Represent number forms and generalize number patterns using algebraic expressions Expanding and simplifying algebraic expressions Factorising using the highest common factor Solve and verify solutions to linear equations
Conceptual Framework
logic representation generalization simplification in the context of Scientific and technical innovation
Statements of Inquiry
Being able to generalize is important and powerful
Factual
How do we solve equations?
Conceptual
Why is generalizing powerful?
Debatable
Is it possible to generalise all observed patterns
Description
Students begin the unit by developing an understanding of how algebra can be used to generalize important number concepts. They become familiar with the terminology associated with a study of algebra and learn to represent familiar number forms using variables. Under the related concept of simplification, students will understand that there are different ways to represent equivalent algebraic expressions. The unit progresses into one-variable linear equations where the concept of equivalence transformations are used to simplify and ultimately solve the equation.
Learning Outcomes
Continuing patterns and generalising rules, addition and subtraction of like terms, multiplication and division of terms, combined operations, simplifying expressions, factorising with common terms, expanding brackets
Use the index laws (multiplication and division only) to simplify expressions
Simplify algebraic fractions with only numbers in denominators
Solve simple one and two step linear equations and extend to equations with grouping symbols and pronumerals on each side
Substitute numbers into formulae to find the value of an expression