Scope and Sequence - Upper Adolescent
Math, Upper Adolescent Unit 1 Money Basics Exponents ● Exponents as repeated Multiplication (A2.1) ● Multiplying and Dividing Exponential Expressions (A2.1) ● Exponential Expressions to Powers ● Fractional exponents ● Radicals Combining like terms (A2.1) ● Combining like objects ● Combining like terms algebraically Factoring (A2.1) ● Distributive property ● Factoring Trinomials ● Perfect Square Trinomials ● Sum and Difference of squares Ratios, proportions and similarity Standard Deviation Transformations (A2.6) ● Parent graphs ● Vertical translations of graphs ● Horizontal translations of graphs ● Transforming graphs by combining translations ● Transforming graphs by a scaling factor ● Combining all three types of transformations Sequences (A2.2)
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Finding patterns in sequences Arithmetic sequences Summation notation Geometric sequences Series and sequences
Masters Probability and Statistics ● Analyze numerical characteristics of univariate data sets (PS.2) ● Methods of data collection in a census, sample survey, experiment, and observational study (PS.8) ● Plan and conduct a survey (PS.9) ● Develop, interpret, and apply the binomial probability distribution for discrete random variables (PS.13) ● Simulate probability distributions (PS.14) ● Identify random variables as independent or dependent and find the mean and standard deviations (PS.15)
Unit 2 Architecture Basics Factoring (A2.1) ● Distributive property ● Factoring Trinomials ● Perfect Square Trinomials
Absolute Value (A2.4) ● Linear Equations ● Linear Inequalities ● Graphing Equations with Absolute Values Binomial Theorem ● Binomial Square and Cube ● Higher powers ● Binomial theorem Proving lines parallel (G.3) Introduction to triangles (G.5) Introduction to polygons (G.9, G.10) Triangle congruence (G.6) Using the Pythagorean theorem (G.8) Surface area and volume (G.13, G.14) ● Prism ● Cylinder ● Pyramid ● Cone ● Hemisphere ● Similar Solids Triangle congruence (G.6) Using the Pythagorean theorem (G.8) Ratios, Proportions and similarity (G.7) Chords, secants, and tangents (G.11, G.12) Sequences (A2.2)
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Finding patterns in sequences Arithmetic sequences Summation notation Geometric sequences Series and sequences
Functions ● Function properties (A2.6) ● Domain and range (A2.7) ● Composition of functions (A2.7) ● Inverses (A2.7)
Masters Trigonometry ● Sine, cosine, tangent, cotangent, secant, and cosecant (T.1) ● Values of trigonometric and inverse trigonometric function (with and without calculater) (T.2, T.4) ● Converting degrees and radians (T.3) ● Basic trigonometric identities (T.5) ● Given a trigonometric function, will (T.6) ○ State the domain and the range of the function ○ Determine the amplitude, period, phase shift, vertical shift, and asymptotes ○ Graph the function by using transformations for at least a two-period interval ○ Observe the effect of changing the parameters in a trigonometric function ● Domain and range of the inverse trigonometric functions (T.7) ● Solving trigonometric equations (T.8) ● Creating and solving real-world problems involving triangles (T.9, MA.13)
Unit 3 Science Basics Ratios, Proportions and similarity (G.7)
Absolute Value (A2.4) ● Linear Equations ● Linear Inequalities ● Graphing Equations with Absolute Values Binomial Theorem ● Binomial Square and Cube ● Higher powers ● Binomial theorem Quadratics (A2.5, A2.4) ● Zero property (A2.7) ● Solving quadratic Equations by Factoring (A2.4) ● Completing the Square ● The Quadratic Formula ● The Discriminant ● Graphing Quadratic Equations (A2.7) ● Finding the Vertex from the x-intercepts (A2.7) ● Finding the Vertex through completing the square Using the Pythagorean theorem (G.8) Chords, secants, and tangents (G.11, G.12) Sequences (A2.2) ● Finding patterns in sequences ● Arithmetic sequences ● Summation notation ● Geometric sequences ● Series and sequences Functions ● Function properties (A2.6) ● Domain and range (A2.7) ● Composition of functions (A2.7) ● Inverses (A2.7) Exponential and logarithmic functions ● Exponential equations (A2.6)
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Logarithmic functions (A2.6)
Polynomials ● Polynomial functions (A2.6) ● Graphs of polynomials (A2.6) ● Rational Functions (A2.4) ● Division ● Roots and Zeros (A2.8)
Masters Precalculus ● Identify the characteristics of polynomial and rational functions (MA.1) ● Apply compositions of functions and inverses of functions to real-world situations (MA.2) ● Investigate and describe the continuity of functions (MA.3) ● Binomial Theorem, the formula for combinations, and Pascal’s Triangle (MA.4) ● Finding the limit of an algebraic function (MA.7) ● Characteristics of exponential and logarithmic functions (MA.9) ● Operations with vectors in the coordinate plane (MA.11) ● Parametric equations (MA.12) ● Matrices
Unit 4 Sports Basics Ratios, Proportions and similarity (G.7) Exponents ● Exponents as repeated Multiplication (A2.1) ● Multiplying and Dividing Exponential Expressions (A2.1) ● Exponential Expressions to Powers ● Fractional exponents ● Radicals Combining like objects and terms (A2.1) Factoring (A2.1) ● Distributive property ● Factoring Trinomials ● Perfect Square Trinomials ● Difference of Squares ● Sum and Difference of squares Quadratics (A2.5, A2.4) ● Zero property (A2.7) ● Solving quadratic Equations by Factoring (A2.4) ● Completing the Square ● The Quadratic Formula ● The Discriminant ● Graphing Quadratic Equations (A2.7) ● Finding the Vertex from the x-intercepts (A2.7) ● Finding the Vertex through completing the square Sequences (A2.2) ● Finding patterns in sequences ● Arithmetic sequences ● Summation notation ● Geometric sequences ● Series and sequences Transformations (A2.6) ● Parent graphs ● Vertical translations of graphs ● Horizontal translations of graphs ● Transforming graphs by combining translations ● Transforming graphs by a scaling factor ● Combining all three types of transformations
Functions ● Function properties (A2.6) ● Domain and range (A2.7) ● Composition of functions and Inverses functions(A2.7) Triangle congruence (G.6) Using the Pythagorean theorem (G.8) Ratios, Proportions and similarity (G.7) Chords, secants, and tangents (G.11, G.12)
Masters Trigonometry ● Sine, cosine, tangent, cotangent, secant, and cosecant (T.1) ● Values of trigonometric and inverse trigonometric function (with and without calculater) (T.2, T.4) ● Converting degrees and radians (T.3) ● Basic trigonometric identities (T.5) ● Given a trigonometric function, will (T.6) ○ State the domain and the range of the function ○ Determine the amplitude, period, phase shift, vertical shift, and asymptotes ○ Graph the function by using transformations for at least a two-period interval ○ Observe the effect of changing the parameters in a trigonometric function ● Domain and range of the inverse trigonometric functions (T.7) ● Solving trigonometric equations (T.8) ● Creating and solving real-world problems involving triangles (T.9, MA.13) Precalculus ● Identify the characteristics of polynomial and rational functions (MA.1) ● Apply compositions of functions and inverses of functions to real-world situations (MA.2) ● Investigate and describe the continuity of functions (MA.3) ● Binomial Theorem, the formula for combinations, and Pascal’s Triangle (MA.4) ● Finding the limit of an algebraic function (MA.7) ● Characteristics of exponential and logarithmic functions (MA.9) ● Operations with vectors in the coordinate plane (MA.11) ● Parametric equations (MA.12) ● Matrices
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Finding patterns in sequences Arithmetic sequences Summation notation Geometric sequences Series and sequences
Masters Probability and Statistics ● Analyze numerical characteristics of univariate data sets (PS.2) ● Methods of data collection in a census, sample survey, experiment, and observational study (PS.8) ● Plan and conduct a survey (PS.9) ● Develop, interpret, and apply the binomial probability distribution for discrete random variables (PS.13) ● Simulate probability distributions (PS.14) ● Identify random variables as independent or dependent and find the mean and standard deviations (PS.15)
Unit 2 Architecture Basics Factoring (A2.1) ● Distributive property ● Factoring Trinomials ● Perfect Square Trinomials
Absolute Value (A2.4) ● Linear Equations ● Linear Inequalities ● Graphing Equations with Absolute Values Binomial Theorem ● Binomial Square and Cube ● Higher powers ● Binomial theorem Proving lines parallel (G.3) Introduction to triangles (G.5) Introduction to polygons (G.9, G.10) Triangle congruence (G.6) Using the Pythagorean theorem (G.8) Surface area and volume (G.13, G.14) ● Prism ● Cylinder ● Pyramid ● Cone ● Hemisphere ● Similar Solids Triangle congruence (G.6) Using the Pythagorean theorem (G.8) Ratios, Proportions and similarity (G.7) Chords, secants, and tangents (G.11, G.12) Sequences (A2.2)
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Finding patterns in sequences Arithmetic sequences Summation notation Geometric sequences Series and sequences
Functions ● Function properties (A2.6) ● Domain and range (A2.7) ● Composition of functions (A2.7) ● Inverses (A2.7)
Masters Trigonometry ● Sine, cosine, tangent, cotangent, secant, and cosecant (T.1) ● Values of trigonometric and inverse trigonometric function (with and without calculater) (T.2, T.4) ● Converting degrees and radians (T.3) ● Basic trigonometric identities (T.5) ● Given a trigonometric function, will (T.6) ○ State the domain and the range of the function ○ Determine the amplitude, period, phase shift, vertical shift, and asymptotes ○ Graph the function by using transformations for at least a two-period interval ○ Observe the effect of changing the parameters in a trigonometric function ● Domain and range of the inverse trigonometric functions (T.7) ● Solving trigonometric equations (T.8) ● Creating and solving real-world problems involving triangles (T.9, MA.13)
Unit 3 Science Basics Ratios, Proportions and similarity (G.7)
Absolute Value (A2.4) ● Linear Equations ● Linear Inequalities ● Graphing Equations with Absolute Values Binomial Theorem ● Binomial Square and Cube ● Higher powers ● Binomial theorem Quadratics (A2.5, A2.4) ● Zero property (A2.7) ● Solving quadratic Equations by Factoring (A2.4) ● Completing the Square ● The Quadratic Formula ● The Discriminant ● Graphing Quadratic Equations (A2.7) ● Finding the Vertex from the x-intercepts (A2.7) ● Finding the Vertex through completing the square Using the Pythagorean theorem (G.8) Chords, secants, and tangents (G.11, G.12) Sequences (A2.2) ● Finding patterns in sequences ● Arithmetic sequences ● Summation notation ● Geometric sequences ● Series and sequences Functions ● Function properties (A2.6) ● Domain and range (A2.7) ● Composition of functions (A2.7) ● Inverses (A2.7) Exponential and logarithmic functions ● Exponential equations (A2.6)
●
Logarithmic functions (A2.6)
Polynomials ● Polynomial functions (A2.6) ● Graphs of polynomials (A2.6) ● Rational Functions (A2.4) ● Division ● Roots and Zeros (A2.8)
Masters Precalculus ● Identify the characteristics of polynomial and rational functions (MA.1) ● Apply compositions of functions and inverses of functions to real-world situations (MA.2) ● Investigate and describe the continuity of functions (MA.3) ● Binomial Theorem, the formula for combinations, and Pascal’s Triangle (MA.4) ● Finding the limit of an algebraic function (MA.7) ● Characteristics of exponential and logarithmic functions (MA.9) ● Operations with vectors in the coordinate plane (MA.11) ● Parametric equations (MA.12) ● Matrices
Unit 4 Sports Basics Ratios, Proportions and similarity (G.7) Exponents ● Exponents as repeated Multiplication (A2.1) ● Multiplying and Dividing Exponential Expressions (A2.1) ● Exponential Expressions to Powers ● Fractional exponents ● Radicals Combining like objects and terms (A2.1) Factoring (A2.1) ● Distributive property ● Factoring Trinomials ● Perfect Square Trinomials ● Difference of Squares ● Sum and Difference of squares Quadratics (A2.5, A2.4) ● Zero property (A2.7) ● Solving quadratic Equations by Factoring (A2.4) ● Completing the Square ● The Quadratic Formula ● The Discriminant ● Graphing Quadratic Equations (A2.7) ● Finding the Vertex from the x-intercepts (A2.7) ● Finding the Vertex through completing the square Sequences (A2.2) ● Finding patterns in sequences ● Arithmetic sequences ● Summation notation ● Geometric sequences ● Series and sequences Transformations (A2.6) ● Parent graphs ● Vertical translations of graphs ● Horizontal translations of graphs ● Transforming graphs by combining translations ● Transforming graphs by a scaling factor ● Combining all three types of transformations
Functions ● Function properties (A2.6) ● Domain and range (A2.7) ● Composition of functions and Inverses functions(A2.7) Triangle congruence (G.6) Using the Pythagorean theorem (G.8) Ratios, Proportions and similarity (G.7) Chords, secants, and tangents (G.11, G.12)
Masters Trigonometry ● Sine, cosine, tangent, cotangent, secant, and cosecant (T.1) ● Values of trigonometric and inverse trigonometric function (with and without calculater) (T.2, T.4) ● Converting degrees and radians (T.3) ● Basic trigonometric identities (T.5) ● Given a trigonometric function, will (T.6) ○ State the domain and the range of the function ○ Determine the amplitude, period, phase shift, vertical shift, and asymptotes ○ Graph the function by using transformations for at least a two-period interval ○ Observe the effect of changing the parameters in a trigonometric function ● Domain and range of the inverse trigonometric functions (T.7) ● Solving trigonometric equations (T.8) ● Creating and solving real-world problems involving triangles (T.9, MA.13) Precalculus ● Identify the characteristics of polynomial and rational functions (MA.1) ● Apply compositions of functions and inverses of functions to real-world situations (MA.2) ● Investigate and describe the continuity of functions (MA.3) ● Binomial Theorem, the formula for combinations, and Pascal’s Triangle (MA.4) ● Finding the limit of an algebraic function (MA.7) ● Characteristics of exponential and logarithmic functions (MA.9) ● Operations with vectors in the coordinate plane (MA.11) ● Parametric equations (MA.12) ● Matrices
