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2D Representations of 3D Objects

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This lesson unit is intended to help teachers assess how well students are able to visualize two-dimensional cross-sections of representations of three-dimensional objects. In particular, the lesson will help you identify and help students who have difficulties recognizing and drawing two-dimensional cross-sections at different points along a plane of a representation of a three-dimensional object.
Middle School, High School
Grade 6, Grade 9, Grade 10, Grade 11, Grade 12
Material Type:
Assessment, Lesson Plan
Shell Center for Mathematical Education, U.C. Berkeley
Provider Set:
Mathematics Assessment Project (MAP), Mathematics Assessment Project (MAP)
Date Added:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Media Format:
Downloadable docs, Text/HTML


Haley Dotson on Mar 27, 10:36am

I like the inclusion of all students. I would like to have seen some technology included but the real life examples exemplified the lesson and related it to the students. I would also like to know how much time you spent on each section and any differentiated modifications you made. Overall, a great group activity!

Anonymous on Jul 05, 07:54pm

Sharing Costs: Travelling to School - Students solve a problem using real-world modeling involving proportional relationships. Lesson plans include instructional strategies and sample questions designed to increase student conceptional understanding.

Laws of Arithmetic: Task provides teachers and students with assessment data to determine how students perform arithmetic operations by recognizing and applying the order of operations. Students apply distributive and commutative properties, write and evaluate numerical expressions.

2D Representations of 3D Objects: Unit asks students to explore relationships between two- and three-dimensional objects by identifying associated shapes of two-dimensional cross sections of three-dimensional objects (i.e., the shape of water level in given objects.

Lesson plans provide instructional strategies along with sample questioning strategies to build student understanding. It also provides potential student misconceptions and questions designed to build understanding.

Authors of the materials suggest alignment to G-GMD 1, G-GMD 2, and G-GMD 3. However, the materials do not address volume formulas, nor do they address Cavalieri’s principle.

The unit demonstrates a strong alignment to G-GMD 4.

Instructional strategies build opportunities for students to utilize mathematical practices 3, 6, and 7. Mathematical Practice 5 was rated as a level 1 because the current lesson design does not require students to determine appropriate / strategic use of available tools for the learning process (i.e., students are given tools to use).



EQuIP Rubric

Average Score (3 Points Possible)
ELA Math
Alignment to the Rigor of the CCSS 3 (1 user)
Key Shifts in the CCSS 3 (1 user)
Instructional Supports 2 (1 user)
Assessment 2 (1 user)
Overall Rating for the Lesson/Unit E/I (1 user)
Alignment to the Rigor of the CCSS N/A
Key Shifts in the CCSS N/A
Instructional Supports N/A
Assessment N/A
Overall Rating for the Lesson/Unit N

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