Pre-calculus 11 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Pre-calculus 11 Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
AN04 Students will be expected to determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials, or trinomials).
AN04.01 Compare the strategies for writing equivalent forms of rational expressions to the strategies for writing equivalent forms of rational numbers.
AN04.02 Explain why a given value is non-permissible for a given rational expression.
AN04.03 Determine the non-permissible values for a rational expression.
AN04.04 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.
AN04.05 Simplify a rational expression.
AN04.06 Explain why the non-permissible values of a given rational expression and its simplified form are the same.
AN04.07 Identify and correct errors in a simplification of a rational expression, and explain the reasoning.
AN05 Students will be expected to perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials, or trinomials).
AN05.01 Compare the strategies for performing a given operation on rational expressions to the strategies for performing the same operation on rational numbers.
AN05.02 Determine the non-permissible values when performing operations on rational expressions.
AN05.03 Determine, in simplified form, the sum or difference of rational expressions with the same denominator.
AN05.04 Determine, in simplified form, the sum or difference of rational expressions in which the denominators are not the same and which may or may not contain common factors.
AN05.05 Determine, in simplified form, the product or quotient of rational expressions.
AN05.06 Simplify an expression that involves two or more operations on rational expressions.
AN06 Students will be expected to solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials, or trinomials).
AN06.01 Determine the non-permissible values for the variable in a rational equation.
AN06.02 Determine the solution to a rational equation algebraically, and explain the process used to solve the equation.
AN06.03 Explain why a value obtained in solving a rational equation may not be a solution of the equation.
AN06.04 Solve problems by modelling a situation using a rational equation.
Additional Resources and Activities for AN04 and AN05 (rational expressions):
Light It Up Lesson - Given a mirror and laser pointer, determine the position where one should stand so that a reflected light image will hit a designated target.
Same and Different discussion prompt - Students compare strategies for simplifying subtraction expressions for rational numbers and rational expressions.
An Extraneous Solution - The goal of this task is to examine how extraneous solutions can arise when solving rational equations.
Rational Expressions Row Game - These activities have students pair up and work on a set of problems. Each student has a different problem #1 but the problems should have the same solution. If the students don't get the same solution, they can work with each other to figure out where the error is. Instant feedback and students helping students.
Add Em Up Activity - A self-checking activity for students to simplify several adding and subtracting rational expressions and then add them all together.
Rational Expressions Question Stack - A self-checking activity with a set of 8 expressions. Students simplify the expressions by adding, subtracting or factoring. From Sarah Carter.
Additional Resources and Activities for AN06 (solve rational equations):
Alike and Different discussion starter - How is solving a quadratic equation similar to solving a rational equation with a quadratic in the numberator? From HowWeTeach
Rational Equations Row Game - These activities have students pair up and work on a set of problems. Each student has a different problem #1 but the problems should have the same solution. If the students don't get the same solution, they can work with each other to figure out where the error is. Instant feedback and students helping students.
Solving Rational Equations Decode the Message activity - Students solve 8 rational equations. The solutions allow them to decode a message. From girlmath.
Create and Solve - Ask students to work in pairs to create and solve their own problem involving rational equations.
Unit 6 Review
Fractions Review - Questions on simplifying, adding/subtracting, multiplying and dividing as well as solving rational equations. Solutions. From Dr. Austin Maths.
SSDD Problem - Four questions that look similar on the surface but require different strategies to solve. Students have to try to determine the correct strategy by analysing the question. From SSDDproblems