Getting Started 
Misconception/Error The student is unable to determine the volume of a right rectangular prism. 
Examples of Student Work at this Level The student does not have any strategy for finding the volume of a right rectangular prism. The student:
 Adds the lengths of the sides.
 Divides and subtracts the values given.
 Multiplies pairs of dimensions and selects one product as the volume.

Questions Eliciting Thinking What is volume? What do you have to do to find it?
What kind of figure is described in this problem? Is there a formula for finding the volume of this figure that you could use? Can you identify the length, width, and height of the brick? 
Instructional Implications Ensure that the student is familiar with rectangular prisms and the terms used to describe their parts and dimensions such as base, face, height, and edge. Be sure the student understands the distinction between volume and area (or surface area) and review both concepts, as needed. If necessary, review area formulas and remind the student that volume of a prism can be found by multiplying the area of the base by the height. Review the specific formula for volume of a right rectangular prism, V = lwh, and clearly identify the meaning of all variables. Ask the student to locate the base and height of the prism and identify the relevant dimensions.
Use manipulatives such as linking cubes to demonstrate how the area of the base of 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. Emphasize that volume is measured in cubic units.
Review operations with fractions, as needed.
Provide additional opportunities for the student to calculate the volumes of rectangular prisms with fractional edge lengths in the context of realworld problems. 
Moving Forward 
Misconception/Error The student is not able to correctly multiply fractions. 
Examples of Student Work at this Level The student identifies the appropriate formula to calculate volume of a rectangular prism and attempts to multiply the three dimensions. The student makes errors multiplying fractions. The student:
 Finds common denominators.
 Multiplies mixed numbers by multiplying whole numbers and multiplying fractions.
 Adds the whole numbers and multiplies the fractions.
 Multiplies mixed numbers incorrectly and makes computational errors when multiplying.

Questions Eliciting Thinking Why did you find common denominators?
How do you convert a mixed number (or whole number) to an improper fraction?
Can you explain how to multiply mixed numbers? 
Instructional Implications Review procedures for converting mixed or whole numbers into improper fractions and procedures for multiplying mixed numbers. Give the student additional multiplication problems in which the factors include mixed numbers.
Provide additional opportunities for the student to calculate the volumes of rectangular prisms with fractional edge lengths in the context of realworld problems. 
Almost There 
Misconception/Error The student does not show work appropriately or mislabels the final answer. 
Examples of Student Work at this Level The student correctly determines the volume is numerically 63, but labels the units incorrectly or not at all. The student writes:
 63 as a final answer and does not include a unit of measure.
 63 inches.
 or inches.
 The student shows no work and explains, “I multiplied.”

Questions Eliciting Thinking What type of unit is typically used when measuring volume? What is the unit of measure for the volume of each brick in this problem?
What does mean? Does this make sense as an answer?
Can you explain how you found the volume?
Can you show your work in a way that someone could readily understand what you did? 
Instructional Implications Review the types of units that are used to measure length, area, and volume. Correct any misconceptions about how these units are written (e.g., writing 63 cubic inches as ) or read (e.g., reading 63 as “63 inches cubed”). Provide feedback on errors made in describing the unit of measure and allow the student to correct his or her work.
If necessary, provide guidance to the student on showing work appropriately. Remind the student to show clearly how the volume is calculated. For example, have the student write V = 2 x 8 x 3. Then have the student indicate in what form he or she is going to multiply these values by rewriting the previous expression with the factors written in that form (e.g., as decimals or as improper fractions). Finally, advise the student to do computational work to the side and to include the final product along with the unit of measure with the formally written work.
Provide additional opportunities for the student to calculate the volumes of rectangular prisms with fractional edge lengths in the context of realworld 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 multiplies the length, width, and height to determine a volume of 63, and explains that volume is calculated by multiplying the three dimensions.

Questions Eliciting Thinking Do you always need three dimensions to calculate the volume of a rectangular prism? Why or why not?
Are the values of the variables interchangeable? Can you explain? 
Instructional Implications If needed, remind the student to show mathematical work in a more formal fashion. Guide the student to show clearly how the volume is calculated. For example, have the student write V = 2 x 8 x 3. Then have the student indicate in what form he or she is going to multiply these values by rewriting the previous expression with the factors written in that form (e.g., as decimals or as improper fractions). Finally, advise the student to do computational work to the side and to include the final product along with the unit of measure with the formally written work.
Challenge the student to multiply the dimensions in a different order and determine if the volume is always the same. Ask the student to describe why this is the case.
Introduce the student to the general formula for calculating volume, V = Bh, and show how the specific formula, V = lwh, is derived by substituting lw for the area of the base. Challenge the student to write specific formulas for calculating the volumes of cylinders and triangular prisms.
Consider implementing the MFAS task Moving Truck (6.G.1.2) for further practice calculating the volume of a right rectangular prism with fractional edge lengths. 