Getting Started 
Misconception/Error The student is unable to identify and use the appropriate formula to solve the problem. 
Examples of Student Work at this Level To find the volume of the cylinder, the student:
 uses a surface area rather than volume formula.
 multiplies its diameter by its height.Â

Questions Eliciting Thinking What is the question asking you to do?
In general terms, what do you need to do or calculate to answer the question?
What are the names of the solids in this problem?
What formulas did you use? 
Instructional Implications Review the difference between surface area and volume in terms of what each describes and how it is measured. Use manipulatives such as linking cubes to demonstrate how the area of the base of a solid such as a rectangular prism represents the number of cubes in each layer of cubes and the height represents the number of layers. So, their product represents the total number of cubes or cubic units that comprise the solid thus describing its volume. Extend this idea to other geometric solids and emphasize that volume is measured in cubic units.
Review threedimensional geometric shapes and their corresponding surface area and volume formulas. Be sure the student understands the meaning of each variable in the formula and the relationship between radius and diameter. Explain the derivation of the formulas and what each part calculates. For example, explain the volume of a cylinder formula consists of a calculation for the area of the base which is then multiplied by the height of the cylinder thus giving the number of cubic units of volume.
Encourage the student to first consider what kind of calculation is needed to answer the question in the problem â€“ surface area or volume, then to identify the types of solids, i.e., cylinder. Then ask the student to describe a general strategy, e.g., calculate the volume of the large container in cubic inches, calculate the combined volumes of the 24 individual containers in cubic inches, and compare the two. Have the student find the appropriate formula, if it is not already known, and complete the calculations.
Give the student more opportunities to calculate the volumes of solids in the context of problems. 
Moving Forward 
Misconception/Error The student makes significant errors in using the volume formulas. 
Examples of Student Work at this Level The student:
 uses the diameter instead of the square of the radius when calculating the volume for the cylindrical cooler.
 does not follow the order of operation rules.
 does not understand the significance of the conversion factor, 57.75.
 does not know that B represents the area of the base and that it should be replaced with .

Questions Eliciting Thinking What do the variables in your formulas represent?
For these figures, are you given the radius or the diameter? How do you convert the diameter into a radius?
What does the capital B represent in the volume formula for the cylinder?
How can you calculate the volume of the 24 drinks in cubic inches? 
Instructional Implications Review the meaning of the variables in the formula and guide the student to find the appropriate values in the given information. Be sure the student understands that when B is used in a volume formula, it stands for the area of the base. Review how to calculate the area of a circle. Remind the student of the relationship between the diameter and radius of a circle.
Review the order of operations rules and remind the student that exponents must be addressed before multiplying.
Ask the student to complete the problem on the worksheet and provide feedback. Give the student more opportunities to calculate the volumes of solids in the context of problems. 
Almost There 
Misconception/Error The student makes a minor error. 
Examples of Student Work at this Level The student identifies the appropriate volume formulas but makes a single substitution error, a small computational error, or neglects to answer the question asked in the problem.

Questions Eliciting Thinking I think your cylinder calculation contains a mistake. Can you find your mistake?
What was the purpose of calculating the volumes? Did you answer the question originally asked? 
Instructional Implications Assist the student in correcting any error in his or her work. Give the student more opportunities to calculate the volume of solids in the context of problems. Guide the student to show work in a complete and logical manner and to be sure that any question asked in the problem is answered. 
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 correctly calculates the volume of the cylindrical container, the combined volumes of the individual containers in cubic inches, and interprets the results to answer the question asked in the problem.
The student says the cylindrical cooler provides the most drink because the volume of 24 juice boxes is 1,386 Â but the volume of the large cylindrical cooler is 1,425 .
An alternate method is to express the volume of the cooler in quarts by dividing 1,425 Â by 57.75 Â which results in 24.67 quarts compared to 24 quarts. 
Questions Eliciting Thinking What unit of measure did you use for each volume? Which unit should give a numerically larger volume? Why? 
Instructional Implications If the student did not do so already, ask the student to express each volume in both cubic inches and in quarts.
Ask the student to solves more complex problems that require calculating the volumes of cones, cylinders, pyramids, and spheres. 