Getting Started 
Misconception/Error The student is unable to select appropriate geometric shapes to model the surface area of the lake. 
Examples of Student Work at this Level The student chooses geometric shapes that do not accurately model the surface area of the lake. For example, the student models:
 The entire lake with a threedimensional solid.
 The surface of the lake using overlapping rectangles or one large rectangle disregarding a portion of the lake.

Questions Eliciting Thinking How would you describe surface of the lake?
Should the surface area of the lake be modeled with a twodimensional or threedimensional figure? Why?
How would surface area calculations of the lake be affected when the geometric shapes overlap?
Should the geometric shape(s) you chose cover area that is not part of the lake? Why or why not? Do the shapes you chose cover the surface area of the lake? What geometric shapes could be used to model the surface area of the lake more precisely?
Can you demonstrate on the diagram how the shape(s) you chose model the surface area of the lake? 
Instructional Implications If needed, explain to the student that even though the lake is threedimensional, its surface is best modeled with twodimensional shapes. Remind the student that the surface area formulas provide the combined areas of all surfaces of a solid. Guide the student to only consider the surface of the lake and to focus calculations on this one surface.
Provide the student with a handout of common geometric shapes (e.g., square, triangle, rectangle, rhombus, and trapezoid) and transparent cut outs of each. Model for the student how geometric shapes can be used to model an irregular surface. Emphasize the objective of approximating the irregular shape as precisely as possible. Provide the student with irregular shapes that can be easily modeled by the shapes provided, increasing the difficulty as needed. If needed, demonstrate for the student how the area of overlapping shapes will exceed a good estimation for the area of the lake and how gaps will fall below that same estimation.
Guide the student in selecting the geometric shapes that could be used to model the surface area of the lake. Help the student identify any overlaps or gaps and explain why either should be avoided. If possible, have the student compare the shape and size of the model he or she chose to those of other students at the same level and to make changes to his or her shapes, if needed. Encourage the student to consider using shapes chosen by other students, if they provide a better model (e.g., using a square and triangle in place of a trapezoid).
Provide the students with another example of an irregular shape that can be modeled using shapes different from those used in this task. Have the student sketch the model including the dimensions and then use this model to estimate the area. 
Moving Forward 
Misconception/Error The student is unable to correctly calculate dimensions and areas of composite shapes. 
Examples of Student Work at this Level The student appropriately models the surface of the lake but:
 Calculates the area of a triangle incorrectly.
 Estimates or calculates unknown lengths with values that are disproportionately large.
 Does not use the dimensions given to calculate the height of the triangle but instead assumes the height is half or a third of 572.

Questions Eliciting Thinking How do you find the area of a triangle?
How did you find these lengths? Can you explain how the lengths you found fit with the given lengths?
How did you find the dimensions of the triangle you used as a model? Are there other measurements on the diagram that would allow you to be more precise in determining the height of the triangle? 
Instructional Implications Provide feedback to the student concerning any errors made and allow the student to revise his or her work [e.g., review with the student how to find the area of a triangle (or other shapes used to model the surface of the lake)]. Remind the student of the importance of carefully identifying the base and the height of the triangle before calculating area. Guide the student to use given lengths to find unknown lengths. Emphasize the importance of checking calculated lengths to determine if they are consistent with given lengths.
Provide the students with another example of an irregular shape that can be modeled using shapes different from those used in this task. Have the student sketch the model including the dimensions and then use this model to estimate the area. 
Almost There 
Misconception/Error The student makes a minor error in modeling or calculating. 
Examples of Student Work at this Level The student does not:
 Sketch and describe a model, although his or her work shows an appropriate model was used.
 Draw the model correctly but calculates the area correctly.
 Add the area of each shape to find the total estimated surface area of the lake.
 Label the final answer with appropriate units.
 Use area formulas to organize his or her work resulting in a careless error.
The student uses the wrong dimension to calculate area because he or she:
 Miscopies a distance from the illustration onto the model.
 Makes a subtraction error when finding the height of the triangle.
 Makes a calculation error when adding together the area of each shape.

Questions Eliciting Thinking Reread the problem. Did you do everything that was asked in this problem?
How could your work have been more clear and precise?
How does your model represent the work you demonstrated?
Do you notice any errors when writing the dimensions of your model or when solving for the area?
What could you do to make it more complete and concise? 
Instructional Implications Remind the student of the mathematical practice of attending to precision. Encourage the student, when working a problem, 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. Encourage the student to always check his or her work to ensure all numbers have been transferred correctly and that no numbers have been transposed. Remind the student to review his or her work by reworking the problem to identify and correct any minor mistakes that may have been made. Review with the student the importance of writing down the formulas he or she is using to calculate the area, to avoid careless mistakes, and to always include the dimensions in the formulas and in the answer.
Provide the students with another example of an irregular shape that can be modeled using shapes different from those used in this task. Have the student sketch the model including the dimensions and then use this model to estimate the area. If possible, have the student compare his or her work with the work of other students at this level to ensure that the work is correct, clear, and precise.
Consider implementing the MFAS tasks Estimating Area, Size It UpÂ and Camping Calculations. 
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 surface of the lake with a rectangle (800 yards by 374 yards) and a right triangle (with a base of 244 yards and a height of 198 yards). The student understands that he or she can estimate the surface area of the lake by summing the area of the rectangle and the area of the triangle.
The student calculates the area of the rectangle as 299,200 square yards and the area of the triangle as 24,156 square yards. He or she estimates the surface area of the lake to be 323,356 square yards.

Questions Eliciting Thinking Could you use different geometric shapes than the ones you chose to model the surface area of the lake?
What strategy could you use to develop a more precise model and area estimation? 
Instructional Implications Illustrate to the student how using smaller geometric shapes to model the surface area of the lake will make the estimation more precise. Have the student use tracing paper to sketch the lake and then use grid paper with squares and diagonals to identify and draw smaller geometric shapes that can be used to estimate the surface area of the lake.
Consider implementing the MFAS tasks Estimating Volume, Size It UpÂ and Camping Calculations. 