Deck 11: Teaching Geometry, Statisticsprobability, and Discrete Mathematics

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.

Answer 1

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.

Answer 2

Grade 7.

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

Answer 3

Discrete Mathematics.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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

Question 21

By how much did undergraduate course taking in statistics increase in the decadebetween 1990 and 2000?

A)15% increase.
B)25% increase.
C)45% increase.
D)65% increase.
E)85% increase.

Question 22

Which statement most accurately compares the NCTM to the Common Core StateStandards for Mathematics with regard to the teaching of statistics and probability?

A)NCTM and the CCSSM recommend holding off study of both topics until highschool.
B)NCTM and the CCSSM recommend studying both topics from prekindergartenthrough high school.
C)NCTM recommends studying both topics from prekindergarten through highschool, which the CCSSM recommends delaying both topics until high school.
D)NCTM recommends studying both topics from prekindergarten through highschool, which the CCSSM recommends delaying both topics until middle school.
E)CCSSM recommends studying both topics from prekindergarten through highschool, which the NCTM recommends delaying both topics until middle school.

Question 23

Which of the following is an important experience for students as they explore thestatistics content strand, as pointed out by the author in Chapter 11?

A)Students should debate which type of graph should represent a given situation.
B)Students should be able to accurately draw circle graphs with a compass.
C)Students should discuss data presented in recent newspapers.
D)Students should be able to calculate a mean and a median.
E)Students should draw histograms on their graphing calculators.

Question 24

What are the three major components that should be included in the study ofstatistics?

A)Collecting, displaying, and discussing data.
B)Displaying, making decisions, and predicting from data.
C)Analyzing, predicting, and discussing data.structor use only.
D)Collecting, displaying, and drawing conclusions from data.
E)Collecting, making decisions, and predicting from data.

Question 25

Which of the following represents the advice given by the American StatisticalAssociation for students who are exploring probability?

A)Students should have experiences with both physical and technologicalsimulations of probabilistic situations.
B)Students should have experience with physical simulations of probabilisticsituations, but technological applications are not necessary.
C)Students should have experience with technological simulations of probabilisticsituations, but physical simulations are not necessary.
D)Students should spend more time with experimental probability and considerablyless time determining theoretical probabilities.
E)Students should spend more time with theoretical probability and considerablyless time determining experimental probabilities.

Question 26

Which of the following practices for the teaching of probability is supported byresearch as an effective way to develop student thinking?

A)Students should simulate probability with manipulatives before the use oftechnology.
B)Students should simulate probability with the use of technology before usingmanipulatives.
C)Students should determine theoretical probabilities before conducting simulations.
D)Students should conduct simulations before determining theoretical probabilities.
E)Students should explore data sets and suggest their own probability questions.

Question 27

Which of the following is NOT one of the high school domains in the Common CoreState Standards for Mathematics that deals with statistics and probability?

A)Conditional probability and the rules of probability.
B)Experimental and mathematical probabilities as models.
C)Interpreting categorical and quantitative data.
D)Using probability to make decisions.
E)Making inferences and justifying conclusions.

Question 28

The authors of the Common Core State Standards for Mathematics note that data doesnot always send a clear message due to which of the following?

A)Miscalculations.
B)Errors in collection.
C)Variability.
D)Lack of technology.
E)Context.

Question 29

The Common Core State Standards for Mathematics calls for the use of technology todo which of the following in the study of probability?

A)To explore and to calculate.
B)To graph and to run simulations.
C)To generate sample spaces and to run simulations.
D)To explore and to graph.
E)To calculate and to run simulations.

Question 30

Which of the following connects the LEAST to the study of probability?

A)Geometry.
B)Fractions.
C)Percents.
D)Equations.
E)Tables.

Question 31

The sample lesson in Chapter 11 in which students take a phony True-False quiz leadsthem to the exploration of which concept?

A)Determining the probability of an event.
B)Constructing a line graph.
C)Finding measures of central tendency.
D)Reading a bar graph.
E)Generating truth tables.

Question 32

Which of the following is NOT considered an area of the study of discretemathematics?

A)Iteration and Recursion.
B)Matrices.
C)Functions.
D)Graph Theory.
E)Combinatorics.

Question 33

Which of the following includes the three categories of discrete mathematicsproblems?

A)Existence, graphing, and optimization.
B)Existence, counting, and optimization.
C)Establishing an algorithm, counting, and optimization.
D)Establishing an algorithm, graphing, and counting.
E)Existence, establishing an algorithm, and counting.

Question 34

Which of the following is most often associated with the study of discretemathematics?

A)Deriving a formula.
B)Recognizing a pattern.
C)Constructing a proof.
D)Establishing an algorithm.
E)Using a calculator.

Question 35

Determining the path that a snowplow should follow to clear all of the roads, whileminimizing how many roads have to be traversed twice, is typical of which type ofdiscrete mathematics problem?

A)Matrices.
B)Recursion.
C)Graph Theory.
D)Combinatorics.
E)Social Choice.

Question 36

Determining how much money would be in a bank account at the end of a period oftime is typical of which type of discrete mathematics problem?

A)Combinatorics.
B)Iteration and Recursion.
C)Matrices.
D)Social Choice.
E)Graph Theory.

Question 37

Why are problems drawn from the area of discrete mathematics often motivating tostudents in a mathematics class?

A)The problems tend to be easier for most students.
B)The problems require the use of technology.
C)The problems are shorter and can be solved more quickly than most.
D)The problems generally do not have a correct answer.
E)The problems tend to be applied to the real world.

Question 38

Which of the following factors has made discrete mathematics problems moreaccessible to students in recent years than the problems had been in the past?

A)New applications of the concepts.
B)Better-written textbooks.
C)Improved teaching strategies.
D)Development of technology.
E)Influence of national and state-level tests.

Question 39

Which statement most accurately characterizes the relationship between how discretemathematics is described in the 1989 compared to the 2000 Standards from NCTM?

A)The 1989 Standards did not mention discrete mathematics, but the 2000 Standardsdevoted a section to the topic.
B)The 1989 Standards made references to discrete mathematics, but the 2000document actually established Standards for including them in the curriculum.
C)The 1989 document featured specific Standards for discrete mathematics, butthere is no mention of the topic in the 2000 document.
D)Neither the 1989 nor the 2000 document specifically addressed discretemathematics as a topical are

Question 40

Which of the following topics was NOT addressed as an area of study for discretemathematics in Principles and Standards for School Mathematics?

A)Social Choice.
B)Iteration and Recursion.
C)Combinatorics.
D)Vertex-Edge Graphs.
E)All of these were included in the Standards.

Question 41

Which of the following most accurately describes discrete mathematics in theCommon Core State Standards for Mathematics?

A)There are no discrete mathematics topics in the CCSSM.
B)There is a discrete mathematics conceptual category for the CCSSM.
C)There is no conceptual category but are several domains devoted to discretemathematics in the CCSSM.
D)Discrete mathematics is a major emphasis throughout the CCSSM.
E)There are discrete mathematics topics included in the CCSSM but not asconceptual categories or domains.

Question 42

The sample lesson in Chapter 11 in which students explore an episode involvingdrinking a pitcher of tea leads them to the exploration of which concept?

A)Fractal geometry.
B)Matrix operations.
C)Iteration and Recursion.
D)Graph Theory.
E)Combinatorics.

Question 43

According to the College Board's Standards, which of the following topics is NOTsuggested for a Pre-Calculus course?

A)Conic sections.
B)Families of functions.
C)Congruence.
D)Trigonometry.
E)Vectors.

Question 44

Which of the following represents a list of functions emphasized on the CollegeBoard's CLEP test?

A)Linear.
B)Absolute value.
C)Square root.
D)Logarithmic.
E)All of these.

Question 45

Which of the following most accurately characterizes the position of the NCTM andthe Mathematical Association of America in terms of taking a calculus course in highschool?

A)All high school students should study calculus in preparation for post-secondarymathematics.
B)High school students should not study calculus and, instead, should preparethemselves for the study of calculus in college.
C)High school students should have an introductory calculus course that includessome of the fundamentals of calculus but not with the rigor of a college-levelcourse.
D)The study of algebra, geometry, and trigonometry is more important to a highschool student than being exposed to fundamentals of calculus.
E)Calculus should be avoided at the high school level since there is no agreed uponsyllabus for such a course.

Question 46

According to the MAA, approximately what percentage of students entering a four-year college have Calculus listed on their transcripts?

A)10%.
B)25%.
C)50%.
D)75%.
E)90%.

Question 47

Which of the following represents the change in the number of high school studentsenrolling in AP Calculus between 1982 and 2013?

A)The number of students declined by one-half.
B)The number of students remained about the same.
C)The number of students increased by 50%.
D)The number of students almost doubled.
E)The number of students increased more than five-fold.

Question 48

Approximately how many high school students took the Advanced PlacementCalculus exam in 2018?

A)25,000.
B)37,000.
C)168,000.
D)448,000.
E)613,000.

Question 49

Discuss what it means to teach "geometry" in the secondary and middle schools.Be sure to include the influence of the research of the van Hieles.Also, describe the types of skills and competencies that are developed in the Common Core State Standards for Mathematics.

Question 50

It has been said that teaching statistics is much more complex than simply teaching students to "draw a bar graph." Describe the types of skills and competencies a student should possess after completing a secondary and middle school program that includes statistics as a content strand.

Question 51

Explain the difference between the expectations of students - including grade level recommendations - for the areas of statistics and probability in the Common Core State Standards when compared to NCTM's Principles and Standards for School Mathematics.

Question 52

(a)List several of the topics that are typical of a discrete mathematics content strand and provide a sample problem that students can solve to illustrate each of the topics.(b)NCTM treated the topic of discrete mathematics very differently in the 1989 curriculum Standards than in 2000.Explain this difference and its implications for textbooks, curriculum writers, and teachers.