Fractions

demonstrates that dividing a whole into two parts can create equal or unequal parts

creates equal halves using all of the whole (e.g. folds a paper strip in half to make equal pieces by aligning the edges; cuts a sandwich in half diagonally; partitions a collection into two equal groups to represent halving)

makes quarters and eighths by repeated halving (e.g. locates halfway then halves each half; eight counters halved and then halved again into four groups of two)

identifies the part and the whole in representations of halves, quarters and eighths (e.g. identifies the fractional parts that make up the whole using fraction puzzles)

represents known fractions using various models (e.g. discrete collections, continuous linear and continuous area)

checks the equality of parts by iterating one part to form the whole (e.g. when given a representation of one-quarter of a length and asked, ‘what fraction is this of the whole length?’, uses the length as a counting unit to make the whole)

identifies fractions in measurement situations and solves problems using halves, quarters and eighths (e.g. quarters in an AFL match; uses two 1/2 cup measures in place of a 1-cup measure)

demonstrates that fractions can be written symbolically and interprets using part-whole knowledge (e.g. interprets 3/4 to mean three one-quarters or three lots of 1/4)

creates thirds by visualising or approximating and adjusting (e.g. imagines a strip of paper in 3 parts, then adjusts and folds)

identifies examples and non-examples of partitioned representations of fractions

divides a whole into different fractional parts for different purposes (e.g. exploring the problem of sharing a cake equally between different numbers of guests)

demonstrates that the more parts into which a whole is divided, the smaller the parts become

identifies the need to have equal wholes to compare fractional parts (e.g. compares the pieces of pizza when two identical pizzas are cut into six and eight and describes how one-sixth is larger than one-eighth)

creates equivalent fractions by dividing the same-sized whole into different parts (e.g. shows two-sixths is the same as one-third of the same whole; creates a fraction wall)

uses partitioning to establish relationships between fractions (e.g. creates one-sixth as one-third of one-half)

connects the concepts of fractions and division: a fraction is a quotient, or a division statement (e.g. two-sixths is the same as 2 ÷ 6 or 2 partitioned into 6 equal parts or to solve ‘Two chocolate bars shared among three people’ understands that it is 2 divided by 3, therefore they each get two-thirds of a chocolate bar)

justifies where to place fractions on a number line (e.g. to show two-thirds on a number line divides the space between 0 and 1 into three equal parts and indicates the correct location)

reasons and uses knowledge of equivalence to compare and order fractions of the same whole (e.g. compares two-thirds and three-quarters of the same collection or whole, by converting them into equivalent fractions of eight-twelfths and nine-twelfths; explains that three-fifths must be greater than four-ninths because three-fifths is greater than a half and four-ninths is less than a half)

uses strategies to calculate a fraction of a quantity (e.g. to calculate two-thirds of 27, determines one-third then doubles; to find three-eighths of 60, knows a quarter is equivalent to two-eighths and so finds a quarter by halving and halving again to get 15, halves to give 7.5 to find an eighth then adds 15 and 7.5 to accumulate three-eighths of 60 as 22.5)

expresses one quantity as a fraction of another (e.g. 140 defective items from the 1120 that were produced represents one-eighth of all items produced