Identify and classify three-dimensional figures into categories based on their defining attributes. Figures are limited to right pyramids, right prisms, right circular cylinders, right circular cones and spheres.


Clarification 1: Defining attributes include the number and shape of faces, number and shape of bases, whether or not there is an apex, curved or straight edges and curved or flat faces.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 5
Strand: Geometric Reasoning
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

  • There are no direct connections outside of this standard; however, teachers are encouraged to find possible indirect connections.


Terms from the K-12 Glossary

  • Cone 
  • Cylinders
  • Edge 
  • Prisms 
  • Pyramids 
  • Sphere 
  • Vertex


Vertical Alignment

Previous Benchmarks


Next Benchmarks


Purpose and Instructional Strategies

The purpose of this benchmark is to begin formal categorization of three-dimensional figures based on attributes of their faces, edges and vertices. Three-dimensional figures were identified informally in Kindergarten and grade 1. The work in grade 5 prepares students for more detailed work with three-dimensional figures, including finding volumes and surface areas using formulas and nets in grade 6 (MA.6.GR.2.4). 
  • Instruction includes having students use language they have already learned and apply it to a larger variety of figures including prisms and pyramids with any number of sides. 
  • Instruction includes explaining that a cone has one flat base, a cylinder has two flat bases and a sphere does not have any flat bases, but each of these figures has a curved surface.


Common Misconceptions or Errors

  • Students may believe that the orientation of a figure changes the three-dimensional shape.


Strategies to Support Tiered Instruction

  • Instruction includes teacher providing a graphic organizer that contains three-dimensional figure names and definitions from the glossary. Students match images of the figures in different orientations to their definitions. 
    • For example, the teacher provides students with a graphic organizer like the one shown below and a set of three-dimensional figure picture cards. Students match the image to the defining attributes listed. 

  • Instruction includes providing three-dimensional figures made of plastic or wood and having students identify the shapes that make up their base or bases and faces. Students then look at the definition for each figure and classify it based on the attributes they identified. 
    • For example, the teacher provides the students with a triangular prism like the one shown below. The students then identify the two bases as triangles and the faces connecting them as rectangles. The teacher provides students with the definitions for three-dimensional figures and has them determine which classification it fits in.
triangular prism


Instructional Tasks

Instructional Task 1 (MTR.4.1

Categorize the three-dimensional figures below into the table. 


  • Right pyramids 
  • Spheres 
  • Right circular cylinders 
  • Right prisms 
  • Right circular cones


Instructional Items

Instructional Item 1 

Select all the shapes that contain an apex. 
  • a. Right pyramids 
  • b. Spheres 
  • c. Right circular cylinders 
  • d. Right prisms 
  • e. Right circular cones May contain a rectangular face Contains no faces 


*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.5.GR.1.AP.2: Identify and sort three-dimensional figures into categories based on their defining attributes. Figures are limited to right rectangular pyramids, right rectangular prisms, right circular cylinders, right circular cones and spheres.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Lesson Plans

Analyzing Polyhedra:

Students will construct several simple polyhedra, then count the number of faces, edges, and vertices. These data should suggest Euler's formula. 

Type: Lesson Plan

Three-Dimensional Play Dough:

This hands-on lesson is a review for three-dimensional figures. The students make models of three-dimensional figures and then use these play dough models to count the vertices, edges, and faces.

Type: Lesson Plan

Unit/Lesson Sequence

Three Dimensional Shapes:

In this interactive, self-guided unit on 3-dimensional shape, students (and teachers) explore 3-dimensional shapes, determine surface area and volume, derive Euler's formula, and investigate Platonic solids. Interactive quizzes and animations are included throughout, including a 15 question quiz for student completion.

Type: Unit/Lesson Sequence

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.