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Using the State Curriculum: Mathematics, Grade 4

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Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 2.0 Knowledge of Geometry

Topic B. Solid Geometric Figures

Indicator 1. Analyze the properties of solid geometric figures

Objective b. Describe solid geometric figures by the number of edges, faces, or vertices

  • Use triangular pyramids, rectangular pyramids, triangular prisms, or rectangular prisms

Clarification

The van Hiele Levels of Geometric Thought

Pierre and Dina van Hiele are two Dutch educators who created a model for developing geometric reasoning. Their model is based on a five-level hierarchy that all students move through as they develop their geometric understandings.

Level 0: Visualization Students are able to recognize and name figures. They are able to group shapes that seem to be alike. They can recognize a square because it looks like a square. But if the square were rotated 45°, students might not recognize it as a square.

geometric image

Level 1: Analysis At this level, students begin to focus more on the properties of a shape rather than its size or orientation. Students are able to think of shapes within a class and know that all shapes in that class have certain properties. Students will recognize that all cubes have faces that are squares. At this level, however, students may not recognize that all cubes are a subclass of rectangular prisms.

Level 2: Informal Deduction Students at this level begin to use logical reasoning by developing relationships between the properties of a class of shapes. For example: If a figure is a square it has four congruent sides. If it has four congruent sides then the figure is a rhombus. If a figure is a square it is a rhombus.

Level 3: Deduction At this level, students are able to evaluate more than just the properties of shapes. They begin to examine geometry as a system with definitions, axioms and theorems. Students at this level work with abstract statements and make conclusions based on logical deduction. This is the level of the traditional high school geometry course.

Level 4: Rigor This is the highest level of geometric reasoning. At this level, students compare relationships of figures within different systems of geometry.

Students that are asked to describe and classify solid geometric figures by edges, faces and vertices are moving from Level 1 to Level 2. They can tell you the properties of a certain geometric solid and they can also tell you what the solid is when given a set of properties.

A Polyhedron is a solid figure which has three dimensions--length, width, and height.
Polyhedra are sorted and classified by their edges, faces, and vertices.

  • An edge is a line segment where two faces meet.
  • A face is a polygon or a flat side.
  • A vertex is a point where two or more edges meet.

geometric image

A pyramid is a three-dimensional polyhedron that has a polygon for the base and triangular sides (faces) that meet in a point. The point at which the faces meet is called the vertex. Pyramids are named by the shape of their base. A triangular pyramid has a triangle base. A rectangular pyramid has a rectangular base. (A rectangular pyramid whose base is a square may also be referred to as a square pyramid.)

geometric image

A prism is a polyhedron with a pair of congruent and parallel bases (faces) that are polygons. The rest of the faces are parallelograms.

A triangular prism has two triangle bases. A rectangular prism has two rectangle bases. (A cube is also a prism, but has all square faces.)

geometric image

Classroom Example 1

Compare a triangular prism and a triangular pyramid and record observations in a Venn diagram.

geometric image

Classroom Example 2

Identify the characteristics of solid figures.

Solid Faces Edges Vertices Base(s)
Triangular Pyramid 4 6 4 Triangle
Triangular Prism    5 9 6 Triangles
Rectangular Pyramid 5 8 5 Rectangle

Classroom Example 3

Jennie and Ken are going camping. They can't agree on whose tent to take. Jennie's mom told them to pack the rectangular pyramid tent. Which tent should they bring?

geometric image

Answer: Tent B. Tent A is an example of a triangular prism.
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Resources for Objective 2.B.1.b:
CLARIFICATIONS | Lesson Seeds | Sample Assessments |