AusVels midlevel Progression Points. AusVels Achievement Standards. (Incorporates elaborations and special notes) L5.5 Number and Algebra L6 Number and Algebra MUL • represent composite numbers as a product of their prime factors MUL • recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers. • representing composite numbers as a product of their prime factors and using this form to simplify calculations by cancelling common primes. • use of the rules for divisibility, e.g. understanding that if a number is divisible by a composite number then it is also divisible by the prime factors of that number. • solve problems that involve all four operations with whole numbers • applying strategies already developed for solving problems involving small numbers to those involving large numbers. Understand effect of ×,÷ on numbers by fractions >1 or <1. • applying a range of strategies to solve realistic problems and commenting on the efficiency of different strategies. • describe the use of integers in everyday contexts. • locate integers on a number line • everyday situations that use integers. • position and order integers around zero. Represent integers on a number line describing size and direction. Calculate differences in temperature, position. • locate fractions on a number line. • connect fractions, decimals and percentages as different representations of the same number. • connecting fractions, decimals and percentages as different representations of the same number, moving fluently between representations and choosing the appropriate one for the problem being solved. Apply all part whole relationships as fractional e.g. Numerical fractions, Percentage fractions and Decimal fractions • solve problems involving the addition and subtraction of related fractions. • extending whole-number strategies to explore and develop meaningful written strategies for addition and subtraction of decimal numbers to thousandths • calculate a simple fraction of a quantity • calculate common percentage discounts on sale items, with and without the use of digital technology. Apply benchmark percentage of 10%, multiples of 10% and later 5% as half of 10% Apply discount as decrease. • make connections between the powers of 10 and the multiplication and division of decimals. • add, subtract decimals ( extending to thousandths) • multiply decimals and divide decimals where the result is rational. • practising efficient methods for solving problems requiring operations on decimals • fluent with calculating with decimals and with recognising appropriate operations. Understand effect of ×,÷ on numbers by decimals >1 or <1. • write number sentences using brackets and order of operations. • apply rules to complete multiple operations within the same number sentence • specify rules used to generate sequences involving whole numbers, fractions and decimals. • identifying and generalising number patterns • identifying additive and multiplicative patterns such as the number of tiles in a geometric pattern, • identifying patterns in the number of dots or other shapes in successive repeats • identify patterns in the way the numbers increase/decrease. MUL MUL • identify the highest common factor (greatest common divisor) and lowest common multiple of two whole numbers. PRO PRO MUL MUL PAT • explore the use of brackets and order of operations to write and evaluate number sentences • continue and create sequences involving whole numbers, fractions and decimals, according to a given rule PAT • use ordered pairs of whole numbers to represent coordinates of points and locate these points on simple grids and in the first quadrant on the Cartesian plane. - • use ordered pairs of integers to represent coordinates of points. • locate a point in any one of the four quadrants on the Cartesian plane. AusVels midlevel Progression Points. AusVels Achievement Standards. (Incorporates elaborations and special notes) L6.5 Number and Algebra L7 Number and Algebra MUL • locate fractions and mixed numbers on a number line • investigate index notation and represent whole numbers as products of powers of prime numbers MUL • solve problems involving the order of integers. • solve problems involving addition and subtraction of integers • make connections between whole numbers and index notation • applying knowledge of factors to strategies for expressing whole numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees. •solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of whole numbers by comparing their prime factorisation. • make connections between index notation and the relationship between perfect squares and square roots. • investigating square numbers such as 25 and 36 and developing square-root notation • investigating between which two whole numbers a square root lies • find equivalent fractions and use them to order fractions. • solve problems involving addition and subtraction of fractions, including those with unrelated denominators. MUL MUL MUL MUL PRO PRO • investigate and calculate 'best buys' and solve problems involving simple ratios, with and without the use of digital technology PRO PRO PRO • use a variety of methods to solve linear equations with whole number solutions PAT VIS PRO • use substitution to check solutions. PRO Apply examples such as 9 as the side of a square with area 9 square units. • solve problems involving all four operations with fractions, Consider multiplying fractions before addition and subtraction of fractions Understand effect of ×,÷ on numbers by fractions >1 or <1. • solve additive problems involving fractions • solve problems involving all four operations with decimals, Understand effect of ×,÷ on numbers by decimals >1 or <1. • solve problems involving all four operations with percentages and their equivalences, For calculators, apply % increase/reduction first, instead of adding or subtracting last. E.g. 10% off $200 = 0.9x200 • express fractions in their simplest form. • Recognise and solve problems involving simple ratios. • solve rate and ratio problems using fractions or percentages • choosing the most efficient form to solve a particular problem • compare the cost of items to make financial decisions, with and without the use of digital technology. •applying the unitary method to identify ‘best buys’ situations, such as comparing the cost per 100g. • make simple estimates to judge the reasonableness of results. • apply the associative, commutative and distributive laws to aid mental and written computation Apply the Hierarchical Order of Operations. Apply rounding before estimating. • use variables to represent arbitrary numbers, • use variables to connect the laws and properties of number to algebra, • identifying order of operations in contextualised problems. • fluent between algebraic and word representations as descriptions of the same situation • substitute numbers into algebraic expressions. • assign ordered pairs to given points on the Cartesian plane • interpret and analyse graphs of relations from real data. • develop simple linear models for situations, • make predictions based on these models, • solve related equations and check their solutions. AusVels midlevel Progression Points. L7.5 Number and Algebra L8 MUL • solve problems involving multiplication of integers by single-digit whole numbers and use the sequence of square numbers to form estimates for square roots MU L MUL • classify rational numbers as having either terminating or infinite recurring decimals. • use equivalent decimals and percentages to order rational expressions PRO • calculate sale price when a percentage discount is applied. MU L MU L PRO PRO PRO PRO • determine gradient and axis intercepts of linear graphs. MU L MU L PRO PRO • represent linear relationships as a table of ordered pairs, classify relationships as linear or non-linear • interpret gradient both as a ratio and as a constant rate of change. PRO AusVels Achievement Standards. (Incorporates elaborations and special notes) Number and Algebra • use efficient mental and written strategies to make estimates and carry out the four operations with integers. • using patterns to assist in finding rules for the multiplication and division of integers • using the number line to develop strategies for adding and subtracting rational numbers • apply the index laws to whole numbers. • evaluating numbers expressed as powers of positive integers • identify and describe rational and irrational numbers in context. • Apply irrational numbers, including π • estimate answers • solve everyday problems involving profit and loss • using percentages to solve problems, including those involving mark-ups, discounts, profit and loss and GST Apply 10% GST increase on retail or 9% component of retail = GST • solve everyday problems involving rates, ratios and percentages, with and without the use of digital technology. • apply fractions or percentages to solve rate and ratio problems • calculating population growth rates in Australia and Asia • simplify a variety of algebraic expressions • connect expansion and factorisation of linear expressions. • solve linear equations, Follow conventions for solving • graph linear relationships on the Cartesian plane.