• MA.5.GR.1 Geometric Reasoning

Classify two-dimensional figures and three-dimensional figures based on defining attributes.

MA.5.GR.1.2

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.

Benchmark Clarifications:
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 surfaces or flat faces.

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 (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.

 During instruction teachers should explain that a cone has one flat face, a cylinder has two flat faces and a sphere does not have any flat faces, 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.

Instructional Tasks
Instructional Task 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

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