- Students should be given opportunities to explore culturally relevant situations and problems that can be represented with rational expressions.
- Students should be able to rewrite rational expressions in various equivalent forms, based on the context of the problem, with the understanding that any factor of the numerator, over itself in the denominator, is equal to a factor of one.
- Limit operations with rational expressions to those that would occur within the context of real-life problems, e.g., uniform motion, work, mixtures.
- Limit division to factorable expressions for which no remainder exists.
- Students should be given graphs, or use technology to generate their own graphs, to identify characteristics of rational functions.
- Students should be able to use technology to graph and identify key features of rational functions, to include x and y-intercepts, roots of multiplicity, zeros, and solutions; domain, range, and intervals where the function is increasing, decreasing, positive, and/or negative (using inequality and interval notations); vertex, extreme value, and axis of symmetry; end behavior, using technology where appropriate.
- Limit solving rational equations to those that would occur within the context of real-world problems, e.g., uniform motion, work, mixtures.
- Students should be able to check for extraneous solutions.
- Students should be encouraged to use technology and tools to solve rational equations in order to enhance conceptual understanding.
- Less time should be devoted to the mechanics of solving rational equations and more time should be devoted to building students capacity for interpreting rational functions within context.
Textbook Connections
Module 9
Lesson 1 Multiplying and Dividing Rational Expressions
Lesson 2 Adding and Subtracting Rational Expressions
Lesson 4 Graphing Rational Functions
Lesson 6 Solving Rational Equations (and Inequalities)
Module 9
Lesson 1 Multiplying and Dividing Rational Expressions
Lesson 2 Adding and Subtracting Rational Expressions
Lesson 4 Graphing Rational Functions
Lesson 6 Solving Rational Equations (and Inequalities)