Getting Started 
Misconception/Error The student does not select an appropriate formula or have an appropriate strategy for finding the volume of the sphere. 
Examples of Student Work at this Level The student:
 Selects and attempts to use an incorrect formula.
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 Attempts to determine the volume by multiplying values given in the problem without regard to the formula for the volume of a sphere.

Questions Eliciting Thinking Can you remember the formula for calculating the volume of a sphere?
Is the formula you used the correct formula? What could you do to fix it? How can you tell that itâ€™s not correct?
Where does the formula for the volume of a sphere come from? 
Instructional Implications Ensure that the student is familiar with spheres and the terms radius and diameter. Provide the student with the formula for finding the volume of a sphere, V = . Be sure the student can identify both the diameter and radius of a sphere on a threedimensional model and in a drawing. Address any misconceptions about the meaning of (e.g., that is a variable). Provide additional opportunities to calculate volumes of spheres in both realworld and mathematical problems. 
Moving Forward 
Misconception/Error The student does not substitute the correct values into the formula for the volume of a sphere. 
Examples of Student Work at this Level The student substitutes the diameter into the formula V = instead of the radius.
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Questions Eliciting Thinking What do the variables in your formula represent?
How are the radius and diameter related? Can you identify the radius of the sphere? 
Instructional Implications Be sure the student can identify both the diameter and radius of a sphere on a threedimensional model and in a drawing. Have the student calculate the radius of a circle or sphere given its diameter (and vice versa). Provide additional opportunities to calculate volumes of spheres given either a radius or a diameter in both realworld and mathematical problems.
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Almost There 
Misconception/Error The studentâ€™s work contains a minor mathematical error. 
Examples of Student Work at this Level The student selects the appropriate formula, substitutes correct values into the formula, and calculates an answer, but the student:
 Does not write the answer in terms of , instead giving the answer in approximate form (e.g., 267.95 cubic centimeters).
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 Uses incorrect units or no units.
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 Makes a multiplication error when evaluating the formula.
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Questions Eliciting Thinking Can you write your answer in terms of ?
What is the unit of measure for volume? Did you include a unit of measure in your answer?
I think you may have made a mistake in your calculations. Can you check your work to see if you can find it? 
Instructional Implications Provide specific feedback, and allow the student to revise his or her work. If needed, assist the student in choosing an appropriate decimal place to round the volume.
Explain the distinction between writing answers in exact form (e.g., in terms of ) and writing answers in approximate form by using an approximation of . Discuss contexts in which one form might be more appropriate than the other. Provide additional opportunities to calculate volumes of spheres with final answers written in either exact or approximate form.
If needed, provide the student with handson activities to better establish the concept of a cubic unit. Ask the student explain the difference among a centimeter, a square centimeter and a cubic centimeter and how each is used to measure length, area, and volume, respectively. Remind the student to always include a unit of measure in length, area, and volume 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 uses the formula V = to correctly calculate the volume of the sphere as Â cubic centimeters.
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Questions Eliciting Thinking What is a cubic centimeter? How does the formula V = determine how many cubic centimeters there are in a sphere? 
Instructional Implications Provide opportunities to solve mathematical and realworld problems by calculating volumes of cylinders, cones, and spheres. Include some figures that are composites of these solids and spheres in which the area of the great circle is given in terms of .
Ask the student to compare the volume of a sphere to that of a cone with the same radius and with aÂ height that is equal to its radius. 