Getting Started 
Misconception/Error The student models the threedimensional object with twodimensional shapes. 
Examples of Student Work at this Level The student describes the threedimensional object using two dimensional shapes.

Questions Eliciting Thinking Is a tree twodimensional or threedimensional? Are the shapes you used to model the tree twodimensional or threedimensional?
Can you give me an example of a geometric solid?
What does it mean “to model” the trunk of the tree? 
Instructional Implications Clarify for the student the distinction between two and three dimensional figures. Remind the student that a geometric solid is a threedimensional figure studied in geometry.
Help the student visualize solids by using an interactive website such as NCTM’s Geometric Solids tool (http://illuminations.nctm.org/). This tool allows the student to virtually explore and manipulate various geometric solids. The student can explore the number of vertices, edges and faces. The student can also make the solid transparent in order to explore other properties. Finally, the student can create a net which can be printed and folded to form a threedimensional solid.
Review the names, types, and properties of prisms, pyramids, cylinders, cones, and spheres. Guide the student to use these solids to model the objects on the worksheet. Explain that models can consist of only part of a solid or the composition of several solids. 
Moving Forward 
Misconception/Error The student is unable to use the model to correctly calculate the volume of the object. 
Examples of Student Work at this Level The student models the object with an appropriate threedimensional solid. When calculating the volume of the model, the student:
 Cannot find the radius of the circle from the circumference.
 Uses different units for the radius and the height.
 Does not round the estimate of the radius correctly and calculates the volume incorrectly.

Questions Eliciting Thinking How is the circumference of a circle found? How can you use the circumference of the circle to find the radius?
Does it matter that the circumference is in inches and the height is in feet?
How did you calculate the volume? 
Instructional Implications Discuss with the student an overall strategy for solving this problem (e.g., find the radius, convert lengths the same unit, and use the appropriate volume formula to calculate volume). Remind the student to check to be sure units are correct and all work is correctly shown.
Provide feedback to the student concerning his or her error (e.g., assist the student in: using the circumference to find the radius, translating the linear measures to the same unit, or identifying and using the appropriate volume formula). Remind the student to correctly label the final answer. 
Almost There 
Misconception/Error The student’s work is incomplete. 
Examples of Student Work at this Level The student models appropriately and calculates correctly, but does not show all necessary work to justify the final answer. For example, the student fails to:
 Sketch and describe a model, although his or her work shows an appropriate model was used.
 Show clear and concise work and does not label the final answer with appropriate units.

Questions Eliciting Thinking Reread the problem. Did you do everything that was asked of you for this problem?
Taking a look at your response. What could you do to make it better or more complete? 
Instructional Implications Remind the student of the mathematical practice of attending to precision. Encourage the student to reread the problem and his or her answer several times to ensure all aspects of the question have been addressed and the solution is expressed clearly and precisely.
Consider exploring NCTM Illuminations to find lessons or interactive activities involving modeling such as Ice Cream Puddle, Dynamic Paper, and Geometric Solids (http://illuminations.nctm.org/).
Consider implementing the MFAS tasks Estimating Area (GMG.1.1), Size It Up (GMG.1.1) and Camping Calculations (GMG.1.1). 
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 models the tree trunk with a right cylinder. The student then finds the radius of the cylinder from the given circumference, 4.77 in. The student converts the radius from inches to feet or the height from feet to inches, r = 4.77 in. or .3979 ft. Volume is then calculated using dimensions of the same units, either feet or inches, or .

Questions Eliciting Thinking Suppose the question had also asked to you estimate the quantity of bark on the tree trunk. How might you do that? 
Instructional Implications Consider exploring NCTM Illuminations to find lessons or interactive activities involving modeling such as Ice Cream Puddle, Dynamic Paper, and Geometric Solids (http://illuminations.nctm.org/).
Consider implementing the MFAS tasks Estimating Area (GMG.1.1), Size It Up (GMG.1.1) and Camping Calculations (GMG.1.1). 