Overarching Standard: MA.1.GR.1: Identify, compare and sort two- and three-dimensional figures based on their defining attributes. Figures are limited to circles, semi-circles, triangles, rectangles, squares, trapezoids, hexagons, spheres, cubes, rectangular prisms, cones and cylinders.

Benchmark of Focus

MA.1.GR.1.1: Identify, compare and sort two- and three-dimensional figures based on their defining attributes. Figures are limited to circles, semi-circles, triangles, rectangles, squares, trapezoids, hexagons, spheres, cubes, rectangular prisms, cones and cylinders.

Benchmark Clarifications

Clarification 1: Instruction focuses on the defining attributes of a figure: whether it is closed or not; number of vertices, sides, edges or faces; and if it contains straight, curved or equal length sides or edges.

Clarification 2: Instruction includes figures given in a variety of sizes, orientations and non-examples that lack one or more defining attributes.

Clarification 3: Within this benchmark, the expectation is not to sort a combination of two- and three- dimensional figures at the same time or to define the attributes of trapezoids.

Clarification 4: Instruction includes using formal and informal language to describe the defining attributes of figures when comparing and sorting.

Related Benchmark/Horizontal Alignment

• MA.1.DP.1.1

Vertical Alignment

Terms from the K-12 Glossary

• circle
• cone
• cube
• cylinder
• edge
• hexagon
• rectangle
• rectangular prism
• square
• sphere
• trapezoid
• triangle
• vertex

Purpose and Instructional Strategies

The purpose of this benchmark is for students to recognize figures by their defining attributes as this will help them sort figures based on attributes rather than orientation, color or size. In Kindergarten, students identified circles, triangles, rectangles, squares, spheres, cubes, cones, and cylinders by a defining attribute. (MTR.2.1, MTR.5.1)

• Instruction includes a variety of examples and non-examples that lack a defining attribute.
• While the K-12 Glossary uses the inclusive definition of a trapezoid, students will not formally identify or classify trapezoids until grade 3.

Common Misconceptions or Errors

• Students may only recognize a figure by its size or orientation. In these cases, students need practice in locating figures by a defining attribute like “find the two-dimensional figures with three vertices” rather than find the triangles.

• What is the difference between a defining attribute and a non-defining attribute?
• Sample answer that indicates understanding: A defining attribute is what you see that always stays the same and is always true about that shape (closed shape, number of sides and vertices, equal length, angles). It helps you identify the shape. For example, the number of sides and vertices of a triangle is always 3 and a cylinder has both flat and curved faces with two of the flat faces being circles.
• Sample answer that indicates understanding: A non-defining attribute is what you see about a shape that can change (size, color, and orientation/position). It cannot help you identify the shape. For example, if you ask the student to draw a red shape, it would not help them identify what shape to draw because any shape could be red.
• What is the difference between a two-dimensional and three-dimensional shape? (Can be more specific: What is the difference between a circle and a sphere?)
• Sample answer that indicates understanding: A two-dimensional shape is a flat closed shape and most of them have sides. A three-dimensional shape is a solid shape that have edges rather than sides.
• What is the name of this shape? How do you know? or What are the defining attributes of this given shape?
• Sample answer that indicates understanding: Student should be able to use defining attributes to identify the shape by name. For example, this is a triangle because it is a closed shape with 3 straight sides and 3 vertices or a sphere is a solid shape with 1 curved face and no vertices.

Provide students pictures of figures like the one provided above.

Part A. Sort the figures by ones that have three sides and ones that have four or more sides.

Part B. Discuss what they notice about the figures they sorted that have three sides. What is a two- dimensional figure called that has three sides? Ask students what they notice about the triangles. Are they all the same size? Do they all look the same? What makes them triangles?

Part C. Have students look at the figures they sorted in the “four or more sides” pile. What could these figures be sorting further by? Once students determine an attribute they can sort by, have students sort by that attribute.

Part D. How did you sort the figures? Ask students what they notice about the figures. Are they all the same size? Do they all look the same? Are they all the same figure?

Part E. Discuss which attributes put all of the same figures together and which did not. Have students take their sorted shapes to create a pictograph by stacking their shapes on top of each other.

Instructional Items

Instructional Item 1

Which of the figures below is a trapezoid? How do you know?

Instructional Item 2

This is a cone. What makes this a cone?

Instructional Item 3

Jill says these two shapes are both cubes. Do you agree with her? Why or why not?

CPALMS

Lessons

Solid Shapes (Near Pod)

Shapes Are Everywhere! by Charles Ghigna

Captain Invincible and the Space Shapes by Stuart J. Murphy

Activities and Resources

Teaching 2D and 3D shapes (Blog Post)

Name the 3D Shape (IXL)

Name the 2D Shape (IXL)

Geometry (Blog Post)