Overarching Standard: MA..K.GR.1 Identify and analyze two- and three-dimensional figures based on their defining attributes.

Benchmark of Focus

MA.1.GR.1.3: Compose and decompose two- and three-dimensional figures. Figures are limited to semi-circles, triangles, rectangles, squares, trapezoids, hexagons, cubes, rectangular prisms, cones and cylinders.

Examples

Example: A hexagon can be decomposed into six triangles.

Example: A semi-circle and a triangle can be composed to create a two-dimensional representation of an ice cream cone.

Benchmark Clarifications

Clarification 1: Instruction focuses on the understanding of spatial relationships relating to part-whole, and on the connection to breaking apart numbers and putting them back together.

Clarification 2: Composite figures are composed without gaps or overlaps.

Clarification 3: Within this benchmark, it is not the expectation to compose two- and three- dimensional figures at the same time.

Related Benchmark/Horizontal Alignment

• MA.1.NSO.1.3
• MA.1.FR.1.1

Vertical Alignment

Terms from the K-12 Glossary

• Cone
• Cube
• Cylinder
• Hexagon
• Rectangle
• Rectangular Prism
• Square
• Trapezoid
• Triangle

Purpose and Instructional Strategies

The purpose of this benchmark is to promote students’ spatial reasoning. Students should begin to see figures as compositions of other figures. In Kindergarten, students combined triangles, rectangles, and squares to form composite figures.

• Instruction should include guiding students to ensure that when composing a new three- dimensional figure those figures should have one set of the faces touching without gaps or overlaps.
• For example, the flat surface of a cone touching one face of a cube.
• Instruction includes making a connection to partitioning shapes.

Common Misconceptions or Errors

• Students may not initially recognize that a figure can be made using other figures. Class activities should promote exploring what figures could make a given figure.
• For example, using pattern blocks a student could manipulate two triangles to make a square, four triangles to make a rectangle, or six triangles to make a hexagon.

• What does it means to compose and decompose a shape?
• Sample answer that indicates understanding: To compose means to arrange or put shapes together to make a new shape or whole. To decompose a shape means to break shapes apart into smaller shapes.
• What figure could you compose using these shapes?
• Sample answer that indicates understanding: Students are able to compose a new shape given a set of shapes. For example, we can compose a trapezoid using 3 triangles.
• What attributes do we look for when trying to compose/decompose a shape?
• Sample answer that indicates understanding: We can look at shape’s defining attributes such as the sides, angles, and vertices.

Provide pattern blocks to students; be sure students get at least six triangles, two squares, two trapezoids and one hexagon. Read the directions to students and give students time to explore to find possible solutions. After students have come up with solutions, have discussion around whether all students found the same solution or if they had different solutions. Ask students if they could come up with a different response.

Instructional Items

Instructional Item 1

What three-dimensional figures make up the composite figure below?

Instructional Item 2

What two-dimensional figures make up the figure below?

Instructional Item 3

How many of the squares would you need to tile the rectangle below with no gaps or overlaps?

CPALMS

Lessons

Composing and Decomposing Shapes Lesson (Blog Post)

Lesson: Composing and Decomposing 2D Shapes (Blog Post)

Compose/Decompose Shapes

Composing and Decomposing 3D Shapes (Blog Post)

Activities and Resources

Composing and Decomposing Shapes (Worksheets)

How to Draw 3D Shapes (Blog Post)

Composition and Decomposition of Shapes (Blog Post)

Composing 2D Shapes Cards (Blog Post)

Composing and Decomposing (Blog Post)