Overview+of+Fractions+and+Decimals

The earliest use of fractions were symbols that were used by the Egyptians to work out tax payable on a farmers land (Siemon, Beswick, Brady, Clark, Faragher & Warren, 2011)and to divide bread amongst workers (Booker et al., 2004). These mathematical origins are still explored and taught in primary schools today. In ACARA’s Fractions and Decimal sub-strand fractions are introduced in Year 1, where students can recognise and describe a representation of one-half as two equal parts of a whole (ACARA, 2012). This fundamental declarative and procedural knowledge is called partitioning and forms a foundation for this sub-strand. Partitioning is essential in developing a strong sense of number (Siemon et al., 2011). Booker et al. (2004) believes that numeracy includes number sense along with problem solving skills. Therefore, fractions cannot be taught in isolation as it relies on a firm understanding and awareness of the Number and Place Value sub-strand. Patterns and sequencing are taught in the early years of schooling in the Patterns and Algebra sub-strand (ACARA, 2012). Patterns are essential to mathematical thinking and lay the foundation for work with symbols such as fraction and decimals. Furthermore fractions used in area and length have a close link to the Measurement and Geometry Strand in the Australian Curriculum.

As students enter the latter years of primary school decimals and percentages are introduced; decimals are introduced in Year 4 and percentages are introduced in Year 6. By now students need to have developed a meaningful foundation in partitioning and rational number in many forms such as proper fractions, mixed fractions, decimal fractions and percentages (Siemon et al., 2011). Place value, numeration and partitioning skills learnt in the early years assist in this transition. Decimal fractions are introduced using partitioning, and per cents can be linked to decimal fractions to indicate a proportion of each hundred (Booker et al., 2004).

ACARA (2012) suggest that while teaching the Fractions and Decimal sub strand teachers use authentic learning experiences. Payne and Rathmell (n.d. as cited in Department of Education, Employment and Workplace Relations [DEEWR], 2010 p.2) recommends that students should progress from ‘real-world situations to concrete or visual representations of a mathematical problem or concept; then to verbal descriptions, and then to symbols to depict the concept’.



The Fractions and Decimal sub-strand is inter-connected with many other strands and sub strands in the Australian Curriculum. DEEWR (2010) believes that teachers who help students to make connections with these inter-connected mathematical concepts allow them to increase and expand their understanding of the key essential ideas in mathematics.

**Mathematical concepts** **connected to the Fraction and Decimal sub-strand.**