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Chapter 19: Geometric Thinking and Geometric Concepts
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) The study of geometry includes all of the following EXCEPT:
A) Reasoning skills about space and properties.
B) Visualization.
C) Transformation.
D) Time.
2) Identify what a student operating van Hiele’s geometric thought level one would likely be
doing.
A) Making and testing hypothesis.
B) Classifying shapes based on properties.
C) Looking at counter examples.
D) Generating property lists.
3) What statement below applies to the geometric strand of location?
A) Study of shapes in the environment.
B) Study of the relationships built on properties.
C) Study of translations.
D) Study of coordinate geometry.
4) Identify what a student product of thought at van Hiele level zero visualization would be.
A) Shapes are alike.
B) Grouping shapes that are alike.
C) Classifying shapes that are alike.
D) Identifying attributes of shapes that are alike.
5) The following are appropriate activities for van Hiele level one analysis EXCEPT:
A) Classifying quadrilaterals into special categories according to certain characteristics.
B) Discovering pi by measuring the circumference and diameter of various circular objects and
calculating their quotient.
C) Sorting pattern blocks by their number of sides.
D) Determining which shapes will create tessellations.
6) What would be a signature characteristic of a van Hiele level two activity?
A) Students can use dot or line grids to construct tessellations.
B) Students can classify properties of quadrilaterals.
C) Students can use logical reasoning about properties of shapes.
D) Students can prepare informal arguments about properties of shapes.
7) The following are all elements of effective early elementary geometry instruction EXCEPT:
A) Opportunities for students to examine an array of shape classes.
B) Opportunities for students to discuss the properties of shapes.
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C) Opportunities for students to use physical materials.
D) Opportunities for students to learn the vocabulary.
8) Tangrams and pentominoes are examples of physical materials that can be used to do all of the
following EXCEPT:
A) Create tessellations.
B) Sort and classify.
C) Compose and decompose.
D) Explore two-dimensional models.
9) Categories of two-dimensional shapes include the following EXCEPT:
A) Triangles.
B) Cylinders.
C) Simple closed curves.
D) Convex quadrilaterals.
10) The study of transformations includes all of the categories below EXCEPT:
A) Line symmetry.
B) Translations.
C) Compositions.
D) Dilations.
11) The activities listed below would guide students in exploring the geometric content of
location. Identify the one that can also be used with transformations.
A) Pentomino positions.
B) Paths.
C) Coordinate reflections.
D) Coordinate slides.
12) What statement would be the description of Visualization?
A) Positional descriptions- above, below, beside.
B) Changes in position or size of a shape.
C) Intuitive idea of how shapes fit together.
D) Geometry in the minds eye.
13) What would be an advantage of dynamic geometry programs over the use of paper pencil
and geoboards?
A) Shapes can be stretched and more examples of the class of that shape.
B) Construct visual model of shapes.
C) Construction of points, lines and figures.
D) Shapes can be moved about and manipulated.
14) What is the purpose of the activity “Minimal Defining Lists”?
A) To list the many properties of shapes.
B) To list the classes of shapes.
C) To list the subset of the properties of a shape.
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D) To list the relationships between the properties of shapes.
15) Movements that do not change the size or shape of the object are called ‘rigid motions.
Identify the movement below that would NOT be considered rigid.
A) Reflections.
B) Translations.
C) Tessellations.
D) Rotations.
16) What is the name given to a set of completely regular polyhedrons?
A) Polyhedron solid.
B) Platonic solids.
C) Polyominoid figures.
D) Polydron shape.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
17) Describe one of the major content goals in geometry, why it is important, and an activity that
could help students develop conceptual understanding of a topic that falls into this content goal.
18) Describe two instructional implications for moving students from level 1 to 2. Explain an
activity for each of the implications.
19) Describe three activities that support learning experiences with composing and decomposing
shapes.
20) What are the reasons and purpose for engaging children in construction activities when
learning geometry?
