Getting Started 
Misconception/Error The student does not attempt to decompose the solid in order to find its volume. 
Examples of Student Work at this Level The student:
 Attempts to use a single formula (e.g., the formula for the volume of a triangular prism).
 Attempts to calculate surface area of some or all of the solid.

Questions Eliciting Thinking Did you try to decompose the house into solids with which you are familiar?
Is there a single formula that can be used to find the volume of this solid?
What is volume? How can the volume of a prism be calculated? 
Instructional Implications ExplainÂ that the volume of a composite solid can be found by decomposing the solid into familiar solidsÂ and summingÂ the volumes of the component parts. Provide opportunities for the student to decompose both twodimensional and threedimensional figures into familiar twodimensional and threedimensional shapes. Ask the student to clearly identify the decomposed parts and any relevant dimensions.
Provide manipulatives such as multilink cubes for the student to explore in order to gain handson experience with decompositions of composite figures.
Be sure the student understands the distinction between volume and area (or surface area), and review both concepts as needed. Ensure that the student is familiar with rectangular prisms and triangular prisms as well as terms used to describe their parts and dimensions such as base, face, height, and edge. If necessary, review area formulas and ensure the student understands that the volume of a prism can be calculated by multiplying the area of the base by the height of the prism.
Provide additional opportunities for the student to find the volumes of composite figures. Guide the student in systematically decomposing the solid, identifying relevant dimensions, and calculating volumes.
Consider implementing the MFAS tasks Moving Truck and Bricks (6.G.1.2). 
Moving Forward 
Misconception/Error The student is unable to correctly calculate the volumes of the component solids. 
Examples of Student Work at this Level The student demonstrates an understanding of the need to decompose the solid figure and, when asked, can correctly describe the component parts. However, the student uses an incorrect formula or procedure to determine the volume of one or both parts.

Questions Eliciting Thinking How did you decompose this solid? What two kinds of prisms make up this solid figure?
How did you calculate the volume of the rectangular prism? How did you calculate the volume of the triangular prism?
What measurements do you need to calculate the volume of each prism? 
Instructional Implications Be sure the student understands the distinction between volume and area (or surface area) and review both concepts, as needed. Ensure that the student is familiar with rectangular prisms and triangular prisms as well as terms used to describe their parts and dimensions such as base, face, height, and edge. If necessary, review area formulas and ensure the student understands that the volume of a prism can be calculated by multiplying the area of the base by the height of the prism.
Guide the student through a systematic analysis of the volume of a shape. Using the solid on the Chilling Volumes worksheet, prompt the student to identify and label every length measurement that can be determined and identify those needed to calculate volumes. Provide additional opportunities for the student to find the volumes of composite figures. Guide the student in systematically decomposing the solid, identifying relevant dimensions, and calculating volumes.
Provide practice problems in which insufficient information is given to calculate volume and ask the student to identify which additional measurement is needed in order to solve the problem. 
Almost There 
Misconception/Error The student makes a minor mathematical error. 
Examples of Student Work at this Level The student successfully decomposes the solid figure and selects appropriate formulas for calculating volumes but:
 Makes a computational error in some part of a calculation.
 Neglects to sum the volumes of the component figures.
 Neglects to label units or labels them incorrectly (e.g., as linear or square units).

Questions Eliciting Thinking I think you may have made a calculation error. Can you check your work?
What one value represents the volume of the house? 
Instructional Implications Provide specific feedback, and allow the student to revise his or her work.
Provide additional practice opportunities. Include shapes whose dimensions are given by fractions and decimals. 
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 successfully decomposes the solid figure, selects appropriate formulas for calculating volumes, and accurately calculates the volume 21,000 Â + 8,400 Â = 29,400 .

Questions Eliciting Thinking How did you determine the volume of the triangular prism? What measurements did you need? How did you find the measurements you needed? 
Instructional Implications Represent the dimensions of the figure with variables and challenge the student to write a single expression for finding the volume of the composite figure.
Provide practice problems involving composite figures with fractional edge lengths and problems in which volume is given and the student must identify a missing measurement.
Provide opportunities for the student to explore how changing a dimension of a figure affects the volume.
Consider implementing other MFAS tasks for standard 7.G.2.6. 