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Victorian Curriculum v2.0
Number and algebra
Algebra
Follow a short sequence of instructions; recognise, copy, continue and create repeating patterns represented in different ways
Recognise, continue and create pattern sequences, with numbers, symbols, shapes and objects including australian coins, formed by skip counting, initially by twos, fives and tens
Recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit and recognising the importance of repetition in solving problems
Recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern
Recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts
Recall and demonstrate proficiency with multiplication facts for twos; extend and apply facts to develop the related division facts using doubling and halving
Apply repetition in arithmetic operations, including multiplication as repeated addition and division as repeated subtraction
Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
Extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator
Recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts
Find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations
Recall and demonstrate proficiency with multiplication facts up to 10 × 10 and related division facts, and explain the patterns in these; extend and apply facts to develop efficient mental and written strategies for computation with larger numbers without a calculator
Recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts
Find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations
Recognise and use rules that generate visually growing patterns and number patterns involving rational numbers
Find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations
Design and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns
Recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown
Apply the associative, commutative and distributive laws to aid mental and written computation, and formulate algebraic expressions using constants, variables, operations and brackets
Solve one-variable linear equations of increasing complexity with natural number solutions; verify equation solutions by substitution
Investigate, interpret and describe relationships between variables represented in graphs of functions developed from authentic data
Generate tables of values from visually changing patterns or the rule of a function; describe and plot these relationships on the cartesian plane
Manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables
Create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties
Graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution
Use mathematical modelling to solve applied problems involving linear relations, including financial contexts involving profit and loss; formulate problems with linear functions, and choose a representation; interpret and communicate solutions in terms of the context, and review the appropriateness of the model
Use algorithms and related testing procedures to identify and correct errors
Experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns
Apply the exponent laws to numerical expressions with integer exponents and the zero exponent, and extend to variables
Simplify algebraic expressions, apply the distributive law to expand algebraic expressions including binomial products, and factorise monic quadratic expressions
Sketch linear graphs of equations in various algebraic forms, using the coordinates of 2 points, and solve linear equations
Find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane
Identify and graph quadratic functions, solve quadratic equations graphically and numerically, and use null factor law to solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate
Use mathematical modelling to solve applied problems involving change, including financial contexts involving simple interest; formulate problems, choosing to use either linear or quadratic functions or other simple variations; interpret solutions in terms of the context; evaluate the model and report methods and findings
Experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns
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