Hoosic Valley Central School District
Core Curriculum Topics
Subject: Math A Grade: 8-11
First Semester Units to be covered:
Logic
Operations and Number sets
Introduction to Algebra
Using formulas and Inequalities
Geometry
Geometric relationships
Real numbers
Trigonometry
Second Semester Units to be covered:
Measurement and Geometry
Polynomials
Factoring
Probability
Statistics
Coordinate Geometry
Transformational Geometry
65

Hoosic Valley Central School District
Core Curriculum Topics
Subject: Math I Grade: 9-11
First Semester Units to be covered:
Operations and number sets
Introduction to Algebra
Using formulas and Inequalities
Aspects of Geometry
Geometric Relationships
Second Semester Units to be covered
Real numbers and Trigonometry
Measurements and Geometry
Polynomials and Factoring
Probability and Statistics
Coordinates Geometry
66

Grade: 9-11
First Semester Units to be covered:
Chapter 1 Introduction to Logic
1.1 Statements and Sentences
1.2 Negations
1.3 Conjunctions
Hoosic Valley Central School District
Core Curriculum Topics
Subject: Math A
Algebra I
1.4 Disjunctions
1.5 The Conditional
1.6 Tautologies
1.7 Converse, Inverse, and Contra positive
1.8 Biconditionals and Equivalent Statements ...
Chapter 2 Operations and Numbers
2.1 Variables
2.2 Order of Operations
2.3 The Integers
2.4 Addition on a Number Line
2.5 Adding Integers
2.6 Subtracting Integers
2.7 Multiplying and Dividing Integers...
2.8 Fractions and Decimals
2.9 Properties of Real Numbers
2.10 The Distributive Property
2.11 Scientific notation
Chapter 3 Introduction to Algebra
3.1 Using Variables
3.2 Writing Equations
3.3 Solving Equations Using Addition
3.4 Solving Equations Using Multiplication
3.5 Solving Problems
3.6 Equations with More Than One Operation....
3.7 More Problem Solving
3.8 Consecutive Integers
3.9 Variables on Both Sides of the Equation
Chapter 4 Using Formulas and Inequalities
4.1 Formulas
4.2 Solving Formulas for Specific Variables
4.3 Inequalities
4.4 Solving Inequalities Using Addition
4.5 Solving Inequalities Using Multiplication
4.6 Problem Solving
4.7 Compound Inequalities
4.8 Sentences Containing Fractions
67

Chapter 5 Aspects of Geometry
5.1 Points, Lines, and Planes
5.2 Rays and Angles
5.3 Special Angles
5.4 Parallel Lines, Transversals, and Angles
5.5 Classifying Polygons
5.6 Angles of a Triangle
5.7 Quadrilaterals
Chapter 6 Geometric Relationships
6.1 Ratio, rates, unit pricing
6.2 Proportion
6.3 Percents in Proportions
6.4 Similar Figures
6.5 Congruence and SAS
6.6 The ASA Axiom
6.7 Directional analysis
6.8 Direct variation
Chapter 7 The Real Numbers
7.1 Rational Numbers as Decimals
7.2 Repeating Decimals for Rational Numbers
7.3 The Real Numbers
7.4 Square Roots
7.5 Approximating Square Roots
7.6 Simplifying Radicals
7.7 Adding and Subtracting Radicals
7.8 The Pythagorean Theorem
7.9 Dividing Square Roots
7.10 Trigonometry
Chapter 8 Measurement and Geometry
8.1 Distance in the Metric System
8.2 Areas of Rectangles and Parallelograms
8.3 The Area of a Triangle
8.4 The Area of a Trapezoid
8.5 Circles and Circumference
8.6 The Area of a Circle
8.7 Measuring Volume
8.8 Solids with Curved Surfaces
8.9 Metric Units of Mass and Capacity
68

Chapter 9 Polynomials
9.1 Monomials
9.2 Multiplying Monomials
9.3 Powers of Monomials
9.4 Polynomials
9.5 Adding and Subtracting Polynomials
9.6 Multiplying a Polynomial by a Monomial
9.7 Multiplying Binomials
9.8 Multiplying Polynomials
9.9 Dividing Monomials
9.10 Dividing Polynomials
9.11 Operations with Rational Expressions
Chapter 10 Factoring
10.1 Factoring Monomials
10.2 Factoring Polynomials
10.3 Factoring the Difference of Squares
10.4 Factoring Quadratic Polynomials
10.5 Solving Equations by Factoring
10.6 Using Factoring in Problem Solving
Chapter 11 Introduction to Probability
11.1 The Probability of an Event
11.2 Impossibilities and Certainties
11.3 Adding Probabilities
11.4 Probability and Sets
11.5 Outcome Sets
11.6 The Counting Principle
11.7 Multiplying Probabilities
11.8 Permutations
Chapter 12 Introduction of Statistics
12.1 Statistics and Sampling
12.2 Averages
12.3 Statistical Graphs
12.4 Histograms
12.5 Cumulative Frequency Histograms
12.6 Empirical Probability
12.7 Organizing Experimental Data
69

Chapter 13 Introduction to Coordinate Geometry
13.1 Graphing
13.2 Linear Equations
13.3 Slope
13.4 Equation of a Line
13.5 Systems of Equations
13.6 Algebraic Solutions
13.7 Using Systems of Equations to Solve Problems
13.8 Graphing Linear Inequalities
Chapter 14 Introduction of Transformation Geometry
14.1 Mappings and Functions
14.2 Line Reflections and Line Symmetry
14.3 Line Reflections in the Coordinate Plane
14.4 Translations
14.5 Rotations
14.6 Dilations
70

Grade: 10-12
Hoosic Valley Central School District
Core Curriculum Topics
First Semester Units to be covered:
Review Unit
Linear equations and inequalities
Subject: Geometry
Coordinate geometry
Triangle
Trigonometry
Polygons
Circles
Logic
Second Semester Unit to be covered
Quadratic equations
Volume of solids
Transformations
Rational expressions
Probability and Statistics
Locus
Systems
Constructions
71

Grade: 11-12
Hoosic Valley Central School District
Core Curriculum Topics
Subject: Pre-calculus
First Semester Units to be covered:
Real numbers
Exponents and radicals
Polynomial and factoring
Fractional expressions
Solving equations and Inequalities
Graphs and graphing utilities
Lines in the Plane and Slope
Functions
Analyzing the Graphs of Functions
Translations and combinations
Inverse functions
Mathematical modeling
Quadratic functions
Polynomials functions of higher degree
Polynomial and synthetic division
Real zeros of polynomial functions
Complex numbers
The fundamental Theorem of Algebra
Rational functions
Partial fractions
Second Semester Units to be covered:
Exponential and Logarithmic functions and Their Graphs
Properties of Logarithms
Exponential and Logarithmic equations and models
Trigonometry
Solving Trigonometric equations
Systems of equations and Inequalities
-two variable, multivariable, and linear programming
Matrices
Sequences and series
Intro to Calculus: limits
72

Grade: 11-12
Hoosic Valley Central School District
Core Curriculum Topics
Subject: Algebra II
First Semester Units to be covered:
Ch. 1 Polynomial and rational expressions
Ch. 2 Complex numbers
Ch. 3 Relations and functions
Ch. 4 Transformation Geometry
Ch. 5 Exponential and Logarithmic functions
*Book – Integrated Mathematics Course III
Second Semester Units to be covered
Ch. 6 Circles
Ch. 7 Circular functions
Ch. 11 Probability and Binomial Theorem
Ch. 12 Statistics
Ch. 13 Sequences and Series
73

Grade: 11-12
Hoosic Valley Central School District
Core Curriculum Topics
Subject: Math Investigations
First Semester Units to be covered:
Unit 1 Trigonometry
Unit 2 System of Equations
Unit 3 Matrices
Unit 4 Exponents/Exponential functions
Unit 5 Quadratics
Unit 6 Math History
Unit 7 Area and Volume
74

Grade: 11-12
Hoosic Valley Central School District
Core Curriculum Topics
Subject: Statistics
First Semester Units to be covered:
Descriptive Statistics Review
Ch. 1 Statistics
Ch. 2 Descriptive Analysis and Single-Variable data
Ch. 3 Descriptive Analysis and bivariate data
Ch. 4 Probability
*Book – Elementary Statistics 9 th edition
Statistics Course
Descriptive Statistics Review
-mean, median, mode
-box-and-whisker plots
-stem and leaf plots
*book - Elementary Statistics 9 th
edition
Ch. 1 Descriptive Statistics
-basic terms
-Measurability/Variability
-Data collection
Ch. 2 Analysis and single-variable data
-Graphic representation
-Numerical descriptive statistics
-Measures of central tendency, dispersion, standard deviation, position
-Interpreting and understanding standard deviation
-Real-world applications (research, project)
Ch. 3 Descriptive Analysis and Bivariate data
-Linear correlation
-Linear Regression
Statistical Description
75

Grade: 9
Hoosic Valley Central School District
Core Curriculum Topics
Subject: Pre-Algebra
First Semester Units to be covered:
Ch. 1 Communicating with Mathematics
Ch. 2 Problem solving
Ch. 3 Operations with numbers
Ch. 4 Signed numbers
Ch. 5 Using Symbols
Ch. 6 Solving equations
Ch. 7 Inequalities
*Book – Integrated Mathematics – Introductory course
Second Semester Units to be covered:
Ch. 8 Using Algebra in Geometry
Ch. 9 Geometric Measures
Ch. 10 Applying Ratio and Proportion
Ch. 11 Probability
Ch. 12 Statistics
Ch. 13 Polynomials
Ch. 14 Straight line
76

Hoosic Valley Central School District
Core Curriculum Topics
Grade: High School
First Semester Units to be covered:
Text: Integrated Mathematics Course 2
Review of equations and inequalities, including word problems
Subject: Math AB/Math B
Chapter 8 - Geometry with Coordinates
Chapter 9 - Using Coordinates and Locus of Points
Chapter 10 - Solving Quadratic Equations
Simplification and Operations with Rational Expressions
Equations with fractions and Fractional Equations
Chapter 13 - Trigonometry
Chapter 12 - Transformational Geometry
Chapter 11 - Probability and Combinatorics
Angles of Polygons
Constructions
Math A Regents in January then begin first semester of Math B
77

Hoosic Valley Central School District
Core Curriculum Topics
Grade: High School
First Semester Units to be covered:
Math B
Text: Integrated Mathematics Course 2
Subject: Math B
Unit I: Laws of Inference/Logic Proofs
1) Chapter 1
Unit II: Euclidean Geometry
1) Introduction to Formal Proofs
Chapter 4 - Sections 4.1 - 4.10
2) Congruent Triangles
Chapter 5 - Sections 5.1 -5.7
3) Quadrilaterals
Chapter 6 - Sections 6.1 - 6.4
4) Similarity
Chapter- Sections 7.1 - 7.10
Unit III: Transformational Geometry
1) Chapter 12 Sections 12.1-12.8
Review for school exam modeled on the Math B exam.
78

Grade: High School
Hoosic Valley Central School District
Core Curriculum Topics
Subject: Math B
Second and Third Semester Units to be covered:
Math B
Text: Glencoe, Integrated Math Course 3. Authors: Bumby, Klutch, Collins and Egbers
Supplemental Text: Amsco, Mathematics B. Author: Keenan, Gantert and Dressier.
Unit IV: Complex Number System
1) Chapter 1 - Sections 1.1 - 1.11
2) Chapter 2 - Sections 2.1-2.10
Unit V: Relations and Functions
1) Chapter 3 - Sections 3.1-3.7
Unit VI: Transformational Geometry and Functions
1) Chapter 4 - Sections 4.1-4.8
2) Chapter 10- Sections 10.1-10.6
Unit VII: Geometry of a Circle
1) Chapter 6 - Sections 6.1 - 6.7
Unit VIII: Trigonometry
1) Chapter 7 - Sections 7.1 - 7.9
2) Transformations of Trigonometric Graphs
3) Chapter 8 - Sections 8.1 - 8.8
4) Navigation Applications
5) Chapter 9 - Sections 9.1 - 9.7
(De-emphasize tangent and proving identities and emphasize trigonometric manipulation)
6) Surveying Applications
7) Chapter 15 - Section 15.7
(Absolute Value of Complex Numbers)
Unit IX: Exponential and Logarithmic Functions
1) Chapter 5 - Sections 5.1-5.9
Unit X: Probability and Statistics
1) Chapter 11-Sections 11.1 11.8
2) Chapter 12-12.1-12.6
3) Curve Fitting
Linear Functions - Scatter Plots, Best fit lines, Modeling,
Regression, and Linear Correlation Coefficient
Exponential, Logarithmic and Power Regression
Final Exam will be the NY State Math B Exam
79

Grade: 12
.Hoosic Valley Central School District
Core Curriculum Topics
First Semester Units to be covered:
Subject: AP Calculus
AP Calculus
Text: Calculus of a Single Variable
Prerequisites - The Cartesian Plane and Functions
Chapter 1 - Limits
Chapter 2 - Differentiation
Chapter 3 - Applications of Differentiation
Chapter 4 - Integration
Second Semester Units to be covered:
Chapter 5 - Logarithmic, Exponential and Other Transcendental Functions
Chapter 6 - Applications of Integration
Chapter 7 - Integration Techniques
80