Florida B.E.S.T. MA.912.AR.7.3
The Standard
Solve and graph mathematical and real-world problems that are modeled with square root or cube root 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 square root and cube root functions and graph the related models. They identify endpoints, intercepts, domain, range, and other meaningful features. They explain which inputs and outputs make sense in the situation.
What Mastery Looks Like
- A student can use a root model, solve it accurately, and check any possible extraneous solutions. The student can graph the function, label key features, and give domain and range that fit the context.
Common Misconceptions
- Students may draw square root graphs as half parabolas or assume cube roots cannot accept negative inputs. They may write ± when evaluating a square root, or forget to check solutions created by squaring. They also use the full algebraic domain when time, length, or volume limits the context.
How to Assess It
- Exit ticket: A spill spreads with radius r(t) = 2√t feet, for 0 ≤ t ≤ 25. Graph the model, find when r = 6, and explain both domain limits.
Lesson moves
Ways to Teach It
Build squares with tiles, record area and side length, then graph side length against area to reveal a square root model.
Write how the endpoint, intercepts, and domain of a graph change the meaning of a water-tank context.
Match cards showing root equations, graphs, solutions, and valid domains, then justify each set to a partner.
Use s = ∛V to find and graph the side length of a cube-shaped package for several volumes.
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