Chapter 20: Geometric Thinking and Geometric Concepts
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
1)
____________________ is an intuition about shapes and the relationships between them.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
2) People are either born with spatial sense or they’re not.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
3) The study of geometry includes all of the following EXCEPT
a) Reasoning skills about space and shape.
b) Visualization.
c) Transformation.
d) Time.
4) A student operating at Van Hiele’s geometric thought level one would likely be
a)
Making and testing hypothesis.
b)
Classifying shapes based on properties.
c)
Looking at counter examples.
d)
Generating property lists.
5) To help a child progress from Van Hiele level 1 to level 2
a) Ask a question such as, “If the sides of a four-sided shape are all congruent, will it always be a
square?”
b) Discourage students from making conjectures.
c) Regularly give them vocabulary spelling quizzes.
d) Make sure that there is lots of time between class discussions, so they don’t get overwhelmed by
all the new vocabulary.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
6) Activities that encourage a transition from Van Hiele’s level zero to one include classifying shapes by
properties.
7) Quadrilaterals provide good models for bringing concepts of line segments, angles, and symmetry together.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
8) Which of the following is NOT an appropriate activity for level-0 thinkers?
a) Sorting and classifying pattern blocks
b) Free exploration with tangrams
c) Building shapes on geoboards
d) Using a geoboard to dilate figures according to a given scale factor
9) Which of the following is NOT an appropriate activity for level-1 thinkers?
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
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
10) The ____________________ relationship states that if a square is made on each side of a right triangle, the
sum of the areas of the two smaller squares will equal the area of the square of the hypotenuse.
11) If a shape can be folded so that the two halves match, the shape has ________________________.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
12) Which of the following statements about tessellations is true?
a) A regular tessellation consists of 5 different shapes.
b) Students can use dot or line grids to construct tessellations.
c) Tiling of the plane may include a few small holes or gaps.
d) A checkerboard is a tessellation.
13) The coordinate plane
a) Is not mentioned in the Common Core State Standards for elementary school students.
b) Can still be relevant to young students when it is related to positional directions.
c) Is not a good setting for transformations.
d) Makes student discovery of the distance formula more difficult.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
14) The algebraic topic of “slope” should not be discussed with students until they learn about equations.
15) Class time should only be devoted to developing visualization if it’s available after learning all needed
vocabulary.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
16) Polyhedrons
a) Are a family of 3D shapes that include spheres
b) Are “completely regular” if every face is a regular polygon and every vertex has the same
number of faces joining at that point.
c) Are too complicated for students with special needs to construct.
d) Can be made entirely from circles.
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.
Chapter 20