Topic 8.1.7: Algebra: expressions Strand: Sub-strand: Recommended teaching time: Number and Algebra Patterns and algebra 2 weeks (approximately 6 hours) Mapping to F–10 curriculum in Victoria Content descriptions 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 . Achievement standard (excerpt in bold) Level 7 Level 8 Level 9 Students solve problems involving the Students use efficient mental and Students apply the index laws using order, addition and subtraction of written strategies to make estimates integer indices to variables and integers. They make the connections and carry out the four operations with numbers, express numbers in between whole numbers and index integers, and apply the index laws to scientific notation, solve problems notation and the relationship between whole numbers. They identify and involving very small and very large perfect squares and square roots. describe rational and irrational numbers, and check the order of They solve problems involving all four numbers in context. Students magnitude of calculations. They solve operations with fractions, decimals, estimate answers and solve everyday problems involving simple interest. percentages and their equivalences, problems involving profit and loss Students use the distributive law to and express fractions in their simplest rates, ratios and percentages, with expand algebraic expressions, form. Students compare the cost of and without the use of digital including binomial expressions, and items to make financial decisions, with technology. They simplify a variety simplify a range of algebraic and without the use of digital of algebraic expressions and expressions. They find the distance technology. They make simple connect expansion and between two points on the Cartesian estimates to judge the factorisation of linear expressions. plane and the gradient and midpoint reasonableness of results. Students Students solve linear equations and of a line segment using a range of use variables to represent arbitrary graph linear relationships on the strategies including the use of digital numbers and connect the laws and Cartesian plane. technology. Students sketch and draw properties of number to algebra and linear and non-linear relations, solve substitute numbers into algebraic simple related equations and explain expressions. They assign ordered the relationship between the graphical pairs to given points on the Cartesian and symbolic forms, with and without plane and interpret and analyse the use of digital technology. graphs of relations from real data. Students develop simple linear models for situations, make predictions based on these models, solve related equations and check
Topic 8.1.7: Algebra: expressions Strand: Number and Algebra Sub-strand: Patterns and algebra Recommended teaching time: 2 weeks (approximately 6 hours) Mapping to F–10 curriculum in Victoria Content descriptions 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 . Achievement standard (excerpt in bold) Level 7 Level 8 Level 9 Students solve problems involving the order, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving all four operations with fractions, decimals, percentages and their equivalences, and express fractions in their simplest form. Students compare the cost of items to make financial decisions, with and without the use of digital technology. They make simple estimates to judge the reasonableness of results. Students use variables to represent arbitrary numbers and connect the laws and properties of number to algebra and substitute numbers into algebraic expressions. They assign ordered pairs to given points on the Cartesian plane and interpret and analyse graphs of relations from real data. Students develop simple linear models for situations, make predictions based on these models, solve related equations and check Students use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. They identify and describe rational and irrational numbers in context. Students estimate answers and solve everyday problems involving profit and loss rates, ratios and percentages, with and without the use of digital technology. They simplify a variety of algebraic expressions and connect expansion and factorisation of linear expressions. Students solve linear equations and graph linear relationships on the Cartesian plane. Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems involving simple interest. Students use the distributive law to expand algebraic expressions, including binomial expressions, and simplify a range of algebraic expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment using a range of strategies including the use of digital technology. Students sketch and draw linear and non-linear relations, solve simple related equations and explain the relationship between the graphical and symbolic forms, with and without the use of digital technology.