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Chester Township Public Schools |
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Mathematics Curriculum |
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Mathematics - Pre-Calculus |
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Equations: Solving/Varying Degree
The learner will be able to
solve equations of varying degrees using graphing calculators, computers, and paper-and-pencil techniques.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Solve Equations |
|
Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.13.17 |
Classroom
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Equations: Interpret
The learner will be able to
interpret equations using tables and graphs as tools.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Equations |
|
Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.13.15 |
Classroom
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Equations: Interpret/Geometrically
The learner will be able to
interpret algebraic equations geometrically and describe geometric objects algebraically.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Equations |
|
Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.13.19 |
Classroom
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Inequalities: Solving/Varying Degree
The learner will be able to
solve inequalities of varying degrees using graphing calculators, computers, and paper-and-pencil techniques.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Inequalities |
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Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.13.17 |
Classroom
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Inequalities: Interpret/Geometrically
The learner will be able to
interpret algebraic inequalities geometrically and describe geometric objects algebraically.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Inequalities |
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Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.13.19 |
Classroom
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Inequalities: Interpret
The learner will be able to
interpret inequalities using tables and graphs as tools.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Inequalities |
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Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.13.15 |
Classroom
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Expressions: Interpret
The learner will be able to
interpret expressions using tables and graphs as tools.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Expressions |
|
Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.13.15 |
Classroom
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Expressions: Operations
The learner will be able to
develop, describe, apply and analyze procedures for operating on algebraic expressions and matrices.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Expressions |
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Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.13.16 |
Classroom
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Polynomials: Factoring/Number Sense
The learner will be able to
demonstrate the relationship between polynomials, factoring, and resulting binomials.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Polynomials |
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Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Polynomials: Applying Exponential Laws
The learner will be able to
apply the laws of exponents to prove the validity of the simplification of a given polynomial expression.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Polynomials |
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Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Polynomials: Factoring/Complex Numbers
The learner will be able to
factor polynomials over complex numbers, and apply these concepts to geometry and real-world scenarios.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Polynomials |
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Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Operations/Procedures: Analyzing/Real
The learner will be able to
extend an understanding of operations (addition, subtraction, multiplication, division) and algebraic procedures to working with the entire real number system.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Basic Operations |
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Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.8.13 |
Classroom
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Operations: Applying
The learner will be able to
extend their understanding and application of operations to algebraic procedures.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Operations |
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Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.8.13 |
Classroom
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Operations: Relationships
The learner will be able to
determine the relationships between synthetic division, synthetic substitution, polynomial factoring, and the rational root theorem.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Polynomials |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Formulas: Quadratic/Applying Roots
The learner will be able to
explain how the nature of roots, the discriminant in particular, applies to quadratic equations and their solutions.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Formulas |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Algebraic Concepts: Analyzing
The learner will be able to
analyze algebraic concepts by dealing with algebraic transformations, expressions, inequalities, equations, and matrices.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Algebraic Concepts |
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Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Algebraic Concepts: Reasoning
The learner will be able to
prove the validity of solutions by applying deductive reasoning, inductive reasoning, and number properties to algebra problems.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Algebraic Concepts |
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Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Algorithms: Problem Solving
The learner will be able to
apply basic principles to solve algorithmic and combinatorial problems.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Algorithms |
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Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.14.12 |
Classroom
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Connecting: Algebra/Geometry
The learner will be able to
determine the relationships between number sentences and lines on the Cartesian plane (numerical coefficients, slopes, y-intercepts).
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Connecting |
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Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Connecting: Algebra/Geometry
The learner will be able to
apply geometric concepts to solve problems in algebra by determining equations of a line (given the graph of the line), by solving quadratic equations by graphing, by solving systems of equations through graphing, by analyzing range, domain, odd/even, relation-functions, zeros of a function, and x and y intercepts, and by exploring relationships.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Connecting |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Problem Solving: Methods
The learner will be able to
analyze, apply, and explain methods for approaching and solving problems involving factorials, exponents, and matrices.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Problem Solving |
|
Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.8.14 |
Classroom
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Problem Solving: Varying Quantities
The learner will be able to
use models to solve problems involving varying quantities by applying concepts of variables, expressions, equations, inequalities, absolute values, vectors, and matrices.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Problem Solving |
|
Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.13.14 |
Classroom
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Problem Solving Strategies: Graphing
The learner will be able to
approach application problems by using graphical representations of the data to deduce possible solutions (including graphing a function and its inverse on a Cartesian plane, analyzing effects of parameter changes on functions, recognizing the equations and corresponding graphs of the conic sections, graphing exponential and logarithmic functions, and determining the maxima and minima of graphs).
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Problem Solving |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Problems Solving: Methods
The learner will be able to
develop methods for solving problems involving factorials, exponents, and matrices.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Problem Solving |
|
Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.8.14 |
Classroom
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Problem Solving: Application
The learner will be able to
solve application problems involving polynomials, rational expressions, radical expressions, exponential equations, quadratic equations, inequalities, and logarithmic equations, by utilizing the binomial theorem, Pascal's triangle, matrices, and geometric models.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Problem Solving |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Problem Solving: Discrete
The learner will be able to
solve real-world scenario problems involving discrete mathematics.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Problem Solving |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Problem Solving: Evaluating Forms
The learner will be able to
solve real-world problems involving whole numbers, fractions, decimals, percents, integers, scientific notation, and exponential notation by determining the operation required (addition, subtraction, multiplication, division), setting up the correct number sentence, solving the problem, and using inverse operations to check the solution.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Problem Solving |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Problem Solving: Application
The learner will be able to
solve real-world application problems involving polynomials, rational algebraic expressions, radical expressions, real number exponential expressions, and logarithmic expressions, while appropriately utilizing matrices, the binomial theorem, Pascal's triangle, probability, synthetic division, polynomial factoring, and rational root theorems, as means to solving such problems.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Problem Solving |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Translate Problems: Complex Coefficients
The learner will be able to
translate a given real-world scenario (delivered orally, through manipulatives, pictures, or in a written prompt) into an equation or inequality involving complex coefficients.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Relating Number Sentences/Problems |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Translate Problems: Complex Coefficients
The learner will be able to
demonstrate an understanding of number sentences by translating a given real-world scenario (delivered orally, through manipulatives, pictures, or in a written prompt) into an equation involving complex coefficients.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Relating Number Sentences/Problems |
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Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Number Sentences: Relating to Real-World
The learner will be able to
formulate expressions and equations (involving radicals, absolute value, the quadratic equation, and exponents) for given scenarios, and justify each variable and coefficient by explaining how each corresponds to an element of the given scenarios, emphasize justifying the set-up (not on simplifying or solving the expressions or equations), and change the equations or expressions, describing why the expressions or equations need to be changed if scenario elements are altered.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Number Sentence |
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Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
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Properties: Distributive/Mental Math
The learner will be able to
use the distributive property as a short cut when performing mental math.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Properties |
Application |
Master |
Applications of Learning, January 1999, Grade 12 |
Classroom
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Properties: Applying
The learner will be able to
apply field properties in problem solving situations.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Properties |
Application |
Master |
Applications of Learning, January 1999, Grade 12 |
Classroom
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Properties
The learner will be able to
identify and apply the following properties of addition and multiplication to determine what number is missing from an equation: multiplication by 0, distributive, associative, commutative, and order of operations.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Properties |
Application |
Master |
Applications of Learning, January 1999, Grade 12 |
Classroom
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Properties
The learner will be able to
use properties of operations in solving problems.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Properties |
Application |
Master |
Applications of Learning, January 1999, Grade 12 |
Classroom
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Properties: Real Numbers
The learner will be able to
apply real number properties by identifying equivalent expressions with one unknown variable.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Properties |
Application |
Master |
Applications of Learning, January 1999, Grade 12 |
Classroom
|
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Equations: Writing
The learner will be able to
develop and write equations based on word problems.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Equations |
Synthesis |
Master |
Higher-Order Learning, January 1999, Grade 12 |
Classroom
|
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Expressions with Exponents: Evaluating
The learner will be able to
evaluate expressions with exponents.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Expressions |
Evaluation |
Master |
Higher-Order Learning, January 1999, Grade 12 |
Classroom
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Quadratic Equation: Standard Form
The learner will be able to
state a quadratic equation in standard form.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Quadratic Equations/Formula |
Comprehension |
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
|
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Exponential Equations
The learner will be able to
solve equations involving exponents.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Exponents |
Application |
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
|
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Logarithms/Exponents: Simplifying
The learner will be able to
use relationships between logarithms and exponents to simplify expressions.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Exponents |
Application |
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
|
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Algebraic Concepts: Procedures
The learner will be able to
understand algebraic procedures.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Algebraic Concepts |
Comprehension |
Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.13.18.; Terra Nova, Complete Battery, 1997, Level 19, Objective Statement #16 week tested: 21 |
Classroom
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Equality/Inequality: Solving
The learner will be able to
solve equations and inequalities.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Equality/Inequality |
Comprehension |
Master |
Foundations of Learning, January 1999, Grade 12 |
Classroom
|
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Logarithms: Simplifying
The learner will be able to
use logarithmic properties to simplify expressions.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Logarithms |
Application |
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
|
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Logarithmic Equations
The learner will be able to
solve equations involving logarithms.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Logarithms |
Application |
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
|
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Systems of Equations: Determinants
The learner will be able to
solve systems of equations by applying determinants.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Systems of Equations |
Application |
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
|
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Binomial Expansion: Finding Terms
The learner will be able to
find an nth term within a binomial expansion.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Binomial Expansion |
Knowledge |
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
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Calculus and Pre-Calculus
|
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Applying: Limits
The learner will be able to
analyze and apply the concept of limits.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Applying Calculus Concepts |
|
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series; National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
|
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Applying: Induction/Sequence/Series
The learner will be able to
use manipulatives, graphs, and technology to demonstrate an understanding of mathematical induction, and sequence and series.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Applying Calculus Concepts |
|
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series; National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
|
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Curves: Interpreting
The learner will be able to
develop an intuitive sense about the concepts of the slope of a curve, interpret the meaning of the slope of a curve for a given graph and apply concepts of the slope to discuss the information contained in the graph.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Curve Sketching |
|
Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.15.17 |
Classroom
|
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Conic Sections: Understanding Loci
The learner will be able to
use manipulatives, graphs, and technology to demonstrate an understanding of conic sections and loci.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Conic Sections |
|
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series; National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
|
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Conic Sections: Circle
The learner will be able to
use a given equation of a circle to find the center and radius and graph the circle.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Conic Sections |
|
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
|
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Conic Sections: Parabola
The learner will be able to
use a given equation of a parabola to find the vector, focus, and direction and then graph the parabola.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Conic Sections |
|
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
|
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Conic Sections: Ellipse
The learner will be able to
use a given equation of an ellipse in standard form to find the center, foci, and vertices, and then graph the ellipse.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Conic Sections |
|
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
|
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Conic Sections: Hyperbola
The learner will be able to
use a given equation of a hyperbola in standard form to find the foci, vertices, and asymptotes and then graph the hyperbola.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Conic Sections |
|
Master |
The EdVISION.com Foundation Core Curriculum, May 1995, Calculus Series |
Classroom
|
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Complex Coefficients: Representing
The learner will be able to
create manipulatives to represent a given equation or inequality with complex coefficients by identifying relationships between coefficients, variables, and the real-world counterparts.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Complex Numbers |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
|
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Complex Numbers: Representing
The learner will be able to
create manipulatives to represent a given equation with complex coefficients by identifying relationships between coefficients, variables, and the real-world counterparts.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Complex Numbers |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
|
|
Complex Numbers: Forms/Relationships
The learner will be able to
demonstrate the ability to focus on the relationship between number forms by relating the absolute value of complex numbers in algebraic, geometric, and vector representations, and by explaining the relationships between exponential expressions and logarithmic expressions, and real number exponents and radical symbolism.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Complex Numbers |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
|
|
Complex Numbers: Exploring
The learner will be able to
explore the properties and structural characteristics of the complex number system and its sub-systems, including identifying the sub-systems which are isomorphic.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Complex Numbers |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
|
|
Complex Numbers: Representing
The learner will be able to
represent situations that involve complex numbers with expressions, equations, and inequalities by setting up number sentences and performing basic operations using diagrams, algebraic procedures, and vector representations.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Complex Numbers |
|
Master |
National Council of Teachers of Mathematics (NCTM), March, 1989, Twelfth Grade |
Classroom
|
|
Limits: Informal Notation
The learner will be able to
formulate an informal notion of limit.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Limits |
|
Master |
NJ: Core Curriculum Content Standards, May 1996, Grade 12, Standard 4.15.14 |
Classroom
|
|
Connecting: Coordinate Systems
The learner will be able to
utilize technology to show how graphs in the polar coordinate system relate to graphs in the Cartesian coordinate system.
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