Getting Started 
Misconception/Error The student does not understand the concept of a twodimensional cross section. 
Examples of Student Work at this Level The student identifies or describes the two threedimensional parts that are created from slicing the cone.
The student may also confuse some or all of the terms: horizontal, vertical, parallel, perpendicular. 
Questions Eliciting Thinking What is the difference between a twodimensional figure and a threedimensional figure? Can you give me an example of each?
Do you know what cross section means? Can you imagine the cross section of the cone that is revealed by the slicing?
What does parallel (perpendicular) mean? Do you know what horizontal and vertical mean? 
Instructional Implications Review the difference between twodimensional and threedimensional figures. Provide the student with examples of figures to be classified as either twodimensional or threedimensional. Ask the student to classify the figures and identify the dimensions of each.
Clarify the meanings of terms used in this task: cross section, parallel, perpendicular, horizontal, and vertical. Model for the student how to draw and describe a cross section of a threedimensional solid. Guide the student to relate dimensions in the drawing to the dimensions of the original solid. For example, explain that the vertical cross section is a rectangle whose height is the same as the height of the solid. The base of the rectangle corresponds to the radius of the base of the solid. Provide additional experience with identifying and drawing twodimensional slices of threedimensional figures and describing their dimensions.
Consider using a virtual manipulative such as Cross Section Flyer – Shodor (CPALMS Resource ID#: 25314) to help the student visualize cross sections of various three dimensional solids. 
Moving Forward 
Misconception/Error The student’s drawing or description contains errors. 
Examples of Student Work at this Level The student understands the cross sections are twodimensional figures but is unable to correctly draw or describe both cross sections. The student:
 Describes both cross sections as triangles.
 Does not sketch either and/or describes the horizontal cross section as a triangle.

Questions Eliciting Thinking How would you describe the threedimensional shape on the paper?
If the wedge of cheese comes from a large circular cylinder of cheese, would all of its edges be segments? 
Instructional Implications Demonstrate cross sections with manipulatives to show how different cross sections can be created by slicing a threedimensional solid. Guide the student to relate dimensions in the drawing to the dimensions of the original solid. For example, explain that the vertical cross section is a rectangle whose height is the same as the height of the solid. The base of the rectangle corresponds to the radius of the base of the solid. Provide additional experience with identifying and drawing twodimensional slices of threedimensional figures and describing their dimensions.
Consider implementing CPALMS Lesson Plan 2D Representations of 3D Objects (ID 32549). This lesson will help students visualize two dimensional cross sections at different levels of a three dimensional object.
Consider implementing MFAS tasks Inside the Box (GGMD.2.4) and Slice of a Cone (GGMD.2.4). 
Almost There 
Misconception/Error The student uses imprecise language to describe the cross section. 
Examples of Student Work at this Level The student sketches and describes a rectangle for the vertical cross section, but describes the horizontal cross section as a curved triangle or a triangle with a semicircle.

Questions Eliciting Thinking What is the geometric term for a “curved triangle”?
If you put several “curved triangles” together, what shape could you create? 
Instructional Implications Review the geometric term sector of a circle. Encourage the student to learn and use appropriate mathematical terminology.
Consider implementing CPALMS Lesson Plan 2D Representations of 3D Objects (ID 32549). This lesson will help students visualize two dimensional cross sections at different levels of a three dimensional object.
Consider implementing MFAS tasks Slice of a Cone (GGMD.2.4) and Inside the Box (GGMD.2.4). 
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 sketches and describes the vertical cross section as a rectangle and the horizontal cross section as a sector.

Questions Eliciting Thinking Could you find a cross section of this shape that is a trapezoid? How?
What other cross sections can you imagine generating by slicing the solid in different ways? 
Instructional Implications Challenge the student with more complex figures such as a double cone and cross sections that are neither parallel nor perpendicular to the base. Use this as an opportunity to introduce the concept of conic sections to the student.
Consider implementing MFAS tasks Inside the Box (GGMD.2.4) and Slice of a Cone (GGMD.2.4). 