Develop an understanding of algebra as a generalisation of number Manipulate and simplify algebraic expressions and solve equations Form equations from a variety of real-life applications, and interpret the solution in the context of the original problem Understand the meaning of ‘show’, ‘verify’ and ‘prove’, and construct simple proofs
Conceptual Framework
relationships generalisation, pattern, simplification, justification in the context of Identities and Relationships
Statements of Inquiry
Students will appreciate that algebra enables them to generalise a numerical relationship, and so understand how to make, verify, test and prove conjectures for mathematical relationships in the real world
Factual
How do equations arise in solving problems?
What are the rules for finding solution(s)?
How can we check our solutions?
Conceptual
What are the similarities and differences between algebraic and numerical operations?
How do we present solutions and reasoning that others can follow?
Debatable
Description
Algebra lies at the heart of Mathematics and the work in Year 9 lays the foundations for students understanding and appreciation of Mathematics through to Year 13 and beyond. The Number and Algebra units are intentionally linked so students develop a deep understanding of algebra as extension and generalisation of number work, with analagous operations but with a far greater power. The ability to ‘predict’ a result for any given number and the power and limitations this leads to are a key theme. The unit begins from simple and familiar number patterns and simple linear relationships to develop the skills and understanding to solve the full range of linear equations - with brackets, repeated unknowns, fractional coefficients and solutions that can be integers or rational numbers. Essential work on developing and practising manipulative skills is interspersed with practical forming and solving equations so that the raison d’etre for studying and mastering algebra - to formulate and then solve practical or word-based problems - underscores all work.
Learning Outcomes
Simplify algebraic sums, products following the order of operations
Use the language of Mathematics to translate words to symbols and vice versa
Find the value of an expression using substitution
Simplify algebraic expressions by combining like terms
Simplify expressions involving products and quotients
Understand and use the distributive property
Simplifying algebraic expressions, expanding brackets up to 3 terms
Expand algebraic expressions using multiplication of up to 2 brackets
Factorise linear and quadratic expressions, difference of two squares and perfect square trinomials
Solve simple and more complex equations involving brackets, fractions and decimals, variables on both sides using a variety of methods including inspection, trial and error and undoing (with emphasis placed on undoing)
Solve rational equations with the unknown in the denominator
Solve quadratic equations by factorising
Use GDC and other software to solve linear and quadratic equations graphically
Solve word problems by setting up an appropriate equation or inequality and communicating the solution clearly.
Solve and interpret the solution of one-variable inequalities
Solve literal equations by finding an unknown from a given formula
Begin to develop an understanding of how to solve simultaneous equations algebraically and graphically
Begin to develop an understanding of mathematical proof and the correct logical presentation of an algebraic proof