Chapter 12 concept mapSample Page
Meanings
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Representations
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Introduction Fractions and decimals have long been a stumbling block for many students. One reason may be that curricula tend to rush to symbolisation and operations without developing the strong conceptual understandings that children must have for fractions and decimals. Therefore. much of this chapter is devoted to helping children develop the concepts they need for working with fractions and decimals. and for the mathematical processes underlying operations with these numbers. Tables 12.1 and 12.2 are extracted from the Australian Curriculum and identify the expectations in relation to students’ understandings of fractions and decimals from the Foundation year of schooling to Year T The recommendations clearly indicate that older children should work to develop fluency in computation of fractions and decimals but to do so after they have developed relevant conceptual understandings about fractions.
TABLE 12.1
Expectations for children “s learning of fractions and decimals from Year 1 to Year 7 based on the Australian Curriculum Number and Algebra content strand
Year level Content description •
Year 1
Fractions and decimals • Recogilse and describe one-nalf as one or tAo equal parts of a whole
Year 2
Fractions and decimals • Recoonise and Interpret common uses of halves, quarters and eighths of shapes and cob:onions (AC lANA1333).
Year 3 Fractions and decimals
1 1 1 1 • Model and represent urit fractions =luting -2 4′ – – 3′ – 5 and tner miltioles to a complete whole
(iad: %IN A.058O. Money and financial mathematics • Represer rncnei values in multiple ways and count the change requred for srrpie trarsactions to the neatest five cents (ACMNA059).
Year 4
Fractions and decimals • Investigate equivaient fractions used In contexts i’,NCM4A3771. • Count by quarters, halves and tnIrcls. IncludIrg with mixed numerals. Locate and represent these fractions on a number Ine l’ACMNA0781. • Recogilse tnal the place value system can te extended to tentns and hurOredths. Mao:, connections between rranons and decimal notation pNCPANA3791. Money and financial mathematics • Solve problems Invorvng purchases and the calcilaikm 01 change to the nearest five cents with and without cignal tectirologles i:Acmweo).
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