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 an appropriate strategy for finding the volume of a right rectangular prism. The student:
 Squares the area of the base “since a base and width were not given.”
 Adds the fractional lengths together.
 Divides the dimensions.

Questions Eliciting Thinking What is volume? What do you have to do to find it?
What does the area of the base mean?
Can you identify the length, width, and height of the moving truck? Is there enough information given to solve the problem?
What kind of figure is described in this problem? Is there a formula for finding the volume of this figure that you could use? 
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, V = Bh. Clearly identify the meaning of the variables and review the connection between the general (V = Bh) and specific formulas (V = lwh) for volume of a rectangular prism. Ask the student to locate the base and height of the prism and identify the relevant measurements.
Use manipulatives such as linking cubes to demonstrate how the area of the base of a rectangular prism is represented by the number of cubes in each layer of cubes and the height is represented by 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 the volume of a rectangular prism and attempts to multiply the area of the base and the height. The student makes errors multiplying fractions. The student:
 Multiplies the whole numbers and multiplies the fractions.
 Multiplies the whole numbers and finds common denominators for the fractions.
 Makes errors converting mixed or whole numbers to improper fractions.
 Makes an error in simplifying the product before 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 writes:
 162 as a final answer and does not include any units of measure.
 .

Questions Eliciting Thinking What type of unit is typically used when measuring volume? What is the unit of measure for volume of the truck 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 162 cubic inches as ) or read (e.g., reading 162 as “162 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 = 22 x 7. 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 writes, V = or V = and explains that the area of the base times the height determines the volume of the truck.

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 variable 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 = 22 x 7. 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.
Give the student the general formula for calculating volume, V = Bh, and challenge the student to substitute for the area of the base to write the specific formulas for calculating the volumes of cylinders and triangular prisms.
Consider implementing the MFAS task Bricks (6.G.1.2) for further practice calculating the volume of a right rectangular prism with fractional edge lengths. 