Key+stages+of+development

__Analysis of the key stages of development__

 * Key findings are represented in the graphic organiser below.

FOUNDATION
 * Although the 'Money and Financial Mathematics' strand is not found in Foundation year it is likely that students will have gained some exposure to money in their home and school context. Exposure to money at this stage would be highly beneficial as it lays the foundation for year one when students are required to begin working with money.
 * In the ‘Number and place value’ sub-stand students are developing language and skills relevant to ordering things based on characteristics - including language using more or less (Australian Curriculum, Assessment and Reporting Authority (ACARA), 2012).

YEAR ONE YEAR TWO
 * In year one students are introduced to all coins in the Australian currency.
 * Students **recognise** and **describe** coins using their distinctive features including size, colour, shape and images.
 * The language of money is being developed as students describe the Australian coins.
 * Using the skills learnt in the 'number and place value' strand in foundation year students further develop as they **order** Australian coins according to their value from least to greatest and vice-versa.
 * Students at this stage of development are using lower-order thinking skills outlined in Bloom's revised taxonomy under //Remembering.// They learn terms, key concepts and facts associated with money retrieving, recognising, and recalling relevant knowledge and information about Australian currency (Frangenheim, 2009).
 * Extending on the knowledge in year one students add notes from the Australian currency to their repertoire.
 * In year one students were **ordering** coins according to their value -now they are ordering **coins and notes** according to their value.
 * Student have moved from **recognition** to **manipulation** of the coins as they **count** collections of currency to make up a particular value (ACARA, 2012).
 * The concept of **equivalency** is introduced and students are required to **identify** equivalent values.
 * In year two the progression is evident as students have moved from the stage of //Remembering// to //Applying// when they use their knowledge of Australian coins and notes to order and count small collections according to their value (Frangenheim, 2009; ACARA, 2012).

YEAR THREE
 * In year two students counted collections of coins to make up a particular value. Students are extending upon this knowledge in year three as they **represent** particular values in multiple ways. This is a key developmental stage that allows students to further develop their sense of number through partitioning (for example that $1 can be shown as 50c and 50c, or with five 20c coins). This involves students moving beyond the recognition of the coins names and numerals to the creation of flexible mental imagery that includes knowledge of the part-part-whole concept (Department of Education and Early Childhood Development (DEECD), 2009). This will support students to develop a deeper understanding of each coin's worth as they 'trust the count'.
 * Students continue to build upon their knowledge of equivalency as they recognise the relationship between dollars and cents.
 * Students begin to use money in real-life situation such as counting change for simple transactions.
 * The ability to round money values to the nearest 5c is introduced. This is necessary for calculating values when adding two costs to a total and when providing change. This is an important stage of development because it must highlight that rounding in money is done to the nearest 5 cent increment rather than the nearest 10 cent.

YEAR FOUR
 * In year three students were required to **count** the change due for simple transactions, now they are required to **calculate** the change themselves (ACARA,2012).
 * Students begin to **solve problems** that include the **calculation** of change. This is a key stage because students must be aware that the 'adding on' approach is preferred over subtraction when calculating change (Siemons, Beswick, Brady, Clark, Faragher, & Warren, 2011).
 * The use of digital technologies begins.
 * While carrying out calculations using both dollars and cents, students **identify money as a decimal system**. This links to the sub-strand of fractions and decimals as year four students "recognise that the place value system can be extended to tenths". This knowledge of decimal notation is also necessary in this year level as they make links between fractions (ACARA, 2011).

YEAR FIVE
 * New concepts will be introduced including budgeting, lending, saving and borrowing. This stage will require a substantial knowledge of money and its relevency to citizens in a modern society.
 * Students are using higher-order thinking skills as they move from knowledge aquisition to knowledge creation -taking what they have learnt in the previous years to **create** a product that has real life application (simple financial plans).
 * The knowledge of GST is introduced and students are expected to be able to **identify** the GST component of an invoice.

YEAR SIX
 * Students at this level begin to **investigate** percentages through exposure to real-life examples such as sale items or discounted services. They will have already had exposure percentages in the 'money and financial mathematics' strand when they were identifying the 10% GST component in year five. This is a key stage of development that will expand upon students prior experiences in year five where they began to solve problems that invovled the multiplication of one and two-digit numbers (ACARA, 2012). This is an expansion on these skills because a number of operations related to percentages require the multiplication of whole and decimal numbers.
 * Students build on prior knowledge of equivalence and decimal systems through the representation of percentage values in decimal notation.
 * The term ‘of’ is introduced and recognised as indicating multiplication. It is then used as students calculate percentage discounts.
 * Students will also be converting whole numbers to decimals before they **calculate** percentages (for example 12% will become 0.12%).

YEAR SEVEN YEAR EIGHT
 * In year seven students are required to **investigate** and **calculate** "best buys". The ability to do this will require a number of prerequisite skills. Students use previous knowledge developed in the sub strands of measurement and geometry -including units of measure, as well as money and financial mathematics. Another skill used in this year is comparing, a skill evident and taught through the curriculum from foundation year.
 * compare costs per item to come to a conclusions regarding ‘best buys’. To enable students to do this, The concept of unitary price is a key stage of development in year seven.
 * The term "best buys" is a key concept at this stage that must be explicitly taught (someone may see a 100g packet of biscuits for $2 and a 250g packet of biscuits for $4 and select the 100g pack because it is cheaper, not realising that they are getting less for their money).
 * In this year students **solve problems** involving profit and loss. This will include students calculating profit and loss using subtraction, calculating percentage profit or loss and comparing. This will involve the application of the knowledge and skills learnt throughout the 'Number and Algebra' strand including basic subtration, multiplication and division.
 * Students investigate different methods of discounting, such as fixed discounts.
 * The different methods of discounting are compared and judgments made on which method provides the best value. This follows on from the work students did in year seven calculating ‘best buys’.
 * Percentages are used to make comparisons extending students learning on percentages from previous years.

YEAR NINE
 * At this level problems begin to involve simple interest.
 * Students are building on the understandings that mathematical calculations are relevant to real-life financial decision-making.
 * This concept began to be developed in year five through the building of financial plans, and is now extended to include application to loans and interest payments.

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