Getting Started 
Misconception/Error The student does not understand the relationship between the height, base edge, and volume of a pyramid. 
Examples of Student Work at this Level The student:
 divides the base area by three to calculate the height.
 divides the volume by the length of the base to calculate the height.
 divides the volume by the perimeter of the base to calculate the height.

Questions Eliciting Thinking What is the question asking you to find?
What kind of pyramid is described in the problem?
What formula did you use? What does the formula tell you about the relationship between base edge, height, and volume of a pyramid? 
Instructional Implications Remind the student that pyramids are named for the shapes of their bases. Show the student a number of examples of different types of pyramids and ask the student to name each one. Review the general formula for calculating the volume of a pyramid, V =Â Bh. Explain the meaning of each variable, emphasizing that the calculation of B depends on the shape of the base. Have the student adapt the formula to particular types of pyramids. For example, ask the student to replace B with the formula for calculating the area of the base given various pyramid types such as square pyramid, rectangular pyramid, right triangular pyramid, and regular hexagonal pyramid. Be sure the student understands the meaning of the variables in the area formulas.
Ask the student to identify the shape of the base of the pyramid in the problem and to calculate its area. Then guide the student to use the volume of a pyramid formula to write an equation that can be solved for h. Ask the student to solve the equation and provide feedback as needed. Then ask the student to calculate the volume and compare it to the given volume as a check on his or her height calculation.
Provide more opportunities to calculate the volumes of a variety of pyramids in the context of problems. 
Moving Forward 
Misconception/Error The student understands the relationship between the height, base area, and volume of a pyramid but makes an error in calculating the area of the base. 
Examples of Student Work at this Level The student:
 calculates the base area by dividing the actual base area by two.
 finds the perimeter of the base rather than its area.

Questions Eliciting Thinking What is the shape of the base of the pyramid? How did you calculate its area? 
Instructional Implications Provide specific feedback to the student regarding the calculation of the base area. Review how to calculate the area of a square and allow the student to correct his or her work and recalculate the height.
Provide more opportunities to calculate the volumes of a variety of pyramids in the context of problems. 
Almost There 
Misconception/Error The student makes a calculation error. 
Examples of Student Work at this Level The student calculates the area of the base correctly as 196,000 square cubits. The student substitutes the base area and the volume into the volume of a pyramid formula but makes an error in solving the formula for h.

Questions Eliciting Thinking How did you solve this equation for h? Can you show me exactly what you did? 
Instructional Implications Provide specific feedback to the student regarding his or her calculation error. Allow the student to correct his or her work and recalculate the height.
Provide more opportunities for the student to solve equations in the context of finding a dimension of a solid given information about other dimensions and the volume. 
Got It 
Misconception/Error The student provides complete and correct responses for all components of the task. 
Examples of Student Work at this Level The student calculates the area of the square base correctly as 196,000 square cubits. The student substitutes the base area and the volume into the volume of a pyramid formula. The student correctly solves for h, getting approximately 280 cubits.

Questions Eliciting Thinking About how many feet is 280 cubits? 
Instructional Implications Challenge the student to convert the pyramidâ€™s volume from cubic cubits to cubic inches and then to cubic feet. 