Rational Expressions Unit Plan

Introduction to Rational Expressions and Equations

General Outcome: Develop algebraic and graphical reasoning through the study of relations.


SO 1. Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials and binomials).[C, ME, R]

1.1 Compare the strategies for writing equivalent forms of rational expressions to writing equivalent forms of rational numbers.
1.2 Explain why a given value is non-permissible for a given rational expression.
1.3 Determine the non-permissible values for a rational expression.
1.4 Determine a rational expression that is equivalent to a given rational expression by multiplying the numerator and denominator by the same factor (limited to a monomial or a binomial), and state the non-permissible values of the equivalent rational expression.
1.5 Simplify a rational expression.
1.6 Explain why the non-permissible values of a given rational expression and its simplified form are the same.
1.7 Identify and correct errors in a given simplification of a rational expression, and explain the reasoning.

SO2. Perform operations on rational expressions (limited to numerators and denominators that are monomials and binomials). [CN, ME, R]

2.1 Compare the strategies for performing a given operation on rational expressions to the
strategies for performing the same operation on rational numbers.
2.2 Determine the non-permissible values when performing operations on rational expressions.
2.3 Determine, in simplified form, the sum or difference of rational expressions that have the same denominator.
2.4 Determine, in simplified form, the sum or difference of two rational expressions that have different denominators.
2.5 Determine, in simplified form, the product or quotient of two rational expressions.

SO3. Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials). [C, CN, PS, R]

3.1 Determine the non-permissible values for the variable in a rational equation.
3.2 Determine, algebraically, the solution to a rational equation, and explain the strategy used to solve the equation.
3.3 Explain why a value obtained in solving a rational equation may not be a solution of the equation.
3.4 Solve a contextual problem that involves a rational equation.

Mathematical Processes

  • Communications [C]
  • Connections [CN]  Students are expected to make connections among mathematical ideas, other concepts in mathematics, everyday experiences and other disciplines
  • Problem Solving [PS]  Students are expected to develop and apply new mathematical knowledge through problem solving
  • Reasoning [R] Students are expected to develop mathematical reasoning
  • Mental Estimation [ME] Students are expected to demonstrate fluency with mental mathematics and estimation.