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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 2. Analyze the relationship between plane geometric figures and surfaces of solid geometric figures

Objective a. Compare a plane figure to surfaces of solid geometric figure

Assessment limit: Analyze or identify the number or arrangement of squares needed to make a cube and triangles/rectangles needed to make a triangular pyramid or rectangular pyramid.

Clarification
The van Hiele Levels of Geometric Thought
Pierre and Dina van Hiele are two Dutch educators who developed 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 figures

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 analyze the types, numbers and arrangement of shapes that are the faces of a solid figure are moving from Level 0 to Level 1.
 
  • They can identify that the faces of a cube are squares (Level 0).
  • But to form a cube, the squares cannot be in any random arrangement. (Level 1).

Classroom Example 1

Look at the cube below:

cube

  • How many squares make up the cube?
  • Which figures below, when cut out, will form a cube?

geometric figures
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Resources for Objective 2.B.2.a:
CLARIFICATIONS | Lesson Seeds |