TOPICS/SUBTOPICS
     
    		 

    NYSED SKILLS
    		 

    ASSESSMENT
     
    Operations and Properties
    ·   Operations in Arithmetic
    ·   Bases, Exponents and Powers
    ·   Order of Operations
    ·   Properties of Operations
    ·   Operations with Sets     		 
    ·   Properties of real numbers including closure, commutative, associative, and distributive properties, and inverse and identity elements
    ·   Rational approximations of irrational numbers
    ·   Venn Diagrams
     
    ·   Teacher -made Tests
     
    Algebraic Expressions, Geometric Formulas and Open Sentences
    ·   Algebraic terms and vocabulary
    ·   Evaluating algebraic expressions
    ·   Translating verbal sentences into formulas
    ·   Formulas for perimeter and area of polygons
    ·   Formulas for circumference and Area of a circumference
    ·   Reasoning with perimeter, area and shade
    ·   Formulas for Volume of a Solid
          		 
    ·   Use of variables/Algebraic representations
    ·   Perimeter of Polygons and Circumference of Circles
    ·   Study of solids: classification of prism, rectangular solid, pyramid, right circular cylinder, cone and sphere
    ·   Area of Polygons and Circles
    ·   Volume of Solids     		 
    ·   Teacher-made Tests
     
    Signed Numbers
    ·   The Absolute of a Number
    ·   Evaluating algebraic expressions using signed numbers     		 
    ·   Signed numbers
    ·   Use of variables: order of operations and evaluating algebraic expressions and formulas     		 
    ·   Teacher-made Tests

     

    TOPICS/SUBTOPICS
     
    		 

    NYSED SKILLS
    		 

    ASSESSMENT
     
    Culminative Problem Solving
    ·   A multitude of problems are integrated throughout the course     		 
    ·   Graphic and algebraic solutions of linear and quadratic functions in the solution of problems
    ·   Determine and model real-life situations with appropriate functions
    ·   Translate linear and quadratic functions, systems of equations, inequalities and quadratic linear pairs between representations that are verbal descriptions, tables, equations or graphs
    ·   Converting to equivalent measurements within metric and English measurement systems
    ·   Direct and indirect measure
    ·   Error of measurement and its consequences on calculation of perimeter of polygons and circumference of circles
    ·   Percent of error in measurements     		 
    ·   Teacher-made Tests
     
    Operations With Algebraic Expressions
    ·   Adding algebraic expressions
    ·   Subtracting algebraic expressions
    ·   Multiplying powers that have the same base
    ·   Multiplying by a monomial
    ·   Multiplying polynomials
    ·   Dividing powers that have the same base
    ·   Powers with zero and negative exponents
    ·   Using scientific notation
    ·   Dividing by a monomial
    ·   Dividing by a Polynomial     		 
    ·   Simplification of algebraic expressions
    ·   Addition and subtraction of polynomials
    ·   Multiplication of polynomials: powers, products of monomials and binomials
    ·   Division of polynomials by monomials
    ·   Scientific notation
    ·   Powers: positive, zero and negative exponents
          		 
    ·   Teacher-made Tests
     
    TOPICS/SUBTOPICS
     
    		 

    NYSED SKILLS
    		 

    ASSESSMENT
     
    First-Degree Equations and Inequalities in One Variable
    ·   Simplifying each side of an equation before solving
    ·   Solving equations that have the variable in both members
    ·   Consecutive-Integer problems
    ·   Solving for a variable in a formula
    ·   Perimeter problems
    ·   Solving for a variable in terms of another variable
    ·   Transforming formulas
    ·   Properties of inequalities
    ·   Finding and graphing the Solution Set of an Inequality
    ·   Using inequalities to solve problems
          		 
    ·   Formulas and literal equations
    ·   Inequalities
    ·   Techniques for solving equations and inequalities
    ·   Solve linear inequalities     		 
    ·   Teacher-made tests

     

    TOPICS/SUBTOPICS
     
    		 

    NYSED SKILLS
    		 

    ASSESSMENT
     
    Angle Measure in Geometry
    ·   Points, lines and planes
    ·   Angles, angle measures and perpendicular lines
    ·   Pairs of angles
    ·   Triangles and angles
    ·   Triangles with congruent angles     		 
    ·   Study of triangles: classifications of scalene, isosceles, equilateral, acute, obtuse and right; triangular inequality; sum of the measures of angles of a triangle; exterior angle of a triangle, base angles of an isosceles triangle
    ·   Undefined terms: point, line and plane
    ·   Parallel and intersecting lines and perpendicular lines
    ·   Angles: degree measure, right, acute, obtuse, straight, supplementary, complementary, vertical, alternate interior and exteriors and corresponding
    ·   Sum of interior and exterior angles of a polygon     		 
    ·   Teacher-made Tests
     
    Congruence and Transformations
    ·   Geometric figures
    ·   Congruent triangles
    ·   Quadrilaterals
    ·   Line Reflections and Line Symmetry
    ·   Point Reflections and Point Symmetry
    ·   Translations
    ·   Rotations     		 
    ·   Simple closed curves: polygons and circles
    ·   Study of quadrilaterals: classification and properties of parallelograms, rectangles, rhombi, squares and trapezoids
    ·   Intuitive notions of line reflection, translation, rotation and dilation
    ·   Line and point symmetry
    ·   Reflection in a line and in a point; translations
    ·   Comparison of volumes of similar solids     		 
    ·   Teacher-made Tests

     

    TOPICS/SUBTOPICS
     
    		 

    NYSED SKILLS
    		 

    ASSESSMENT
     
    Ratio and Proportion
    ·   Ratio
    ·   Using a ratio to express a rate
    ·   Verbal problems involving ratio
    ·   Proportion
    ·   Direct variation
    ·   Percent and percentage problems
    ·   Similar polygons
    ·   Similar triangles
    ·   Dilations
    ·   Ratio of perimeters and ratio of areas of similar polygons     		 
    ·   Ratio
    ·   Proportion
    ·   Scale drawings
    ·   Percent
    ·   Similar figures
    ·   Similar polygons: ratio of perimeters and areas
    ·   Direct variation
    ·   Comparison of triangles: congruence and similarity
    ·   Dilations     		 
    ·   Teacher-made Tests
     
    Graphing Linear Functions and Equations
    ·   Solutions of open sentences in two variables
    ·   Graphing linear functions using their solutions
    ·   Graphing a line parallel of an axis
    ·   The slope of a line
    ·   The slope-intercept form of a linear equation
    ·   Graphing linear functions using their slopes
    ·   Writing an equation of a line
    ·   Graphing Direct Variation
    ·   Graphing first-degree inequalities in two variables     		 
    ·   Graphs of linear relations: slope and intercept
    ·   Graphic solution of systems of linear equations and inequalities     		 
    ·   Teacher-made Tests

     

    TOPICS/SUBTOPICS
     
    		 

    NYSED SKILLS
    		 

    ASSESSMENT
     
    Systems of Linear Open Sentences in Two Variables
    ·   Using a graph to solve a system of linear equations
    ·   Using addition to solve a system of linear equations
    ·   Using substitution to solve a system of linear equations
    ·   Using systems of equations to solve verbal problems
    ·   Graphing the solution set of a system of inequalities     		 
    ·   Algebraic solution of systems of linear equations, inequalities, substitution method and addition-substraction method
    ·   Solve systems of linear equation and inequalities
    ·   Systems of linear equations and inequalities     		 
    ·   Teacher-made Tests
     
    Statistics
    ·   Collecting data
    ·   Organizing data
    ·   The Histogram
    ·   The Mean, the Median and the Mode
    ·   Measures of Central Tendency and Grouped Data
    ·   Quartiles, Percentiles and Cumulative Frequency     		 
    ·   Collecting and organizing data: sampling, tally, chart, frequency table, circle graphs, broken line graphs, frequency histogram, box and whisker plots, scatter ;plots, stem and leaf plots, and cumulative frequency histogram
    ·   Measures of central tendency: mean, median, mode
    ·   Quartiles and percentiles     		 
    ·   Teacher-made Tests

     

    TOPICS/SUBTOPICS
     
    		 

    NYSED SKILLS
    		 

    ASSESSMENT
     
    Special Products and Factors
    ·   Factors and factoring
    ·   Common monomial factors
    ·   The square of a monomial
    ·   Multiplying the sum and difference of two terms
    ·   Factoring the difference of two squares
    ·   Multiplying binomials
    ·   Factoring trinomials
    ·   Factoring a polynomial completely     		 
    ·   Distributive field property as related to factoring
    ·   Prime factorization
    ·   Factoring: common monomials, binomial factors of trinomials
    ·   Difference of two squares     		 
    ·   Teacher-made Tests
     
    Algebraic Fractions, and Equations and Inequalities Involving Fractions
    ·   The meaning of an algebraic fraction
    ·   Reducing fractions to lowest terms
    ·   Multiplying fractions
    ·   Dividing Fractions
    ·   Adding or Subtracting fractions that have the same denominator
    ·   Adding or Subtracting fractions that have different denominators
    ·   Solving equations containing fractional co-efficients
    ·   Solving inequalities containing fractional co-efficients
    ·   Solving fractional equations
    ·   Equations and formulas involving several variables     		 
    ·   Simplification of fractions; combining like terms and fractions with like denominators; equivalent fractions with unlike denominators and multiplication of fractions
    ·   Division of fractions
    ·   Solve linear equations with integral, fraction or decimal co-efficients     		 
    ·   Teacher-made Tests

     

    TOPICS/SUBTOPICS
     
    		 

    NYSED SKILLS
    		 

    ASSESSMENT
     
    Operations with Radicals
    ·   Radicals and the rational numbers
    ·   Radicals and the irrational numbers
    ·   Finding the principal square root of a monomial
    ·   Simplifying a square-root radical
    ·   Addition and subtraction of radicals
    ·   Multiplication of square-root radicals
    ·   Division of square-root radicals
          		 
    ·   Rational approximations of irrational numbers
    ·   Operations with radicals: simplification, multiplication and division, and addition and subtraction
    ·   Real numbers including irrational numbers such as non-repeating decimals, irrational roots and pi
          		 
    ·   Teacher-made Tests
     
    Quadratic Equations
    ·   The standard form of a quadratic equation
    ·   Solving a quadratic equation by factoring
    ·   Solving incomplete quadratic equations
    ·   The Theorem of Pythagoras
    ·   Using quadratic equations to solve problems     		 
    ·   Pythagorean Theorem
    ·   Distributive and associative field properties as related to the solution of quadratic equations
    ·   Techniques for solving factorable quadratic equations
    ·   Solve factorable quadratic equations     		 
    ·   Teacher-made Tests
     
    Logic
    ·   Sentences, statements and truth values
    ·   Negations and symbols
    ·   Conjunctions
    ·   Disjunctions
    ·   Conditionals
    ·   Compound statements and truth values
    ·   Compound sentences and truth tables
    ·   Biconditionals
    ·   Inverses, converses and contrapositives
    ·   Drawing conclusions     		 
    ·   Truth value of compound sentences (conjunction, disjunction, conditional, related conditionals such as converse, inverse and contrapositive and biconditional)
    ·   Truth value of simple sentences (closed sentences, open sentences with replacement set and solution set, negations)
    ·   Truth value compound sentences     		 
    ·   Teacher-made Tests
     
    TOPICS/SUBTOPICS
     
    		 

    NYSED SKILLS
    		 

    ASSESSMENT
     
    Probability
    ·   Empirical probability
    ·   Theoretical probability
    ·   Evaluating simple probabilities
    ·   The probability of (A and B)
    ·   The Probability of (A or B)
    ·   The probability of (not A); probability as a sum
    ·   The counting principle and sample spaces
    ·   Probabilities and the counting principle
    ·   Probabilities with two or more activities
    ·   Permutations
    ·   More about permutations
    ·   Probability with replacement; probability with replacement     		 
    ·   Sample spaces: list of ordered pairs of
    n-tuples, tree diagrams
    ·   Theoretical vs empirical probability
    ·   Single and compound events
    ·   Problems involving and and or
    ·   Probability of the complement of an event
    ·   Mutually exclusive and independent events
    ·   Counting principle
    ·   Sample space
    ·   Probability distribution
    ·   Probability of the complement of an event
    ·   Factorial notation
    ·   Permutations: nPn and nPc     		 
    Teacher-made Tests

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