Chester Township Public Schools
Mathematics Curriculum

Mathematics - Geometry

Mathematics

The National Council of Teachers of Mathematics Curriculum and Evaluation Standards provide educators with goals for school mathematics and guidelines for achieving these goals. The fifty-four standards are presented as a vision for school mathematics based on societal goals, student goals, research on teaching and learning, and professional guidelines.


The Foundations of Learning (1999) curriculum offers Kindergarten through Grade 12 objectives for the Knowledge and Comprehension levels of Bloom's Taxonomy. EdVISION.com developed this curriculum based on extensive research of standardized and state tests. Additional objectives were added to enhance the content areas.

The Mathematics component of the Foundations of Learning curriculum focuses on basic skills. Objectives primarily involve the identification, recognition, comprehension, or understanding of various math topics.


The Applications of Learning (1999) curriculum offers Kindergarten through Grade 12 objectives for the Application and Analysis levels of Bloom's Taxonomy. EdVISION.com developed this curriculum based on extensive research of standardized and state tests. Additional objectives were added to enhance the content areas.

The Mathematics component of the Applications of Learning curriculum focuses on intermediate skills. The objectives primarily involve the application, examination, or analysis of various math topics.


The Higher Order Learning (1999) curriculum offers Grade 4 through Grade 12 objectives for the Synthesis and Evaluation levels of Bloom's Taxonomy. EdVISION.com developed this curriculum based on extensive research of standardized and state tests. Additional objectives were added to enhance the content areas.

The Mathematics component of the Higher Order Learning curriculum focuses on advanced skills. The objectives primarily involve the synthesis and evaluation of various math topics.


The purpose of New Jersey's statewide assessment program is to measure what students at benchmark grade levels know and are able to do. The Mathematics Content Clusters that are covered in the tests unavoidably contain some overlapping content, since mathematical topics are not disconnected but are part of an interconnected whole.


The New Jersey Curriculum Content Standards for Mathematics is focused on achieving one crucial goal:

"To enable ALL of New Jersey's children to move into the twenty-first century with the mathematical skills, understandings, and attitudes that they will need to be successful in their careers and daily lives."

The environment in the mathematics classroom should reflect the following two standards:

"1. All students' mathematical learning will embody the concepts that engagement in mathematics is essential, and that the decision-making, risk-taking, cooperative work, perseverance, self-assessment, and self-confidence are frequently keys to success."

"2. All students will be evaluated using a diversity of assessment tools and strategies, to provide multiple indicators of the quality of every student's mathematical learning and of overall program effectiveness."

The New Jersey Standards for Mathematics are as follows:

*"All students will develop the ability to pose and solve mathematical problems in mathematics, other disciplines, and everyday experiences."

*"All students will communicate mathematically through written, oral, symbolic, and visual forms of expression."

*"All students will connect mathematics to other learning by understanding the interrelationships of mathematical ideas and the roles that mathematics and mathematical modeling play in other disciplines and in life."

*"All students will develop reasoning ability and will become self-reliant, independent mathematical thinkers."

*"All students will regularly and routinely use calculators, computers, manipulatives, and other mathematical tools to enhance mathematical thinking, understanding, and power."

*"All students will develop number sense and an ability to represent numbers in a variety of forms and use numbers in diverse situations."

*"All students will develop spatial sense and an ability to use geometric properties and relationships to solve problems in mathematics and everyday life."

*"All students will understand, select, and apply various methods of performing numerical operations."

*"All students will develop an understanding of and will use measurement to describe and analyze phenomena."

*"All students will use a variety of estimation strategies and recognize situations in which estimation is appropriate."

*"All students will develop an understanding of patterns, relationships, and functions and will use them to represent and explain real-world phenomena."

*"All students will develop an understanding of statistics and probability and will use them to describe sets of data, model situations, and support appropriate inferences and arguments."

*"All students will develop an understanding of algebraic concepts and processes and will use them to represent and analyze relationships among variable quantities and to solve problems."

*"All students will apply the concepts and methods of discrete mathematics to model and explore a variety of practical situations."

*"All students will develop an understanding of conceptual building blocks of calculus and will use them to model and analyze natural phenomena."

*"All students will demonstrate high levels of mathematical thought through experiences which extend beyond traditional computation, algebra, and geometry."


In this area students concentrate on making mathematical connections and using principles of mathematics to communicate, reason, and solve problems. Students engage in projects which require them to apply number systems, operations, and forms in real-world contexts.

Geometry

The Foundations of Learning curriculum provides objectives for eleventh grade students.

The Applications of Learning curriculum provides objectives for eleventh grade students.

The Higher Order Learning curriculum provides objectives for eleventh grade students.

The mathematics section of the Grade 11 HSPA assesses students' knowledge and skills in four content clusters of mathematics:

1. Number Sense, Concepts, and Applications
2. Spatial Sense and Geometry
3. Data Analysis, Probability, Statistics, and Discrete Mathematics
4. Patterns, Functions, and Algebra

In this course students learn foundational geometry concepts from synthetic (Euclidean), algebraic, and industry perspectives. Students engage in activities which require them to identify, analyze, and solve problems involving the following topics: segments, angles, triangles, quadrilaterals, polyhedra, circles, spheres, transformations, if-then statements, and proofs. Course work includes studying how geometry relates to algebra, and how geometry concepts are applied in industrial and technological career fields. The course emphasizes the need for students to comprehend the abstract and symbolic nature of geometry. The Terra Nova Complete Battery assesses students in ninth grade (Level 19).


Algebraic Concepts
The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. This unit includes studying number systems, operations, and forms. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties.

    Properties: Rational/Real Numbers
The learner will be able to show their comprehension of, and/or apply properties as they apply to rational and/or real numbers.
Strand Bloom's Scope Source
Properties Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.42,I.A.1 week tested: 34.
  
    Properties: Number Sense
The learner will be able to identify, classify, and compare whole numbers, integers, rational numbers, irrational numbers, and field properties of the real number system with regard to structural characteristics, and build logical arguments using these properties.
Strand Bloom's Scope Source
Properties Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Properties: Operations
The learner will be able to conceptually understand the properties of operations, including zero (additive, multiplicative), one (multiplicative), grouping (associative), and order (commutative).
Strand Bloom's Scope Source
Properties Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.42,I.A.6 week tested: 34.
  
    Expressions: Powers/Roots/Factorials
The learner will be able to simplify expressions that contain powers, roots, and factorials.
Strand Bloom's Scope Source
Simplify Expressions Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.42,I.A.10 week tested: 34.
  
    Algebraic Concepts: Real-World
The learner will be able to accurately describe, study and model real-world situations using algebraic concepts and processes.
Strand Bloom's Scope Source
Algebraic Concepts Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.41,IV.C week tested: 34.
  
    Algebraic Concepts: Apply
The learner will be able to use appropriate mathematical abilities to apply absolute values, exponents, and estimations for roots of numbers in real-life problem situations.
Strand Bloom's Scope Source
Algebraic Concepts Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.42,I.A.13 week tested: 34.
  
    Number Sentences: Relating to Real-World
The learner will be able to explore expressions, equations, and inequalities involving whole numbers, fractions, decimals, and integers within the context of real-world scenarios, identify relationships between the variables and coefficients, and articulate how each relates to a corresponding real-world problem (in coordinate geometry, measurement, career fields, etc.).
Strand Bloom's Scope Source
Number Sentence Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Order of Operations: Exponents
The learner will be able to determine the correct order of operations for an exponential equation.
Strand Bloom's Scope Source
Order of Operations Comprehension Master Foundations of Learning, January 1999, Grade 11
  
    Equations: Story Problems
The learner will be able to determine equations for and solve problems in the context of real world scenarios.
Strand Bloom's Scope Source
Solve Equations Application Master Applications of Learning, January 1999, Grade 11
  
    Absolute Value: Understand
The learner will be able to understand absolute value.
Strand Bloom's Scope Source
Absolute Value Comprehension Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.42,I.A.3 week tested: 34.
  
    Exponents: Roots
The learner will be able to understand exponents and roots.
Strand Bloom's Scope Source
Exponents Comprehension Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.42,I.A.2 week tested: 34.
  
    Exponents: Integral and Square Roots
The learner will be able to apply laws of integral exponents and/or square roots to simplify and/or evaluate algebraic expressions.
Strand Bloom's Scope Source
Exponents Synthesis Master Higher-Order Learning, January 1999, Grade 11
  

Calculus and Pre-Calculus
The Calculus and Pre-Calculus Unit includes studying the following concepts: limits, matrix algebra, functions, vectors, conic sections, mathematical induction, and sequence and series using graphical calculators, computers, and models.

    Derivatives: Deriving Formulas
The learner will be able to use the definition of the derivative as the limit of a sum to derive formulas for the derivatives.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Synthesis Master Higher-Order Learning, January 1999, Grade 11
  
    Derivatives: Derived Function
The learner will be able to find a derived function given the definition.
Strand Bloom's Scope Source
Derivatives/Antiderivatives Comprehension Master Foundations of Learning, January 1999, Grade 11
  
    Complex Numbers: Trig Form
The learner will be able to apply the trigonometric form of complex numbers.
Strand Bloom's Scope Source
Complex Numbers Application Master Applications of Learning, January 1999, Grade 11
  
    Complex Numbers: Absolute Value
The learner will be able to determine absolute value of complex numbers and relate that to real numbers.
Strand Bloom's Scope Source
Complex Numbers Analysis Master Applications of Learning, January 1999, Grade 11
  
    Complex Numbers: DeMoivre's Theorem
The learner will be able to determine powers and roots of complex numbers by using DeMoivre's theorem.
Strand Bloom's Scope Source
Complex Numbers Application Master Applications of Learning, January 1999, Grade 11
  
    Complex Numbers: DeMoivre's/Prove
The learner will be able to prove DeMoivre's theorem.
Strand Bloom's Scope Source
Complex Numbers Synthesis Master Higher-Order Learning, January 1999, Grade 11
  
    Matrices: Understand
The learner will be able to understand the concept of matrices.
Strand Bloom's Scope Source
Matrices Comprehension Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.50,II.B.6 week tested: 34.
  
    Matrices: Scalar Multiplication
The learner will be able to perform scalar multiplication with matrices.
Strand Bloom's Scope Source
Matrices Comprehension Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.50,II.B.12 week tested: 34.
  
    Matrices: Evaluate Results
The learner will be able to make evaluations of the results of matrix operations.
Strand Bloom's Scope Source
Matrices Evaluation Master Higher-Order Learning, January 1999, Grade 11
  
    Matrices: Analyzing
The learner will be able to evaluate the use of matrices with systems of equations to determine advantages and disadvantages of this solution method.
Strand Bloom's Scope Source
Matrices Evaluation Master Higher-Order Learning, January 1999, Grade 11
  
    Matrices: Interpret Linear Systems
The learner will be able to interpret linear systems of equations as matrices consisting of their coefficients.
Strand Bloom's Scope Source
Matrices Analysis Master Applications of Learning, January 1999, Grade 11
  
    Vectors: Position of Objects
The learner will be able to apply vectors to show the position of an object.
Strand Bloom's Scope Source
Vectors Application Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.50,II.B.13 week tested: 34.
  
    Vectors: Understand
The learner will be able to understand the concept of vectors.
Strand Bloom's Scope Source
Vectors Comprehension Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.50,II.B.8 week tested: 34.
  
    Parametric Equations: Define/Derive
The learner will be able to determine a definition for and derive parametric equations.
Strand Bloom's Scope Source
Parametric Equations Synthesis Master Higher-Order Learning, January 1999, Grade 11
  
    Parametric Equations: Graph
The learner will be able to sketch the graph of a set of parametric equations.
Strand Bloom's Scope Source
Parametric Equations Application Master Applications of Learning, January 1999, Grade 11
  
    Parametric Equations: Problem Solving
The learner will be able to solve problems using parametric equations, using technology when necessary.
Strand Bloom's Scope Source
Parametric Equations Application Master Applications of Learning, January 1999, Grade 11
  

Data Interpretation
The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. The Data Interpretation Unit includes data collection and classification, organization and display of data, logical reasoning and problem solving.

    Scatterplots: Construct
The learner will be able to create a scatterplot of data.
Strand Bloom's Scope Source
Scatterplots Comprehension Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.58.III.B. week tested: 34.
  
    Scatterplot: Draw/Line of Best Fit
The learner will be able to sketch a line of best fit.
Strand Bloom's Scope Source
Scatterplots Knowledge Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.58.III.B. week tested: 34.
  
    Scatterplot: Understand
The learner will be able to understand the concept of a scatterplot.
Strand Bloom's Scope Source
Scatterplots Comprehension Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.58.III.B.1 week tested: 34.
  
    Line of Best Fit: Understand
The learner will be able to understand the concept of line of best fit.
Strand Bloom's Scope Source
Scatterplots Comprehension Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.58.III.B.2 week tested: 34.
  
    Bar Graphs: Proportional Relationships
The learner will be able to use proportional relationships to extrapolate values on a bar graph.
Strand Bloom's Scope Source
Bar Graphs Application Master Applications of Learning, January 1999, Grade 11
  
    Graphs: Evaluate Appropriateness
The learner will be able to evaluate the appropriateness of a given graphical form for a given set of data.
Strand Bloom's Scope Source
Graphing Evaluation Master Higher-Order Learning, January 1999, Grade 11
  
    Data Collection
The learner will be able to collect data.
Strand Bloom's Scope Source
Data Collection and Classification Knowledge Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.41,III.C week tested: 34.
  
    Data Collection: Organization
The learner will be able to organize data in many different ways.
Strand Bloom's Scope Source
Data Collection and Classification Comprehension Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.41,III.C week tested: 34.
  
    Graphs: Identify Question
The learner will be able to analyze a given graph and determine what question can be answered using this information.
Strand Bloom's Scope Source
Analyzing/Evaluating Graphical Forms Analysis Master Applications of Learning, January 1999, Grade 11
  
    Graphs: Evaluate Data Analysis
The learner will be able to determine the validity of an argument based on a given set of data.
Strand Bloom's Scope Source
Analyzing/Evaluating Graphical Forms Evaluation Master Higher-Order Learning, January 1999, Grade 11
  

Discrete Mathematics
The Discrete Mathematics Unit includes the concepts of discrete math, matrices and recursion.

    Discrete Mathematics: Apply Concepts
The learner will be able to apply the concepts and methods of discrete mathematics to illustrate and investigate many different practical scenarios.
Strand Bloom's Scope Source
Discrete Mathematics Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.41,III.D week tested: 34.
  
    Discrete Math: Interative/Recursive
The learner will be able to apply iterative and recursive patterns and processes to illustrate many different practical scenarios and solve problems.
Strand Bloom's Scope Source
Discrete Mathematics Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.41,III.E week tested: 34.
  

Fractions
The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. The Fractions Unit includes comparison, ordering, fractions parts, estimation, reasoning and problem solving.

    Fractions: Understand
The learner will be able to understand fractions.
Strand Bloom's Scope Source
Fractions Comprehension Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.45,I.B.1 week tested: 34.
  

Functions
The Functions Unit includes exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions.

    Functions: Illustrate
The learner will be able to apply different types of functions to illustrate mathematical or real-world situations.
Strand Bloom's Scope Source
Functions Application Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.41,IV.B week tested: 34.
  

Geometry
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. The Geometry Unit includes properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving.

This unit includes exploring geometric concepts from multiple perspectives.

    Figures: Recognize/Classify/Explain
The learner will be able to recognize, classify, and explain two- and three-dimensional figures using properties, terms, and relationships.
Strand Bloom's Scope Source
Figures: Two-/Three-Dimensional Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.47,II.A.7 week tested: 34.
  
    Figures: Analyze
The learner will be able to use appropriate mathematical abilities to study properties of three-dimensional figures by using models and by drawing and interpreting two-dimensional representations of them in problem scenarios.
Strand Bloom's Scope Source
Properties of Figures Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.47,II.A.11 week tested: 34.
  
    Figures: 2-D Illustrations of 3-D Object
The learner will be able to draw two-dimensional illustrations of three-dimensional objects through sketching shadows, projections, perspectives, and map views.
Strand Bloom's Scope Source
Figures: Representations Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.47,II.A.8 week tested: 34.
  
    Congruence/Similarity/Symmetry: Problem
The learner will be able to apply the ideas of symmetry, similarity, and congruence to problem solving.
Strand Bloom's Scope Source
Congruence/Similarity/Symmetry Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.47,II.A.10 week tested: 34.
  
    Congruency/Similarity/Proportionality
The learner will be able to demonstrate an understanding of congruency, similarity, and proportionality through deductive reasoning.
Strand Bloom's Scope Source
Congruence/Similarity/Symmetry Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Congruent/Similar: Figures
The learner will be able to demonstrate an understanding of congruent and similar figures by utilizing the properties of these figures to solve problems and to prove solutions.
Strand Bloom's Scope Source
Congruence/Similarity/Symmetry Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Congruence/Similarity/Symmetry
The learner will be able to understand the idea of symmetry, congruence, and similarity.
Strand Bloom's Scope Source
Congruence/Similarity/Symmetry Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.50,II.B.1, p.50,II.B.2, p.50,II.B.3 week tested: 34.
  
    Angles
The learner will be able to identify, describe, estimate, and apply knowledge of various angles (including adjacent, vertical, straight, acute, right, obtuse, supplementary, and complementary).
Strand Bloom's Scope Source
Angles Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Circle: Determine Properties
The learner will be able to determine properties of circles and their related parts such as arcs, chords, secants, tangents, and other angles, by inductively and deductively formulating and applying logical arguments.
Strand Bloom's Scope Source
Circles Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Circle: Problem Solving
The learner will be able to develop strategies for approaching and solving real-world circle problems (determining relevant factors, discounting irrelevant factors, isolating the problem, using lists, webbing, graphical forms, pictures, and reasoning skills to solve problems and justify solutions).
Strand Bloom's Scope Source
Circles Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Pythagorean Theorem: Problem Solving
The learner will be able to use appropriate mathematical abilities to solve problems applying the Pythagorean Theorem.
Strand Bloom's Scope Source
Pythagorean Theorem Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.54,II.C.10 week tested: 34.
  
    Transformations: Understand
The learner will be able to understand transformations including rotations, reflections, translations, and dilations.
Strand Bloom's Scope Source
Transformations Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.50,II.B.4 week tested: 34.
  
    Transformations: Predict/Model
The learner will be able to use appropriate mathematical abilities to predict and model resulting figures when combining, subdividing, and changing figures in problem scenarios.
Strand Bloom's Scope Source
Transformations Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.50,II.B.17 week tested: 34.
  
    Transformations: Sequence
The learner will be able to use appropriate mathematical abilities to identify the sequence of transformations necessary to map one figure onto another figure in problem scenarios.
Strand Bloom's Scope Source
Transformations Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.50,II.B.14 week tested: 34.
  
    Geometric Concepts: Properties/Pattern
The learner will be able to identify, visualize, study and use geometric properties, relationships, and patterns in real-world and/or problem solving scenarios using models, manipulatives, or technology.
Strand Bloom's Scope Source
Geometric Relationships Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.41,II.A, p.47,II.A week tested: 34.
  
    Reasoning: Inductive/Deductive
The learner will be able to apply appropriate mathematical abilities to use inductive and deductive reasoning to solve real-world problems and confirm solutions.
Strand Bloom's Scope Source
Reasoning Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.47,II.A.12 week tested: 34.
  
    Inductive Reasoning: Understand
The learner will be able to apply inductive reasoning to understand and illustrate mathematical and other real-world phenomena.
Strand Bloom's Scope Source
Reasoning Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.41,IV.A week tested: 34.
  
    Points/Lines/Planes: Compare/Contrast
The learner will be able to explore similarities and differences within the relationships between points, lines, and planes.
Strand Bloom's Scope Source
Planes/Points/Lines Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Logic: Applying
The learner will be able to utilize inductive and deductive reasoning to solve real-world scenario problems involving parallelism, perpendicularity, angles, lines, circles, arcs, chords, secants, and tangents.
Strand Bloom's Scope Source
Logic Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Logic: Understanding Concepts
The learner will be able to understand and apply the concepts of facts, indirect and direct proof, hypotheses, conditional statements, and validity.
Strand Bloom's Scope Source
Logic Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Logic: Deductive Arguments
The learner will be able to incorporate definitions, postulates, theorems, and logical reasoning techniques to develop deductive arguments in paragraph or flow chart form, to solve real-world scenario problems.
Strand Bloom's Scope Source
Logic Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Logic: Conditional Statements
The learner will be able to recognize the hypothesis and conclusion of a conditional statement, and be able to state the converse, inverse, and contrapositive of a conditional statement.
Strand Bloom's Scope Source
Logic Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Logic: Applying Arguments
The learner will be able to demonstrate an understanding of logic by applying deductive and inductive arguments to proofs appropriately.
Strand Bloom's Scope Source
Logic Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Logic: Proving Validity
The learner will be able to test the validity of possible solutions by utilizing inverse operations, truth tables, and other methods.
Strand Bloom's Scope Source
Logic Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Symmetry: Pyramids
The learner will be able to explore right hexagonal pyramids, and determine the symmetry planes and the angles of rotational symmetry.
Strand Bloom's Scope Source
Symmetry Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Connecting: Transformations
The learner will be able to use appropriate mathematical abilities to connect the ideas of symmetry, similarity, and congruence to transformations in problem scenarios.
Strand Bloom's Scope Source
Connecting Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.50,II.B.16 week tested: 34.
  
    Connecting: Geometry/Algebra
The learner will be able to apply geometric concepts to solve problems in algebra by solving systems of equations through graphing and by exploring number sentence relationships (numerical coefficients, slopes, and the y and x intercepts).
Strand Bloom's Scope Source
Connecting Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Constructions: Manipulatives
The learner will be able to use manipulatives to identify, describe, and compare polygons and circles, and each of their parts, and to construct two- and three-dimensional figures.
Strand Bloom's Scope Source
Constructions Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Constructions: Relating
The learner will be able to use constructions to analyze and draw conclusions about geometric patterns, reflections, rotations, translations, similarity, congruency, and transformations, and concentrate on how these geometric themes relate to each other.
Strand Bloom's Scope Source
Constructions Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Properties: Understand/Dimensions/Shapes
The learner will be able to understand dimensions, shapes, and attributes of figures and objects.
Strand Bloom's Scope Source
Properties of Figures Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.54,II.C.3 week tested: 34.
  
    Properties: Identify/Explain
The learner will be able to identify and explain geometric properties and relationships as they are present in nature, art, and other real-world scenarios.
Strand Bloom's Scope Source
Properties of Figures Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.47,II.A.9 week tested: 34.
  
    Problem Solving: Models
The learner will be able to use appropriate mathematical abilities to solve real-life and mathematical problems applying geometric models.
Strand Bloom's Scope Source
Problem Solving Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.47,II.A.13 week tested: 34.
  
    Problem Solving: Trigonometric Ratios
The learner will be able to use appropriate mathematical abilities to solve problems involving indirect measurement.
Strand Bloom's Scope Source
Problem Solving Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.54,II.C.8 week tested: 34.
  
    Problem Solving: Transformations
The learner will be able to use appropriate mathematical abilities to solve geometry problems using transformations, coordinates, and vectors.
Strand Bloom's Scope Source
Problem Solving Master NJ: Assessments (ESPA, GEPA, HSPA), February 1998, Grade 11, p.50,II.B.15 week tested: 34.
  
    Problem Solving: Area/Perimeter
The learner will be able to solve real-world problems (involving the area and perimeter of quadrilaterals) which require logical deductions and reasoning based on geometric properties, and utilize geometric concepts as proof or evidence of a self-generated solution theory.
Strand Bloom's Scope Source
Problem Solving Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Proving: Geometric Properties
The learner will be able to use a coordinate plane, distance, mid-point, and slope formulas to prove the validity of geometric properties.
Strand Bloom's Scope Source
Geometric Proofs/Theorems Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Proving: Geometric Principles
The learner will be able to prove that the altitude from the vertex angle of an isosceles triangle contains the midpoint of the opposite side, that translations and rotations are isometries (given that an isometry preserves collinearity, betweenness, and angle measures, and a triangle and its image under an isometry are congruent), and that two triangles (with two sides each and congruent angles) are congruent.
Strand Bloom's Scope Source
Geometric Proofs/Theorems Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Spatial Thinking: Geometric Figures
The learner will be able to demonstrate spatial sense by comparing and classifying geometric figures, using representations to describe how two to three dimensional figures compare, solving problems, and justifying solutions by using geometric figures and their properties as proof.
Strand Bloom's Scope Source
Spatial Thinking Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Exploring: 2-3 D Figures
The learner will be able to explore, compare, and classify two- and three-dimensional figures, and make predictions about the unseen faces of three-dimensional figures based on a working knowledge of geometric properties and spatial sense.
Strand Bloom's Scope Source
Exploring Spatial Concepts Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Triangles: Exploring Properties
The learner will be able to investigate the following triangle issues: the relationship between the bisectors of an interior angle of a triangle and its corresponding exterior angle, the equations of the altitudes and the intersection of two altitudes (for the coordinates of a given triangle), the possible bilateral and rotational symmetry of specific triangles, triangle properties deduced from symmetry information, and Pythagorean implications for triangles.
Strand Bloom's Scope Source
Triangles Master The EdVISION.com Foundation Core Curriculum, May 1995, Geometry Series
  
    Angles/Lines: Properties/Logic
The learner will be able to apply inductive and deductive logical arguments to determine properties of angles and lines.
Strand