Deck 10: Teaching Number Sense and Algebra

Question 1

Which of the following is a typical memory of most people when they think of thestudy of algebra?

A)Conducting hands-on activities.
B)Participating in long-term projects.
C)Factoring trinomials.
D)Exploring functions with technology.
E)Solving problems in teams.

Answer 1

Factoring trinomials.

Question 2

Which of the following is a typical memory of most people when they think of thestudy of geometry?

A)Exploring shapes with technology.
B)Creating geometric designs as projects.
C)Studying the history of geometry.
D)Writing two-column proofs.
E)Conducting hands-on activities.

Answer 2

Writing two-column proofs.

Question 3

Which of these most accurately describes the roles of "number sense" and "algebra"in the mathematics curriculum, according to Common Core State Standards for Mathematics?

A)Courses.
B)Textbook titles.
C)Cognitive levels.
D)First- and second-year high school topics.
E)Content strands.

Answer 3

Content strands.

Question 4

The authors of Principles to Actions (NCTM, 2014)stated that which of the followingshould be the emphasis of curriculum designed to address the content standards?

A)Discourse.
B)Connections.
C)Individual courses.
D)Distinct content strands.
E)Gatekeeper courses.

Question 5

According to Common Core State Standards for Mathematics, which content areashould decrease in emphasis and which should increase in the secondary and middlegrades?

A)Number decreases, Algebra increases.
B)Geometry decreases, Algebra increases.
C)Algebra decreases, Geometry increases
D)Number decreases, Algebra increases
E)Algebra decreases, Number increases

Question 6

Which of the following documents was published in 2009 and suggested that contentareas should be used as tools to promote mathematical thinking?

A)Principles and Standards for School Mathematics.
B)Common Core State Standards for Mathematics.
C)Focus on High School Mathematics: Reasoning and Sense Making.
D)Principles to Actions: Ensuring Mathematical Success for All.
E)Curriculum Focal Points.

Question 7

Which of the following represents a recent shift in thinking about the high schoolmathematics curriculum?

A)Courses should be integrated.
B)Courses such as algebra and geometry should be taught separately.
C)A more rigid sequence of courses should be required.
D)Courses should emphasize thinking and problem solving.
E)Mathematical Practices should be studied prior to specific content.

Question 8

Approximately what percentage of high schools in the United States follow anintegrated sequence of courses?

A)5%.
B)10%.
C)25%.
D)40%.
E)60%.

Question 9

When a student draws conclusions based on evidence that has been presented, whichof the following is being developed in the mathematics classroom?

A)Reasoning.
B)Mathematical Practice.
C)Problem Solving.
D)Sense Making.
E)Representation.

Question 10

When a student develops understanding by connecting ideas with pre-existingknowledge, which of the following is being developed in the mathematics classroom?

A)Reasoning.
B)Mathematical Practice.
C)Problem Solving.
D)Sense Making.
E)Representation.

Question 11

Which of the following most accurately describes the relationship between theprocesses of reasoning and sense making?

A)Reasoning skills should be taught prior to students developing sense making.
B)Sense making is necessary to develop reasoning skills.
C)Reasoning and sense making should work together when solving problems.
D)Reasoning and sense making are developed best in informal situations.
E)Reasoning and sense making are developed best in formal situations.

Question 12

Which of these is NOT a recommendation in Chapter 10 for teachers to developreasoning and sense making in the classroom?

A)Ask students to reword problems.
B)Encourage students to draw diagrams.
C)Allow students to struggle.
D)Establish a risk-free classroom environment.
E)Ask good questions that probe student thinking.

Question 13

Which of the following is NOT a rationale for using games in the mathematicsclassroom?

A)Games have the potential to develop conceptual ideas.
B)Games are engaging.
C)Games require relatively little preparation time.
D)Games play into the interests of students.
E)Games are often enjoyable to students.

Question 14

Which term refers to a number whose sum of its factors equals the number itself?

A)Deficient.
B)Prime.
C)Abundant.
D)Composite.
E)Perfect.

Question 15

Which term(s)apply to the number "12"?

A)Abundant and Prime.
B)Composite and Perfect.
C)Deficient and Prime.
D)Abundant and Composite.
E)Composite and Deficient.

Question 16

By which grade level do the Common Core State Standards for Mathematics expectstudents to perform operations on positive and negative integers?

A)Grade 5.
B)Grade 6.
C)Grade 7.
D)Grade 8.
E)Grade 9.

Question 17

Which of the following is considered a high school number topic, according to theCommon Core State Standards for Mathematics?

A)Negative Numbers.
B)Integer Operations.
C)Imaginary Numbers.
D)Irrational Numbers.
E)Percentages.

Question 18

According to Catalyzing Change from NCTM, which of these should be examinedwhen studying rational and irrational numbers?

A)Operations with integers.
B)Appropriate use of measurements.
C)Base ten modeling.
D)Real number lines.
E)Vectors with imaginary numbers.

Question 19

According to the author in Chapter 10, equally important to adding and subtractingdecimals is a student's ability to do which of the following?

A)Use technology to perform decimal operations.
B)Look for structure in the numbers.
C)Properly line up decimal places.
D)Sketch drawings of decimal related problems.
E)Relate the operations to one another.

Question 20

In Chapter 10, the example of the students exploring a burning candle addressedwhich of the following content strands?

A)Algebra.
B)Geometry.
C)Number.
D)Discrete Mathematics.ier 2020.For instructor use only.
E)Probability.

Question 21

Which key algebra concept can be explored and discussed by recording data about theheight of a burning candle over a particular period of time?

A)Solving quadratic equations.
B)Factoring trinomials.
C)Writing the equation of a line.
D)Simplifying a rational expression.
E)Estimating the value of a square root.

Question 22

Which of the following is NOT considered a possible representation of a function?

A)Graph.
B)Table.
C)Verbal Description.
D)Problem whose solution involves a function.
E)Equation.

Question 23

Which of the following LEAST accurately describes the ideal contemporary view ofthe study of algebra?

A)Algebra is a course.
B)Algebra is a language.
C)Algebra is a content strand.
D)Algebra is a K-12 experience.
E)Algebra is a responsibility for all teachers.

Question 24

Which of the following does NOT comprise the language of algebra?

A)Variables.
B)Polygons.
C)Placeholders.
D)Formulas.
E)Patterns.

Question 25

Which of the following does NOT comprise a type of algebraic reasoning?

A)Generalizing patterns.
B)Studying functions.
C)Using tools, such as a straightedge.
D)Using algebra for modeling.
E)Manipulating variables.

Question 26

How many types of algebraic reasoning are described in Chapter 10?

A)1.
B)3.
C)5.
D)7.
E)9.

Question 27

Operations and Algebraic Thinking is a domain of the Common Core State Standardsfor Mathematics at which grade level?

A)Grade 5.
B)Grade 6.
C)Grade 7.
D)Grade 8.
E)Grade 9.

Question 28

Which of the following is NOT listed as a topic of the Functions domain at Grade 8 inthe Common Core State Standards for Mathematics?

A)Defining functions.
B)Evaluating functions.
C)Graphing functions.
D)Using functions to describe real-world situations.
E)Comparing functions to one another.

Question 29

Which of the following statements most accurately represents NCTM's vision of theteaching of algebra?

A)Algebra should be a course for all eighth graders.
B)Algebra should be integrated into the curriculum so that all students have accessto the topic.
C)Algebra should be offered as an honors-level option for middle school students.
D)The study of algebra should precede high school-level geometry courses.
E)The study of algebra should be included only for college-bound students, as theywill need it in their career preparation.

Question 30

According to NCTM (2011), which of the following should be emphasized as earlyalgebra skills for Grades 3-5?

A)Generalize, express, and justify relationships.
B)Simplify algebraic expressions.
C)Graph linear functions.
D)Identify types of functions.
E)Perform operations on fractions.

Question 31

Which of the following is considered an "essential component" of algebra in highschool, according to Catalyzing Change?

A)Using CAS technology.
B)Examining problems with manipulatives.
C)Making predictions based on algebraic models.
D)Using algebraic properties.
E)Graphing non-linear equations.

Question 32

The sample lesson in Chapter 10 that uses a "how well do you know yourself" data setleads students to the exploration of which algebraic concept?

A)Graphing linear functions.
B)Solving linear equations.
C)Calculating slopes of lines.
D)Simplifying algebraic expressions.
E)Graphing inequalities.

Question 33

The example in Chapter 10 with students changing the scale on a graphing calculatoremphasizes which mathematical idea? For instructor use only.

A)Graphing absolute value functions.
B)Labeling axes.
C)Using a straightedge.
D)Plotting points.
E)None of these.

Question 34

According to the author in Chapter 10, which of the following represents a commonflaw in the structure and order of traditional textbooks in mathematics?

A)Mathematical topics may appear to be disconnected.
B)More difficult topics tend to be left to the end of the book.
C)The structure of chapters often confuses students.
D)Not enough practice problems are often included.
E)Explanations provided in the books are generally difficult to understand.

Question 35

Explain what it means for schools to emphasize the study of algebra and geometry as "content strands," rather than as courses to be taken in middle and high school.What is the vision of school mathematics in the Common Core State Standards for Mathematics, Catalyzing Change, and related state-level Standards documents.

Question 36

Describe what it means to develop "reasoning and sense making" in the mathematics classroom.Provide examples of how the processes work together and how they can be developed informally as well as formally.

Question 37

Explain how the philosophy of how "number sense" and "algebra" should be taught in schools has evolved from a traditional to a more contemporary view.

Question 38

Discuss what it means to teach "algebra" in the secondary and middle schools.Be sure to include the types of algebraic reasoning that are developed.Also, describe the types of skills and competencies that are developed in the Common C.ore State Standards and in NCTM's Catalyzing Change and Principles and Standards for School Mathematics.