognise and describe" to "recognise and interpret" ======

=
- use materials to split in half to using shapes to demonstrate fractions ======

||

__Content Descriptor/s __ <span style="background-color: #ffffff; font-family: Helvetica,sans-serif; font-size: 12px;">Recognise and describe one-half as one of two equal parts of a whole
 * __<span style="font-family: Arial,sans-serif;">Year One __**

__<span style="font-family: Arial,sans-serif;">Analysis of Declarative and Procedural Knowledge __ The fractions and decimals sub-strand is explored for the first time in Year One. Knowledge and skills regarding this strand are developed in the Foundation Year, as students obtain a strong understanding of number and place value (ACARA, 2012). Knowledge of number and place value is the foundation upon which fractions and decimals is taught (Booker et al., 2010). In Year One students focus on **//recognising//** and **//describing//** one-half. ACARA (2012) adds the significant comment that one-half should be recognised as one of two equal parts of a whole. This is significant because it introduces the idea of //**partitioning 'one whole'**//. At this stage of learning it is important for students to recognise the **//whole//** as well as the **//two equal parts//** (ACARA, 2012). This can be demonstrated by splitting an object in half and examining the two equal pieces or by "sharing a collection of materials into two equal portions" (ACARA, 2012). In both cases it is important to use concrete materials to make strong connections to the mathematical knowledge (Booker et al., 2010). The Year One Achievement Standards - Maths Portfolio supports the notion that exploration with fractions should expose students to recognising and describing one-half using various forms, shapes and sizes to ensure a deep understanding in these early stages of learning (ACARA, 2012).



__<span style="font-family: Arial,sans-serif;">Content Descriptor/s __ <span style="background-color: #ffffff; font-family: Helvetica,sans-serif; font-size: 12px;">Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
 * __<span style="font-family: Arial,sans-serif;">Year Two __**

__<span style="font-family: Arial,sans-serif;">Analysis of Declarative and Procedural Knowledge __ In Year Two students continue to explore fractions, building on basic knowledge gained in previous years. Students are introduced to quarters and eighths, as well as continuing with halves (ACARA, 2012). One of the main progressions from the previous year level is the key word **//interpret//**. In Year One students **//recognise//** and **//describe//**, but in Year Two, they **//recognise//** and **//interpret//** fractions using shapes and collections (ACARA, 2012). Interpretation of common fractions requires students to develop language and understanding of concepts such as partitioning, parts and whole. Students learn that objects and collections can be partitioned in different ways, other than two equal parts, such as four or eight equal parts(ACARA, 2012). Significant knowledge and skills are developed by analysing the parts and the whole. The size of the fraction is explored, as is the relationship between the number of parts and the size of the fraction (ACARA, 2012).