Question 1

According to the Common Core State Standards for Mathematics, a formal study ofstatistics that includes the study of variability and describing distributions, should begin at which grade level?
A)Grade 5.
B)Grade 6.
C)Grade 7.
D)Grade 8.
E)Grade 9.

Accepted Answer

According to the Common Core State Standards for Mathematics, a formal study of statistics, including the study of variability and describing distributions, begins at Grade 6.

Question 2

The Common Core State Standards for Mathematics calls for the introduction ofprobability in the curriculum at which grade level?
A)Grade 5.
B)Grade 6.
C)Grade 7.
D)Grade 8.
E)Grade 9.

Accepted Answer

C

Question 3

Which of the following content areas is LEAST likely to have been part of mostpeople's mathematical experiences?
A)Discrete Mathematics.
B)Algebra.
C)Measurement.
D)Geometry.
E)Statistics

Accepted Answer

Discrete Mathematics is less commonly taught at basic levels of education compared to Algebra, Measurement, Geometry, and Statistics, which are foundational and typically included in most curricula.

Question 4

Which of the following educational theorists studied the way that children learngeometry?
A)van Hiele.
B)Piaget.
C)Bruner.
D)Skemp.
E)Bloom.

Accepted Answer

The van Hiele model specifically addresses how children learn geometry, focusing on levels of understanding in geometric thinking.

Question 5

The research of the van Hieles has suggested which of the following in the teachingand learning of geometry?
A)Technology has a significant impact on the teaching of geometry.
B)Manipulatives should be used in all lessons when teaching geometry.
C)Students have different developmental needs when learning geometry.
D)Students should experience higher levels of proof than are currently beingaddressed in learning geometry.
E)Textbooks have little impact on the achievement of students in geometry.

Accepted Answer

The van Hiele model of geometric thought suggests that students progress through levels of understanding in geometry, each with distinct characteristics and developmental needs. This model emphasizes that teaching and learning strategies in geometry should be aligned with these developmental stages to be effective.

Question 6

Which of the following would be considered teaching tools in a geometry class?
A)Pattern blocks.
B)Algebra tiles.
C)Paper folding.
D)Geoboards.
E)All of these.

Accepted Answer

All of these options are considered teaching tools in a geometry class. Pattern blocks help with understanding shapes and patterns, algebra tiles can be used to visualize geometric concepts, paper folding introduces concepts of symmetry and geometry, and geoboards are used for exploring shapes, area, perimeter, and angles.

Question 7

Which of the following describes a geometric shape that is generated by starting withan initial image and then applying successive iterations of a rule?
A)Fractal.
B)Tessellation.
C)Seed.
D)Function Image.
E)Pre-Image.

Accepted Answer

Fractals are geometric shapes that are created by starting with an initial shape (the seed) and then applying a rule repeatedly to create complex patterns. Each iteration applies the rule to the result of the previous iteration, leading to self-similar patterns at different scales.

Question 8

Which of the following refers to the initial image on which a fractal image isgenerated?
A)Initial Value.
B)Seed.
C)Term.
D)Koch.
E)Image.

Accepted Answer

The term "Seed" refers to the initial image or starting point from which a fractal image is generated. This seed serves as the base pattern that is repeatedly scaled and transformed to create the complex fractal design.

Question 9

Which of the following is a property of all fractal images?
A)Fractals are symmetrical.
B)Fractals are finite.
C)Fractals are self-similar.
D)Fractals are rational.
E)All of these.

Accepted Answer

Fractals are characterized by self-similarity, meaning parts of the fractal resemble the whole. This property is fundamental to fractals and distinguishes them from other geometric shapes.

Question 10

Which of the following is a paradox of Koch's Snowflake?
A)The successive stages can be imagined but never seen.
B)A computer can generate images, but they cannot be drawn by hand.
C)The perimeter is infinite, but the area is bounded.
D)The seed is complex, but the fractal is simple.
E)The volume is bounded, but the area is infinite.

Accepted Answer

Koch's Snowflake is a fractal curve that starts with an equilateral triangle, and new triangles are added at each iteration, increasing the perimeter without limit. However, the area enclosed by the curve remains finite, creating a paradox where the perimeter is infinite, but the area is bounded.

Question 11

Within the context of a geometry problem, which other mathematical strands can bereadily connected when studying a fractal image such as Koch's Snowflake?
A)Number and data analysis.
B)Algebra and probability.
C)Discrete mathematics and number.
D)Measurement and algebr

Accepted Answer

The answer of Within the context of a geometry problem,...

Question 12

Which of the following topics, commonly studied in the middle grades, lends itself toa geometric representation?
A)Percents.
B)Fractions.
C)Decimals.
D)Ratios.
E)All of these.

Accepted Answer

All of these topics (Percents, Fractions, Decimals, Ratios) can be represented geometrically, such as through pie charts, bar models, or number lines, facilitating visual understanding and comparison.

Question 13

The exploration of geometry without using coordinates is referred to as which of thefollowing?
A)Integrated.
B)Analytic.
C)Transformational.
D)Synthetic.
E)Dimensional.

Accepted Answer

Synthetic geometry is the study of geometry without the use of coordinates or formulas. It relies on axioms, definitions, and theorems derived logically from those axioms, unlike analytic geometry which uses coordinates to solve geometric problems.

Question 14

The exploration of geometry by using coordinates is referred to as which of thefollowing?
A)Integrated.
B)Analytic.
C)Transformational.
D)Synthetic.
E)Dimensional.

Accepted Answer

The exploration of geometry using coordinates is referred to as analytic geometry. This approach combines algebra and geometry to solve problems involving shapes and curves by plotting them on a coordinate system.

Question 15

Which of the following statements is specifically included in the Common Core StateStandards for Mathematics for what a high school student should be able to do ingeometry?
A)Develop proofs.
B)Use precise definitions.
C)Work with 2-dimensional shapes.
D)Work with 3-dimensional shapes.
E)All of these.

Accepted Answer

The Common Core State Standards for Mathematics for high school students include developing proofs, using precise definitions, and working with both 2-dimensional and 3-dimensional shapes, making all of the listed options correct.

Question 16

Which of the following is NOT considered an essential area of focus of geometryaccording to NCTM's Catalyzing Change document?
A)Measurement.
B)Trigonometry.
C)Transformations.
D)Geometric models to solve problems.
E)Proof.

Accepted Answer

The National Council of Teachers of Mathematics (NCTM) does not list trigonometry as an essential area of focus in its Catalyzing Change document. The document emphasizes the importance of deep understanding in areas such as measurement, transformations, geometric models to solve problems, and proof, but it does not specifically highlight trigonometry as an essential focus area.

Question 17

The sample lesson in Chapter 11 in which students use protractors leads them to theexploration of which geometric concept?
A)Similarity.
B)Congruence.
C)Sum of angles in a polygon.
D)Area of a polygone.Perimeter.

Accepted Answer

Using protractors typically involves measuring angles, and the exploration of the sum of angles in a polygon is a direct application of understanding and measuring angles, which is why this option is correct.

Question 18

Which of the following has significantly influenced the collection and analysis of datain society in the recent past?
A)Increased accountability.
B)Enhanced technology.
C)Educated public.
D)Increase in mathematics courses taken by college students.
E)Demographic changes.

Accepted Answer

Enhanced technology has significantly influenced the collection and analysis of data in society in the recent past.

Question 19

Which of the following are considered the "three V's" of big data?
A)Volume, Velocity, Variety.
B)Volume, Variables, Values.
C)Velocity, Variety, Values.
D)Variety, Variables, Volume.
E)Velocity, Variables, Values.

Accepted Answer

The "three V's" of big data are Volume (the amount of data), Velocity (the speed at which data is generated and processed), and Variety (the different types of data).

Question 20

Which of the following represents a definition of "statistics," as determined by aconference on the teaching of statistics?
A)Statistics is the study of information.or instructor use only.
B)Statistics is the science of prediction.
C)Statistics is the process of analysis.
D)Statistics is the study of graphs and trends.
E)Statistics is the science of learning from dat

Accepted Answer

Statistics is defined as the science of learning from data, which encompasses collecting, analyzing, interpreting, and presenting data. This definition captures the broad scope of statistics beyond just the creation of graphs or the act of prediction, emphasizing its role in making informed decisions based on data analysis.

Quiz 11: Teaching Geometry, Statisticsprobability, and Discrete Mathematics

According to the Common Core State Standards for Mathematics, a formal study ofstatistics that includes the study of variability and describing distributions, should begin at which grade level?

The Common Core State Standards for Mathematics calls for the introduction ofprobability in the curriculum at which grade level?

Which of the following content areas is LEAST likely to have been part of mostpeople's mathematical experiences?

Which of the following educational theorists studied the way that children learngeometry?

The research of the van Hieles has suggested which of the following in the teachingand learning of geometry?

Which of the following would be considered teaching tools in a geometry class?

Which of the following describes a geometric shape that is generated by starting withan initial image and then applying successive iterations of a rule?

Which of the following refers to the initial image on which a fractal image isgenerated?

Which of the following is a property of all fractal images?

Which of the following is a paradox of Koch's Snowflake?

Within the context of a geometry problem, which other mathematical strands can bereadily connected when studying a fractal image such as Koch's Snowflake?

Which of the following topics, commonly studied in the middle grades, lends itself toa geometric representation?

The exploration of geometry without using coordinates is referred to as which of thefollowing?

The exploration of geometry by using coordinates is referred to as which of thefollowing?

Which of the following statements is specifically included in the Common Core StateStandards for Mathematics for what a high school student should be able to do ingeometry?

Which of the following is NOT considered an essential area of focus of geometryaccording to NCTM's Catalyzing Change document?

The sample lesson in Chapter 11 in which students use protractors leads them to theexploration of which geometric concept?

Which of the following has significantly influenced the collection and analysis of datain society in the recent past?

Which of the following are considered the "three V's" of big data?

Which of the following represents a definition of "statistics," as determined by aconference on the teaching of statistics?