Getting Started |
| Misconception/Error The student does not understand that a net represents the surface area of a three-dimensional shape. |
| Examples of Student Work at this Level The student:
- Attempts to calculate volume or perimeter.
- Adds or multiplies given measurements without any evident strategy.
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| Questions Eliciting Thinking What is a net?
Can you explain how this diagram represents a three-dimensional shape?
Can you explain the problem in your own words? |
| Instructional Implications Define a net as a two-dimensional representation of a three-dimensional shape that will fold to re-create the three-dimensional shape. Ensure the student is familiar with the terms used to describe the parts and dimensions of three-dimensional figures including face, edge, vertex, slant height, and base. Provide opportunities for the student to decompose three-dimensional figures into nets composed of familiar two-dimensional shapes. Guide the student to clearly identify the decomposed parts and label the relevant dimensions.
Have the student create a net of a given solid that is large enough to cut out and fold. Have the student label all dimensions as given in the original solid. Allow the student to cut out and fold the net in order to check its accuracy.
Provide the student with the diagram of a net, and ask the student to identify the following:
- The three-dimensional shape represented by the net.
- The sides that will come together to form an edge if the net is folded into a three-dimensional shape.
- The sides having the same length.
Ensure the student is aware that sides that will come together to form an edge must have the same length.
Provide manipulatives such as pattern blocks and folding three-dimensional shapes for the student to explore to gain hands-on experience with creating nets by decomposing figures. Partner the student with a classmate to practice decomposing shapes into familiar figures to create nets. Ask the student to identify the faces, edges, and vertices of the three-dimensional figure that will connect to create the net.
Guide the student to understand that the net for a three-dimensional shape includes all of its faces. The sum of the areas of the shapes that compose the net is therefore equal to the surface area of the three-dimensional shape.
Consider implementing CPALMS activity Decomposing 3-D Shapes (ID 13187) or an activity from National Council of Teachers of Mathematics called Fishing for the Best Prism, http://illuminations.nctm.org/Lesson.aspx?id=2911, to create nets of rectangular prisms in context. |
Moving Forward |
| Misconception/Error The student is unable to use the net to correctly calculate the surface area of a triangular pyramid. |
| Examples of Student Work at this Level The student understands that the combined areas of the triangles in the net are equivalent to surface area but the student:
- Uses an incorrect formula (e.g., A = bh instead of A =
 bh) or an incorrect measurement to calculate the area of a triangle.
- Omits one or more faces from any calculations.
- Neglects to find the sum of the areas of the triangles within the net.
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| Questions Eliciting Thinking How is the area of a triangle determined?
How can you use this diagram to find the surface area of a three-dimensional shape? |
| Instructional Implications Review the concept that the area of a composite figure can be found by decomposing the figure into familiar shapes and finding the areas of the parts. Ask the student to label relevant dimensions, calculate the areas, and find the sum.
Review the procedure for finding the area of a triangle. Ask the student to identify all measurements needed to calculate area and clearly label them on the figure. Then, guide the student to accurately calculate the area of each triangle and sum them to find the total surface area.
Encourage the student to develop an organized method to ensure that the areas of all shapes that compose the net are calculated and included in the sum. Advise the student to do calculations on the side to prevent them from interfering with major written work. |
Almost There |
| Misconception/Error The student makes a minor error. |
| Examples of Student Work at this Level The student calculates and combines the areas of the triangles composing the net but:
- Makes a calculation error when adding the areas of the component figures.
- Makes a multiplication error when calculating an area.
- Makes an error in decimal placement.
- Labels units incorrectly or not at all.
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| Questions Eliciting Thinking I think you may have made a calculation error. Can you check your work?
Which one value represents the surface area of the tetrahedron?
What type of unit is used when measuring surface area?
How should the units be labeled? |
| Instructional Implications Provide specific feedback and allow the student to revise the work. Provide additional opportunities to find surface area using nets. Include shapes with dimensions given by fractions and decimals.
Review the types of units that are used to measure length, area, and volume. Correct any misconceptions about how these units are written. Provide feedback on errors made in describing the unit of measure and allow the student to correct the work. |
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 determines the surface area of the tetrahedron is 173.2  and provides work to justify the answer.
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| Questions Eliciting Thinking Can you think of another way this net could be drawn?
If the net is drawn so the triangles connect in a different way, will the surface area change? |
| Instructional Implications Challenge the student to represent the tetrahedron using a different net with the dimensions labeled. Ask the student to use the net to determine the surface area of the tetrahedron.
Provide the student with a physical three-dimensional shape. Ask him or her to measure the edges of the shape, draw and label a net to represent the surface of the shape, and calculate the surface area. Challenge the student to create multiple nets that represent the surface of the same solid.
Consider implementing other MFAS tasks for standard (6.G.1.4). |
