Florida B.E.S.T. MA.912.AR.8.3
The Standard
Solve and graph mathematical and real-world problems that are modeled with rational functions. Interpret key features and determine constraints in terms of the context.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve equations involving rational expressions and graph rational models. They identify intercepts, holes, asymptotes, and allowed input values. They explain what solutions and graph features mean in the situation.
What Mastery Looks Like
- Students solve rational equations and reject values that violate the model. They graph the function, label intercepts, holes, and asymptotes, then explain what those features mean in context.
Common Misconceptions
- Students may include values that make the denominator zero or accept extraneous solutions after clearing fractions. They often confuse holes with vertical asymptotes. They may also ignore limits such as positive, whole-number inputs.
How to Assess It
- Give students C(n) = 240/n + 8 for 1 ≤ n ≤ 40, where n is the number of students. Ask them to solve C(n) = 20, graph the relevant domain, and explain the constraints and horizontal asymptote.
Lesson moves
Ways to Teach It
Have students place sticky-note points on a large grid, approaching each side of a vertical asymptote without crossing it.
Compare f(x) = (x² − 1)/(x − 1) with g(x) = x + 1, and explain why their graphs differ.
Run a card sort matching rational formulas, graphs, domain restrictions, intercepts, holes, and asymptotes.
Model a bus trip with C(n) = 300/n + 5, then choose realistic group sizes and explain the changing cost per person.
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