Getting Started |
| Misconception/Error The student is unable to decompose the solid in order to find its surface area. |
| Examples of Student Work at this Level The student does not demonstrate an understanding that the areas of individual faces must be calculated and combined. The student:
- Attempts to use a single formula to find the surface area of the entire figure.
- Finds the surface area of either the prism or pyramid.
- Finds the area of a single triangle and/or rectangle.
- Combines the volume of one figure and area of another.
|
| Questions Eliciting Thinking Can you decompose the figure into familiar solids? Can you find the area of a triangle (rectangle)?
Is there a single formula for surface area that will work for this solid?
What is surface area? What do you have to do to find it?
How many faces are going to be painted? Can you describe the shape and dimensions of each one? |
| Instructional Implications Review the concept that the surface area of a composite solid can be found by decomposing the solid into familiar shapes and finding the area of the parts. Provide opportunities for the student to decompose both two-dimensional and three-dimensional figures into familiar two-dimensional shapes. Ask the student to clearly identify the decomposed parts and any relevant dimensions. Review the process of finding surface area by constructing nets.
Be sure the student understands the distinction between volume, area, and surface area, reviewing each concept as needed. Ensure that the student is familiar with rectangular prisms and square pyramids as well as the terms used to describe their parts and dimensions such as base, face, height, slant height, and edge. If necessary, review area formulas and ensure the student understands that the surface area of a prism or pyramid can be calculated by adding the areas of its component parts. Guide the student in systematically decomposing the solid, drawing the net, identifying relevant dimensions, and calculating areas.
Provide manipulatives for the student to explore in order to gain hands-on experience with decompositions of composite figures. Partner the student with a classmate to practice decomposing figures into nets and creating other strategies to calculate surface area. Provide additional opportunities for the student to decompose figures and calculate surface area. Include scenarios involving whole numbers, fractions, and decimals.
Consider implementing other MFAS tasks. |
Moving Forward |
| Misconception/Error The student makes significant errors when calculating areas. |
| Examples of Student Work at this Level The student demonstrates an understanding of the need to decompose the solid figure but:
- Uses an incorrect formula to calculate the area of a component.
- Uses an incorrect length when substituting into a formula (e.g., uses the height of the square pyramid rather than the slant height).
- Uses order of operations incorrectly when evaluating a formula.
- Uses an incorrect procedure when evaluating total surface area.
- Neglects to sum the surface areas of the component shapes.
- Calculates a total volume instead of a total surface area.
|
| Questions Eliciting Thinking How many faces does this figure have? Can you describe them?
How did you calculate the surface area of the rectangular prism? How did you calculate the surface area of the square pyramid?
What measurements do you need to calculate the surface area of each figure? Can you draw and label the dimensions on a net?
What is the difference between volume and surface area? Which is asked for here? How do you know? |
| Instructional Implications Be sure the student understands the distinction between volume and surface area and review both concepts, as needed. Ensure that the student is familiar with rectangular prisms and square pyramids as well as the terms used to describe their parts and dimensions such as base, face, height, slant height, and edge. If necessary, review area formulas and ensure the student understands that the surface area of a prism or pyramid can be calculated by adding the areas of its component parts.
Guide the student through a systematic analysis of the surface area of the solid. Using the solid on the worksheet, prompt the student to identify and label every length measurement that can be determined and identify those needed to calculate the surface area.
Provide additional opportunities for the student to find the surface area of solids and composite figures. Guide the student in systematically decomposing the solid, drawing the net, identifying relevant dimensions, and calculating the area of each figure.
Provide practice problems in which insufficient information is given to calculate surface area, and ask the student to identify which additional measurement is needed in order to solve the problem.
Consider implementing the MFAS task Prismatic Surface Area for further practice. |
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 into familiar shapes and selects appropriate formulas for calculating the area of each but:
- Makes a calculation error.
- Neglects to label units or labels them incorrectly (e.g., as linear or cubic units).
- Neglects to sum all the areas of the component parts.
- Includes the areas of the bases rather than recognizing that the problem context only requires lateral surface area.
|
| Questions Eliciting Thinking I think you made a calculation error. Can you check your work?
Which one value represents the surface area of the figure?
How did you decide which dimensions to use for each shape? Can you draw each face and label the dimensions needed?
How should the units be labeled? |
| 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.
Provide practice problems in which insufficient information is given to calculate surface area and ask the student to identify which additional measurement is needed in order to solve the problem. |
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 into familiar shapes, selects appropriate formulas for calculating area, and accurately calculates the surface area as 760  .
Note: The student may include the floor of the entire structure as part of the exterior surfaces to paint which would involve adding one base equal to 100 resulting in a total surface area of 860 .
|
| Questions Eliciting Thinking How did you decide whether to include the bases of the prism and pyramid? In what kind of problems might you include them and when would you not? Which parts of each surface area formula represent the bases?
How did you decide which height to use for the triangle faces?
Could you determine the volume of the composite figure? What measurements would you need that were not needed to find surface area? How could you find those measurements? |
| Instructional Implications Represent the dimensions of the figure with variables and challenge the student to write a single expression for finding the surface area of the composite figure.
Provide practice problems involving composite figures with fractional edge lengths and problems in which surface area is given, but the student must identify a missing measurement.
Provide opportunities for the student to explore how changing a dimension of a figure affects the surface area.
Consider implementing other MFAS tasks. |
![Cpalms [Logo]](/Public/images/cpalms_color.png)
Word (.docx)
Acrobat (.pdf)
Congratulations
