Number+&+Algebra+Overview+Yrs+7-9

ACARA Number and Algebra Overview Year 7- Year 9

**//Analysis of//** **//ACARA Year Levels and Descriptors://** **//Years 7, 8 and 9//** **Year 7;** In Year 7 students aim to extend and refine mathematic knowledge and understanding gained from previous mathematic experiences. Throughout Year 7 students make connections, interpret information, apply formulas and relate real life experiences in order to solve problems involving the laws and properties from the number and algebra strand.

The following has been adapted from the Year 7 Level Description – //Number and algebra// (ACARA, 2010) to outline understanding, fluency, problem solving and reasoning objective achieved throughout the year.


 * // At this year level: //**


 * // Understanding //****// includes: //** describing patterns in uses of indices with whole numbers, recognising equivalences between fractions, decimals, percentages and ratios, plotting points on the Cartesian plane, identifying angles formed by a transversal crossing a pair of lines, and connecting the laws and properties of numbers to algebraic terms and expressions (ACARA, 2010).

**// Fluency includes: //** calculating accurately with integers, representing fractions and decimals in various ways, investigating best buys, finding measures of central tendency and calculating areas of shapes and volumes of prisms (ACARA, 2010). **// Problem Solving includes: //** formulating and solving authentic problems using numbers and measurements, working with transformations and identifying symmetry, calculating angles and interpreting sets of data collected through chance experiments (ACARA, 2010).
 * // Reasoning includes: //** applying the number laws to calculations, applying known geometric facts to draw conclusions about shapes, applying an understanding of ratio and interpreting data displays (ACARA, 2010).

**References**
Australian Curriculum Assessment and Reporting Authority. (2010). //The Australian Curriculum: Mathematics.// Retrieved April 5, 2012, from Australian Curriculum Assessment and Reporting Authority Web site: [|http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10?layout=2&y=6&y=7&y=8&y=9&s=NA#level=8] Matt.

**Year 8;** Students apply knowledge from Year 7 mathematics and assert it into the challenges of the Year 8 - Mathematics strand of the Australian Curriculum. Number and algebra continue to investigate and solve problems through the application of mental and written strategies as well as incorporating digital technologies. Students build upon their knowledge of index notation exploring index laws with positive integral indices and zero. Year 8 students progress from comparing, ordering and adding and subtracting integers to using efficient mental and written strategies and appropriate digital technologies to carry out four operations with rational numbers and integers (ACARA, 2010). In Year 8 students progress from finding percentage quantities to investigating and solving problems involving percentage increases and decrease. Learners do this with and without technologies. Money and financial mathematics takes learners from ‘best buys’ (Year 7) to solving problems involving ‘profit and loss.’ Students apply their past knowledge of solving simple linear equations (Year 7) and apply it to solving linear equations using algebraic and graphical techniques.

The following has been adapted from the Year 8 Level Description – //Number and algebra// (ACARA, 2010) to outline understanding, fluency, problem solving and reasoning objective achieved throughout the year.

**// A //****// t this year level: //**
 * // Understanding //****// includes: //** describing patterns involving indices and recurring decimals, identifying commonalities between operations with algebra and arithmetic, connecting rules for linear relations their graphs, explaining the purpose of statistical measures, and explaining measurements of perimeter and area (ACARA, 2010).

**// Fluency includes: //** calculating accurately with simple decimals, indices and integers, recognising equivalence of common decimals and fractions including recurring decimals, factorising and simplifying basic algebraic expressions, and evaluating perimeters, areas of common shapes and their volumes and three dimensional objects (ACARA, 2010). **// Problem Solving includes: //** formulating, and modeling practical situations involving ratios, profit and loss, areas and perimeters of common shapes, and using two-way tables and Venn diagrams to calculate probabilities (ACARA, 2010). **// Reasoning includes //** : justifying the result of a calculation or estimation as reasonable, deriving probability from its complement, using congruence to deduce properties of triangles, finding estimates of means and proportions of populations (ACARA, 2010).

**References**
Australian Curriculum Assessment and Reporting Authority. (2010). //The Australian Curriculum: Mathematics.// Retrieved April 5, 2012, from Australian Curriculum Assessment and Reporting Authority Web site: [|http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10?layout=2&y=6&y=7&y=8&y=9&s=NA#level=8]


 * Matt. **

**Year 9;**
During the course of Year 9 students adapt their knowledge and understanding to the theories and practices of others in order to investigate and find the unknown. Students begin to estimate the probability of outcomes by applying their knowledge of the fundamentals of mathematics gained throughout the earlier years of school. In Year 9 there are four content descriptors which are used to organise the Number and Algebra strand this is opposed to the five used in previous years. Previously in Year 8 students used index notation with numbers to explore the index laws this evolves in Year 9 to the application of index laws to numerical expressions with integer indices (ACARA, 2010). Students apply their past knowledge of calculating ‘best buys’ and ‘profit and loss’ to solving problems involving ‘simple interest.’ The Year 9 Patterns and algebra sub-strand extends on the application of the distributive law from Year 8 to include binomials and collect like terms where appropriate (ACARA, 2010). Students continue to use the Cartesian plane to investigate linear and non-linear relationships. Students continue to investigate applying mental and written strategies and appropriate technologies to solve problems. The following has been adapted from the Year 9 Level Description – //Number and algebra// (ACARA, 2010) to outline understanding, fluency, problem solving and reasoning objective achieved throughout the year. **// A //****// t this year level: //** **// Understanding //****// includes: //** describing the relationship between graphs and equations, simplifying a range of algebraic expressions, explaining the use of relative frequencies to estimate probabilities, and the use of the trigonometric ratios for right-angle triangles (ACARA, 2010). **// Fluency includes: //** applying the index laws to expressions with integer indices, expressing numbers in scientific notation, listing outcomes for experiments and developing familiarity with calculations involving the Cartesian plane and calculating areas of shapes and surface areas of prisms (ACARA, 2010). **// Problem Solving includes: //** formulating, and modeling practical situations involving surface areas and volumes of right prisms, applying ratio and scale factors to similar figures, solving problems involving right-angle trigonometry, and collecting data from secondary sources to investigate an issue (ACARA, 2010). **// Reasoning includes //** : following mathematical arguments, evaluating media reports and using statistical knowledge to clarify situations, developing strategies in investigating similarity and sketching linear graphs (ACARA, 2010).

**References**
Australian Curriculum Assessment and Reporting Authority. (2010). //The Australian Curriculum: Mathematics.// Retrieved April 5, 2012, from Australian Curriculum Assessment and Reporting Authority Web site: [|http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10?layout=2&y=6&y=7&y=8&y=9&s=NA#level=8]


 * Matt **.