AND NOW FOR SOME FRACTIONS AND DECIMALS AND PLACE VALUE!
Fractions and Decimals and Place Value are inextricably related. Fractions came about 3000 years before place value was extended to include fractions as decimals. Students in Years K-3 investigate fractions, to develop deep understanding, before beginning to investigate fractions as decimals in Year 4. (See the diagram below.)
Students begin investigating fractions of shapes in Kindergarten/Prep/Reception when they investigate halves of shapes (FD 1).
Students begin investigating fractions of groups in Year 1 when they investigate halves of groups, relating this to dividing into 2 equal groups (FD 2 PA 9).
Students begin investigating more fractions that can be created by halving – quarters and eighths in Year 2 (FD 3, 4, 5, 6, MD 8).
Students begin investigating the meaning of the denominator in Year 3 (FD 7) while they are dividing by 2, 4, 3 and 5 (MD 10, 11, 12, 13). They investigate multiplicative relationships between fractions, non-unit fractions and the role of numerator, and placing fractions on a number line (FD 8, 9, 10).
Students continue their investigation of additive and multiplicative place value in Year 4, with an investigation of tenths and hundredths (PV 20, 21, FD 11, 12), money as decimal to 2 places (PV 22, FD 16), and rounding decimals (PV 23, FD 17). Students investigate equivalent fractions with concrete material and using the relationship between numerator and denominator, place equivalent fractions on a number line, and fractions in number patterns (). (FD 13, 14, 15, AS 26, PA 22).
Students begin investigating using multiplicative place value to multiply and divide by 10, 100 and 1000 (FD 18, PV 24) in Year 5, and extend their investigation of additive and multiplicative place value to thousandths (FD 21, PV 25). They investigate the meaning of the vinculum (FD 19) to divide the remainder to create a fraction (MD 22, FD 20). They investigate ordering numbers to thousandths and number patterns with decimals (FD 22, 24, PV 26, 27, PA 27). Students investigate adding and subtracting fractions with the same denominator ( FD 23, AS 28).
Students begin to investigate additive and multiplicative place value of numbers of any size (FD 25, PV 28) in Year 6, multiplying and dividing by decimals (FD 26, PV 29, MD 25). They use their understanding of the relationship between division and fractions to explain that division is multiplication by a fraction (FD 27, MD 26). The investigate fractions in their simplest form (FD 28) percentages as hundredths and percentage discounts (FD 29, 30). Students investigate probabilities using fractions, decimals and percentages (FD 31, PV 30, SP 16). They investigate adding and subtracting decimals and fractions with related denominators (FD 32, 33, PV 32, AS 29,30) and patterns with fractions and decimals (FD 34, PV 31, AS 31, PA 28).