Deck 16: Developing and Extending Geometric Concepts and Systems

Question 1

Classifying squares by the size of their angles is a basic concept associated with:

A)topological geometry.
B)Euclidean geometry.
C)transformational geometry.
D)coordinate geometry.

Answer 1

Euclidean geometry.

Question 2

Which of the following reasons is the least valid for including geometry in the elementary school curriculum?

A)Spatial visualization skills are developed.
B)Geometry connects mathematics to aesthetic aspects of the world.
C)Children learn skills that are applicable in other areas of mathematics.
D)Measurement and fraction concepts are developed as geometric concepts are learned.

Answer 2

Measurement and fraction concepts are developed as geometric concepts are learned.

Question 3

Identifying whether an object is inside or outside of a fence is a basic concept associated with:

A)topological geometry.
B)Euclidean geometry.
C)transformational geometry.
D)coordinate geometry.

Answer 3

topological geometry.

Question 4

The research of Dina van Hiele-Geldof and Pierre Marie van Hiele suggests that:

A)describing, classifying, and generalizing attributes of geometric figures should be central to the study of geometry in the elementary school curriculum.
B)recognizing and naming geometric figures is the central purpose of elementary school geometry.
C)elementary school students should develop proofs using postulates and axioms.
D)geometry is too difficult for elementary school students and should be delayed until later grades.

Question 5

If a child can distinguish between the similarities and differences of rectangles and squares, that child is said to have the skill called:

A)figure - ground perception.
B)perception of special relationships.
C)visual discrimination.
D)visual memory.

Question 6

The ability to see two or more objects in relation to oneself or in relation to each other is the visual skill known as:

A)perceptual constancy.
B)position-in-space perception.
C)perception of spatial relationships.
D)visual discrimination.

Question 7

Research about spatial sense has established all of the following except for :

A)Young boys outscore young girls in several areas of spatial sense such as mazes and block designs.
B)Mental rotations are especially difficult for young girls compared to young boys.
C)Practice with spatial sense activities does not appear to improve young girls' spatial sense.
D)Access to early exposure to spatial sense activities gives children a head start on developing spatial sense awareness.

Question 8

Identifying shapes which have been turned or flipped is a basic concept associated with:

A)topological geometry.
B)Euclidean geometry.
C)transformational geometry.
D)coordinate geometry.

Question 9

The Pythagorean Theorem is useful for all of the following except for :

A)determining if a given triangle is a right triangle.
B)determining if a set of three numbers constitutes a Pythagorean triple.
C)determining if a triangle is isosceles.
D)determining one side of a right triangle, given the other two sides.

Question 10

If children stand in a tight circle, then slowly expand the circle by walking backwards, then reverse their positions by walking forward to the tight circle again, they are practicing with a topological geometry relationship known as:

A)proximity and relative position.
B)separation.
C)order.
D)enclosure.

Question 11

The ability to recognize figures or objects in space, regardless of size, position, or orientation is the visual skill known as:

A)figure - ground perception.
B)perceptual constancy.
C)position-in-space perception.
D)visual memory.

Question 12

If a fixed figure slides from one position to another, that motion is described as a:

A)rotation.
B)reflection.
C)translation.
D)dilation.

Question 13

All of the following statements are true about similar figures except :

A)They have the same shape but not the same size.
B)They have congruent corresponding angles.
C)They have corresponding sides in the same ratio.
D)They are dilations in transformational geometry.

Question 14

Choosing the highest possible level, a student who can write and understand two-column proofs has reached which van Hiele level?

A)deduction
B)analysis
C)informal deduction
D)rigor

Question 15

A parallelogram has:

A)rotational symmetry.
B)line symmetry.
C)both rotational and line symmetry.
D)neither rotational nor line symmetry.

Question 16

Describing locations of objects with respect to a two- or three- dimensional grid space is a basic concept associated with:

A)topological geometry.
B)Euclidean geometry.
C)transformational geometry.
D)coordinate geometry.

Question 17

Choosing the highest possible level, a child who recognizes that all squares are rectangles has reached which van Hiele level?

A)analysis
B)informal deduction
C)visualization
D)deduction

Question 18

A child who cannot recognize the six parts of a triangle is still operating at which of the following van Hiele levels?

A)analysis
B)visualization
C)informal deduction
D)rigor

Question 19

A three-dimensional object which has four congruent faces the same shape and size, four vertices, and six edges is:

A)a cube.
B)a prism.
C)a pyramid.
D)a rectangular solid.

Question 20

If a child can isolate alternate interior angles in a complex drawing, that child is said to possess the visual skill known as:

A)figure - ground perception.
B)perception of spatial relationships.
C)visual discrimination.
D)visual memory.

Question 21

Explain the progression of the van Hiele levels of geometric understanding. Give an example to illustrate each level.

Question 22

Which of the following triangles can also be an equilateral triangle?

A)acute
B)scalene
C)right
D)obtuse

Question 23

TIMSS: Of the following options, which is NOT true for all rectangles?

A)The opposite sides are parallel.
B)The opposite sides are equal.
C)All angles are right angles.
D)The diagonals are equal.
E)The diagonals are perpendicular.

Question 24

Which of the following combinations of regular polygons will tessellate?

A)2 squares, 2 triangles
B)2 pentagons, 1 square
C)2 octagons, 1 triangle
D)3 hexagons

Question 25

An octahedron has 8 faces and 6 vertices. It has ___ edges.

A)14
B)12
C)10
D)8

Question 26

A seven-sided figure called:

A)a hexagon.
B)a heptagon.
C)a decagon.
D)an octagon.

Question 27

NAEP: Which of the following cannot be folded into a cube?

A)
B)
C)
D)

Question 28

A parent asks why geometry is taught in the elementary school curriculum when students do not yet know their basic facts and therefore should be spending time on learning them instead. How would you reply to this parent?

Question 29

All of the following are true about a parallelogram except:

A)two pairs of parallel sides.
B)two pairs of congruent sides.
C)congruent diagonals.
D)diagonals bisect each other.

Question 30

Why is it important for a child to develop spatial sense?

Question 31

Explain the differences between congruence and similarity of geometric figures.

Question 32

Which of the following is true?

A)All squares are rectangles.
B)All rectangles are squares.
C)All parallelograms are rhombuses.
D)All rhombuses are rectangles.

Question 33

Teacher Licensing Examination Questions
Praxis: In this circle with center O and radius 2, AP has length 3 and is tangent to the circle at P .

If CP is a diameter of the circle, what is the length of AC ?

A)1.3
B)2.0
C)3.2
D)5.0

Question 34

Give four different types of manipulatives you could use to introduce geometric concepts to elementary children. Explain how these help children to understand these concepts.

Question 35

What are some activities you could use to introduce children to three-dimensional geometry? Explain how these activities encourage the development of these geometric concepts.

Question 36

The following translation will move point Q from (3, − 4)to ______.

A)(6, 1)
B)(0, 9)
C)(0, 1)
D)(6, 9)

Question 37

Explain the differences between the four geometry systems that are taught in the elementary school curriculum (topological, Euclidean, transformational, and coordinate geometry).

Question 38

How many lines of symmetry are there in a regular hexagon?

A)3
B)4
C)6
D)8

Question 39

What is the area of a figure on a grid with 12 interior points and 8 boundary points?

A)15
B)19
C)13
D)14

Question 40

The legs of a right triangle are 5 cm and 12 cm. The length of the third side is:

A)17 cm.
B)13 cm.
C)60 cm.
D)119 cm.

Question 41

Use pattern blocks to demonstrate and represent each geometric concept.

A) tessellation
B) line symmetry
C) rotational symmetry
D) similarity
E) congruence

Question 42

A student contended that if a line cuts a figure into two congruent parts, that line must be a line of symmetry. Is this a true or false statement? Defend your position.

Question 43

You are asked to design a new set of coins. All coins will be circular and colored silver, but of different diameters

Researchers have found that an ideal coin system meets the following requirements:
Diameters of coins should not be smaller than 15 mm and not be larger than 45 mm.
Given a coin, the diameter of the next coin must be at least 30% larger.
The minting machinery can only produce coins with diameters of a whole number of millimeters (e.g., 17 mm is allowed, but 17.3 mm is not.). You are asked to design a set of coins that satisfy the above requirements. You should start with a 15-mm coin, and your set should contain as any coins as possible. What would be the diameters of the coins in your set?

Question 44

Explain the differences between translations, rotations, reflections, and dilations.

Question 45

Use paper figures to derive the area formulas for a triangle and a parallelogram from the area formula of a rectangle.

Question 46

Illustrate each of the following geometric figures or concepts with a quick sketch. Label the sketches as needed.
Point, ray, line segment
Congruency and similarity
Regular polygon
Irregular Polygon
Open/closed figure
Three kinds of angles
Two tessellations
Three different triangles
Line symmetry
Rotational symmetry
A slide
A flip
A turn
A pantomime shape that will fold into an open box
A pentomino shape that will not fold into an open box

Question 47

Why is it important to teach children about coordinate geometry?