GLEN RIDGE PUBLIC SCHOOL

Curriculum Guide

Course Title: GEOMETRY HONORS

Subject: Geometry

Grade: 9

Department/School: Mathematics/ Glen Ridge High School

Duration: Full Year

Number of Credits: 5

Prerequisite: Algebra 1 grade of “A+” or grade 8 Algebra grade of “B” or higher

Elective or Required: Required

Author: Anne Curcio

Date Submitted: Summer 2007

Course Description

The emphasis of this full year course is placed on the traditional Euclidean Geometry (Theorems and Proofs). Attention is placed on classical constructions, and skills are developed using mathematical tools. Then, additional work is completed on orthographic and isometric drawings. The distance formula is developed and a study in coordinate geometry follows. Major geometric theorems are reviewed and proved algebraically. Extensive study is done in trigonometry and the course closes with transformational geometry.

Mission Statement

Mathematics and Computer Science are an integral part of our lives. Students must be actively involved in their mathematics education with problem solving being an essential part of the curriculum. The mathematics and computer science curricula should emphasize thinking skills through a balance of computation, intuition, common sense, logic, analysis and technology. Students will be engaged and challenged in a student-centered learning environment that is developmentally appropriate. Students will communicate mathematical ideas effectively by applying hands-on manipulatives, basic computational skills, mathematical models, and technology in order to solve practical problems.

New Jersey Core Curriculum Standards

The Mathematics Standards consist of five statements, which describe what is essential to an excellent mathematics education, and present a view of mathematics teaching and learning that integrates the processes of mathematical activity, the content of mathematics, and the learning environment in the classroom. The following standards were adopted by the New Jersey State Board of Education.

This course will cover the following Core Curriculum Standards:

Descriptive Statement:  Numbers and arithmetic operations are what most of the general public think about when they think of mathematics; and, even though other areas like geometry, algebra, and data analysis have become increasingly important in recent years, numbers and operations remain at the heart of mathematical teaching and learning.  Facility with numbers, the ability to choose the appropriate types of numbers and the appropriate operations for a given situation, and the ability to perform those operations as well as to estimate their results, are all skills that are essential for modern day life.

Number Sense

Numerical Operations

Estimation

Descriptive Statement:  Spatial sense is an intuitive feel for shape and space. Geometry and measurement both involve describing the shapes we see all around us in art, nature, and the things we make.  Spatial sense, geometric modeling, and measurement can help us to describe and interpret our physical environment and to solve problems. 

Geometric Properties

Transforming Shapes

Coordinate Geometry

Units of Measurement

Measuring Geometric Objects

Descriptive Statement: Algebra is a symbolic language used to express mathematical relationships.  Students need to understand how quantities are related to one another, and how algebra can be used to concisely express and analyze those relationships.  Modern technology provides tools for supplementing the traditional focus on algebraic procedures, such as solving equations, with a more visual perspective, with graphs of equations displayed on a screen.  Students can then focus on understanding the relationship between the equation and the graph, and on what the graph represents in a real-life situation. 

Patterns

Functions and Relationships

Modeling

Procedures

Descriptive Statement:  Data analysis, probability, and discrete mathematics are important interrelated areas of applied mathematics.  Each provides students with powerful mathematical perspectives on everyday phenomena and with important examples of how mathematics is used in the modern world.  Two important areas of discrete mathematics are addressed in this standard; a third area, iteration and recursion, is addressed in Standard 4.3 (Patterns and Algebra).

Data Analysis

Probability

Discrete Mathematics – Systematic Listing and Counting

Discrete Mathematics – Vertex-edge Graphs and Algorithms

Descriptive Statement:  The mathematical processes described here highlight ways of acquiring and using the content knowledge and skills delineated in the first four mathematics standards.

Problem Solving Reasoning

Communication Representations

Connections Technology

Scope and Sequence

STANDARD 4.1 (NUMBER AND NUMERICAL OPERATIONS) ALL STUDENTS WILL DEVELOP NUMBER SENSE AND WILL PERFORM STANDARD NUMERICAL OPERATIONS AND ESTIMATIONS ON ALL TYPES OF NUMBERS IN A VARIETY OF WAYS.
A.	Number Sense	9	10	11	12
	By the end of Grade 12, students will:
A.1	Extend understanding of the number system to all real numbers.	R	R	M
A.2	Compare and order rational and irrational numbers.	R	R	M
A.3	Develop conjectures and informal proofs of properties of number systems and sets of numbers.	R	R	M
B.	Numerical Operations
B.1	Extend understanding and use of operations to real numbers and algebraic procedures.	R	R	R	M
B.2	Develop, apply, and explain methods for solving problems involving rational and negative exponents.	R	R	M
B.3	Perform operations on matrices: addition and subtraction, scalar multiplication.	R	R	M
B.4	Understand and apply the laws of exponents to simplify expressions involving numbers raised to powers.	R	R	M
C.	Estimation
C.1	Recognize the limitations of estimation, assess the amount of error resulting from estimation, and determine whether the error is within acceptable tolerance limits.	R	R	R	M

STANDARD 4.2  (GEOMETRY AND MEASUREMENT)  ALL STUDENTS WILL DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES, RELATIONSHIPS, AND MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA.
A.	Geometric Properties	9	10	11	12
	By the end of Grade 12, students will:
A.1	Use geometric models to represent real-world situations and objects and to solve problems using those models (e.g., use Pythagorean Theorem to decide whether an object can fit through a doorway).	R	M
A.2	Draw perspective views of 3D objects on isometric dot paper, given 2D representations (e.g., nets or projective views).	M
A.3	Apply the properties of geometric shapes: Parallel lines--transversal, alternate interior angles, corresponding angles; Triangles (a) conditions for congruence, (b) segment joining midpoints of two sides is parallel to and half the length of the third side, (c) triangle inequality; minimal conditions for a shape to be a special quadrilateral; Circles--arcs, central and inscribed angles, chords, tangents; self-similarity.	R	M
A.4	Use reasoning and some form of proof to verify or refute conjectures and theorems: verification or refutation of proposed proofs; simple proofs involving congruent triangles; counterexamples to incorrect conjectures.		I/R/M
A.5	Recognize, describe, extend, and create space-filling patterns.		R/M
B.	Transforming Shapes
B.1	Determine, describe and draw the effect of a transformation, or a sequence of transformations, on a geometric or algebraic object, and, conversely, determine whether and how one object can be transformed to another by a transformation or a sequence of transformations.		R/M
B.2	Recognize three-dimensional figures obtained through transformations of two-dimensional figures (e.g., cone as rotating an isosceles triangle about an altitude), using software as an aid to visualization.		I/R/M
B.3	Determine whether two or more given shapes can be used to generate a tessellation.		M
B.4	Generate and analyze iterative geometric patterns: fractals (e.g., Sierpinksi's Triangle); patterns in areas and perimeters of self-similar figures; outcome of extending iterative process indefinitely.