Getting Started 
Misconception/Error The student does not select an appropriate formula or have an appropriate strategy for finding the height of the pyramid. 
Examples of Student Work at this Level The student:
 Selects and attempts to use an incorrect formula such as V = Bh.
 Attempts to determine the height by dividing the volume by the square of the base edge.

Questions Eliciting Thinking Can you remember the formula for the volume of a pyramid?
Is the formula you used the correct formula? What could you do to fix it? How can you tell that it is not correct? 
Instructional Implications Ensure that the student is familiar with prisms and pyramids as well as terms used to describe their parts and dimensions such as base, lateral surface, height, slant height, and radius. If necessary, review the formula for finding the area of a square. Explain that the volume of a prism or cylinder can be determined by multiplying the area of a base by the height. Similarly, the volume of a pyramid or cone can be found by multiplying the product of the base area and height by onethird.
Emphasize the general formulas for finding the volumes of prisms and cones. Explain to the student that the general formulas along with some basic area formulas are all that is needed to calculate volumes of prisms, cylinders, pyramids, and cones.
Provide the student with the general formula for finding the volume of a pyramid, V = Bh, and explain how to apply this formula to a square pyramid. Clearly identify the meaning of the variables in the formula and discuss how to calculate B, the area of the base. Ask the student to identify the unknown quantity in the problem on the Louvre Pyramid worksheet, and guide the student to use the volume formula to write an equation that can be solved for h. Review the process of solving equations, as needed.
Provide additional problems involving volumes of prisms, cylinders, pyramids, and cones in which either the volume, base area, or a specified length must be calculated. 
Moving Forward 
Misconception/Error The student is unable to apply the formula for the volume of a pyramid to solve a realworld problem. 
Examples of Student Work at this Level The student identifies the correct formula but does not demonstrate understanding of how to use the formula to solve the problem. The student:
 Substitutes incorrect values for variables in the formula.
 Writes the equation 8820 = h but is unable to solve for h.

Questions Eliciting Thinking What does this formula mean?
How can you use this formula to solve the problem?
What can you do to the equation 8820 = h to eliminate the fraction ? What operation â€śundoesâ€ť multiplying? 
Instructional Implications Review terms used to describe the parts and dimensions of pyramids and prisms such as base, lateral surface, height, and slant height. Be sure the student can locate these measurements on a threedimensional model and on a drawing of a pyramid.
Review the meaning of the variables in the formula and discuss how to calculate B, the area of the base. Ask the student to identify the unknown quantity in the problem on the Louvre Pyramid worksheet and guide the student to use the volume formula to write an equation that can be solved for h. Review the process of solving equations, as needed.
Provide additional problems involving volumes of prisms, cylinders, pyramids, and cones in which either the volume, base area, or a specified length must be calculated. 
Almost There 
Misconception/Error The studentâ€™s work contains a minor mathematical error. 
Examples of Student Work at this Level The student selects an appropriate formula, substitutes correct values into the formula, and calculates an answer, but the student:
 Uses incorrect units or no units.
 Makes a multiplication error when squaring 35.

Questions Eliciting Thinking What is the unit of measure for height? Did you include a unit of measure in your answer?
I think you may have made a mistake. 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.
Provide additional problems involving volumes of prisms, cylinders, pyramids, and cones in which either the volume, base area, or a specified length must be calculated. 
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 correctly identifies the formula V = (where s is the length of a side of the base) or V = Bh (where B is the area of the base). The student writes the equation 8820 = h, solves for h, and identifies the height of the pyramid as 21.6 meters.

Questions Eliciting Thinking What is a cubic meter? How does the formula V = determine how many cubic meters there are in a square pyramid? 
Instructional Implications Provide additional problems involving volumes of prisms, cylinders, pyramids, and cones in which either the volume, base area, or a specified length must be calculated.
Ask the student to develop a model in which the volume of a pyramid can be approximated with stacked rectangular prisms. Ask the student to consider how his or her model could be improved (e.g., by increasing the number and decreasing the height of the rectangular prisms).
Provide practice problems in which the student must calculate the volume of pyramids with different bases (e.g., triangular pyramids, hexagonal pyramids). 