Getting Started 
Misconception/Error The student does not understand how to use the function to answer the question. 
Examples of Student Work at this Level The student:
 Tries to combine unlike terms in the function.
 Attempts to factor the quadratic expression but is unable to do so correctly.Â

Questions Eliciting Thinking What do the variables in this function represent?
What are you trying to find? How can you use the function to write an equation that will help you answer this question? How would you solve the equation?
What type of function is this? How do you know?
What methods have you learned for solving quadratic equations? What method do you think would work best for this problem? 
Instructional Implications Guide the student to write an appropriate equation that can be solved to find the values of t that indicate when the dolphin exited and reentered the water. If necessary, assist the student with solving the equation. Explain the meaning of the solutions in the context of the problem. Ask the student to use the solutions to determine the length of time the dolphin was out of the water.
Provide additional opportunities to find the zeros of quadratic functions in the context of real world problems.
Consider using MFAS task Zeros of a Quadratic (AAPR.2.3). 
Moving Forward 
Misconception/Error The student attempts to solve the equation but makes minor errors. 
Examples of Student Work at this Level The student writes the equation and attempts to solve it but makes errors. For example, the student:
 Correctly factors the quadratic expression and sets each factor equal to zero but makes an error solving one of these resulting linear equations.
 Makes a sign error when factoring the greatest common factor from the terms of the equation.

Questions Eliciting Thinking Look back over your work. Do you see a mistake? Does your answer make sense?
What should you always look for when factoring? Is there a greatest common factor of the terms of this trinomial?
I see that you factored out positive 16 resulting in the trinomial . Is there anything else you could do to make this easier to factor?
I see that you factored out a negative eight. Is that the greatest common factor? 
Instructional Implications Review with the student how to identify the greatest common factor and factor it from the terms of an expression. Remind the student that when factoring, it is sometimes helpful to factor out a negative value, so the leading coefficient is positive. Guide the student to correctly solve the equation. Then ask the student to use the solutions to answer the question posed in the problem.
Provide additional opportunities to find zeros of quadratic functions in the context of real world problems. 
Almost There 
Misconception/Error The student correctly solves the equation but does not answer the question in the problem. 
Examples of Student Work at this Level The student writes the equation , correctly factors to solve the equation, finds the solutions t = 2 or t = 4, but:
 Adds 2 and 4 and states the dolphin was out of the water for 6 seconds.
 Does not indicate the meaning of the solutions or answer the question that was asked.

Questions Eliciting Thinking What are the zeros of this equation? What do the zeros tell you about the dolphinâ€™s path?
What were you asked to find in this problem? Did you do that? 
Instructional Implications Ask the student to graph the function. Then ask the student to highlight the part of the graph that corresponds to when the dolphin was above the surface of the water. Guide the student to relate the solutions t = 2 seconds and t = 4 seconds to the times when the dolphin exited and reentered the water. Then ask the student to answer the question posed in the problem.
Provide additional opportunities to find zeros of quadratic functions in the context of real world problems. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student makes h = 0 and writes the equation as . The student divides both sides of the equation by 16 resulting in the equation . The student solves the equation by factoring and finds that t = 2 or t = 4, meaning that the dolphin jumps out of the water after 2 seconds and reenters after 4 seconds. Therefore, the dolphin was above the surface of the water for 2 seconds.

Questions Eliciting Thinking Can you determine the maximum height the dolphin reached on this jump?
What was the dolphinâ€™s height above the water 0.5 seconds before it reentered the water? 
Instructional Implications Provide additional opportunities to find zeros of quadratic functions in the context of real world problems. Include functions that cannot be solved by factoring and functions that contain extraneous solutions. 