Represent number forms and generalize number patterns using algebraic expressions Expanding and simplifying algebraic expressions Factorising expressions Solve and verify algebraic equations and inequalities using a variety of strategies
Conceptual Framework
form representation, simplification, generalization
Statements of Inquiry
Moving from the particular case of number properties into the generalized forms provided by algebra is one of the most important steps in developing mathematical competence
Factual
How can we represent number forms and patterns algebraically?
Conceptual
How do we apply our knowledge of algebra to represent a real-world problem?
Debatable
Who needs algebra?
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. The same ideas are used to solve linear inequalities, the key difference being in how we represent the solution sets.
Intended Learning
Demonstrate understanding of each of the following terms: variable, term, coefficient, like terms, constant, polynomial, monomial, binomial, trinomial, simplify, evaluate, expand, expression
Write algebraic expressions to represent word phrases or simple real life situations
Use substitution to find the value of an algebraic expression that requires the use of the order of operations
Use the following index laws to simplify expressions: \(a^m)^n=a^{mn}\), \(a^m\times a^n=a^{m+n}\), \(a^m\div a^n=a^{m-n}\)
Multiply and divide monomial expressions using laws of exponents
Divide polynomials by monomials using the laws of exponents
Application of index laws to scientific notation
Simplify algebraic expressions by combining like terms
Understand and use the distributive property to multiply a monomial by a polynomial, binomial by a binomial including \((a\pm b)^2\) and \((a-b)(a+b)\)
Understand that expressions in written in different forms are equivalent
Develop understanding of factoring as the reverse of expanding and then factor algebraic expressions using: a) greatest common factor; b) perfect trinomial square; c) difference of two squares; and d) simple trinomials of the form \(x^2+bx+c\)
Use the notation and terminology associated with equations
Apply the properties of equality to reduce an equation to a simpler one
Solve simple one and two step equations by applying the properties of equality
Solve 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 word problems by setting up an appropriate equation or inequality and communicating the solution clearly.
Check the validity of a solution by substituting back into the original equation
Solve linear inequalities (simple and compound) containing parentheses, fractions and decimals
Simple introduction to simultaneous equations
Solve literal equations by changing the subject of a formula