Algebra

Number and Algebra are developed together, as each enriches the study of the other. Students apply number sense and strategies for counting and representing numbers. They explore the magnitude and properties of numbers. They apply a range of strategies for computation and understand the connections between operations. They recognise patterns and understand the concepts of variable and function. They build on their understanding of the number system to describe relationships and formulate generalisations. They recognise equivalence and solve equations and inequalities. They apply their number and algebra skills to conduct investigations, solve problems and communicate their reasoning.

Australian National Curriculum Learning Map

  • Copy, continue and create patterns with objects and drawings
  • Investigate and describe number patterns formed by skip counting and patterns with objects
  • Describe patterns with numbers and identify missing elements
  • Solve problems by using number sentences for addition or subtraction
  • Describe, continue, and create number patterns resulting from performing addition or subtraction
  • Explore and describe number patterns resulting from performing multiplication
  • Solve word problems by using number sentences involving multiplication or division where there is no remainder
  • Use equivalent number sentences involving addition and subtraction to find unknown quantities
  • Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction
  • Use equivalent number sentences involving multiplication and division to find unknown quantities
  • Continue and create sequences involving whole numbers, fractions and decimals.
  • Describe the rule used to create the sequence
  • Introduce the concept of variables as a way of representing numbers using letters
  • Create algebraic expressions and evaluate them by substituting a given value for each variable
  • Extend and apply the laws and properties of arithmetic to algebraic terms and expressions
  • Extend and apply the distributive law to the expansion of algebraic expressions
  • Factorise algebraic expressions by identifying numerical factors
  • Simplify algebraic expressions involving the four operations
  • Extend and apply the index laws to variables, using positive integer indices and the zero index
  • Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
  • Factorise algebraic expressions by taking out a common algebraic factor
  • Simplify algebraic products and quotients using index laws
  • Apply the four operations to simple algebraic fractions with numerical denominators
  • Expand binomial products and factorise monic quadratic expressions using a variety of strategies
  • Substitute values into formulas to determine an unknown
  • Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems