Developing whole-number place-value concepts, 1st Australian ed.

Developing whole-number place-value concepts, 1st Australian ed.

Number sense is linked to a complete understanding of place value, including extensions to decimal numeration as it develops across the primary and middle years. In Year 1, students count and are exposed to patterns in numbers up to 100 and they learn to think about groups of ten objects as a unit. By Year 2, these initial ideas of patterns and groups of ten are formally connected to three-digit numbers, and in Year 4 students extend their understanding to numbers up to 1 000 000 in a variety of contexts. In Year 4 and Year 5, the ideas of whole numbers are extended to decimals (ACARA, 2016). A significant part of this development includes students putting numbers together (composing) and taking them apart (decomposing) in a wide variety of ways as they solve addition and subtraction problems with two- and three-digit numbers. Place value is a way for students to think about larger quantities (Mix, Prather, Smith, & Stockton, 2014) and to enhance their ability to invent their own computation strategies. Without a firm foundation and understanding of place value, students may face chronic low levels of mathematics performance (Chan & Ho, 2010; Moeller, Martignon, Wessolowski, Engel, & Nuerk, 2011). The following big ideas are the foundational concepts that will lead students to a full understanding of place value.