iSEEK - Education

a conic, the ratio of the distance of a point from a fixed point to its distance from a fixed line End Behavior A reference to the graph of a polynomial function as rising or falling to the right and rising or falling to the left Exponential Functions A function in which variable(s) occur in exponent(s) Finite Sequence A finite sequence with n terms is a function whose domain is the set of integers {1, 2, 3, …, n} Finite Series The indicted sum of a finite sequence Geometric Sequence A

12 0 http://arkansased.org/teachers/pdf/precalculus.pdf#page=12 arkansased.org/teachers/pdf/precalculus.pdf#page=12

a conic, the ratio of the distance of a point from a fixed point to its distance from a fixed line End Behavior A reference to the graph of a polynomial function as rising or falling to the right and rising or falling to the left Exponential Functions A function in which variable(s) occur in exponent(s) Finite Sequence A finite sequence with n terms is a function whose domain is the set of integers {1, 2, 3, …, n} Finite Series The indicted sum of a finite sequence Geometric Sequence A

arkansased.org/teachers/pdf/precalculus.pdf#page=12

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Core Content For Mathematics Assessment

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CCA 4.1 Middle School Science AUGUST 2006 Bold – State Assessment Content Standard 190 Italics – Supporting Content Standard SC-08-1.1.4 Students will describe interactions which cause the movement of each element among the solid Earth, oceans, atmosphere and organisms (biogeochemical cycles). Earth is a system containing essentially a fixed amount of each stable chemical atom or element that can exist in several different reservoirs. The interactions within the earth system cause the

84 0 http://www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=84 www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=84

an explicit rule for the nth term of a geometric sequence. MA-HS-1.3.4 Students will recognize and solve problems that can be modeled using a finite geometric series, such as home mortgage problems and other compound interest problems. Ratios and Proportional Reasoning MA-HS-1.4.1 Students will apply ratios, percents and proportional reasoning to solve real-world problems (e.g., those involving slope and rate, percent of increase and decrease) and will explain how slope determines a rate of change in

193 0 http://www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=193 www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=193

CCA 4.1 Middle School Science AUGUST 2006 Bold – State Assessment Content Standard 190 Italics – Supporting Content Standard SC-08-1.1.4 Students will describe interactions which cause the movement of each element among the solid Earth, oceans, atmosphere and organisms (biogeochemical cycles). Earth is a system containing essentially a fixed amount of each stable chemical atom or element that can exist in several different reservoirs. The interactions within the earth system cause the

www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=193

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Microsoft Word - mathsol2009.doc

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this course serves as appropriate preparation for a calculus course. Graphing calculators, computers, and other appropriate technology tools will be used to assist in teaching and learning. Graphing utilities enhance the understanding of realistic applications through modeling and aid in the investigation of functions and their inverses. They also provide a powerful tool for solving and verifying solutions to equations and inequalities. MA.1 The student will investigate and identify the characteristics of

47 0 http://www.doe.virginia.gov/VDOE/Superintendent/Sols/mathsol2009.pdf#page=47 www.doe.virginia.gov/VDOE/Superintendent/Sols/mathsol2009.pdf#page=47

this course serves as appropriate preparation for a calculus course. Graphing calculators, computers, and other appropriate technology tools will be used to assist in teaching and learning. Graphing utilities enhance the understanding of realistic applications through modeling and aid in the investigation of functions and their inverses. They also provide a powerful tool for solving and verifying solutions to equations and inequalities. MA.1 The student will investigate and identify the characteristics of

www.doe.virginia.gov/VDOE/Superintendent/Sols/mathsol2009.pdf#page=47

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VT_04_Math GLEs_pf.indd

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command of conventional English spelling by… • Independently applying spelling knowledge in proofreading and editing of writing • Correctly spelling grade-appropriate, high-frequency words, including homonyms, homophones, and homographs • Correctly spelling grade-appropriate word groups that share a common root (e.g., “inspire,” “respiration,” “conspire,” “perspire”) • Recognizing spelling-meaning connections EXAMPLES: “sign/signal,” “defi ne/defi nition,” “critic/criticize” • Applying conventional and

104 0 http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_writing.pdf#page=104 education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_wri...

W6 Kindergarten Writing Conventions WK:2 In independent writing, students demonstrate command of appropriate English conventions by… No GLE at this grade level WK:3 In independent writing, students demonstrate command of conventional English spelling by… • Using phonemic awareness and letter knowledge to spell independently (phonetic or temporary spelling) and logically represent initial and fi nal consonant sounds Grade 1 Writing Conventions W1:2 In independent writing, students demonstrate command

105 0 http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_writing.pdf#page=105 education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_wri...

W7 Grade 2 Writing Conventions W2:2 In independent writing, students demonstrate command of appropriate English conventions by… • Using capital letters for the beginning of sentences and names • Using correct end punctuation in simple sentences (e.g., period) W2:3 In independent writing, students demonstrate command of conventional English spelling by… • Correctly spelling grade-appropriate, high-frequency words • Correctly spelling past tense (three sounds for -ed) and plural endings (-s and -es

106 0 http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_writing.pdf#page=106 education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_wri...

structures W–4–9.4 W4:3 In independent writing, students demonstrate command of conventional English spelling by… • Applying spelling knowledge in proofreading and editing of writing • Correctly spelling grade-appropriate, high-frequency words and recognizing syllables and affi x patterns/rules that are characteristic of the English spelling system EXAMPLES: consonant doubling, change y to i, drop silent e, spelling rules for affi xes W–4–9.5 • Using within-word patterns and common syllable patterns to

107 0 http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_writing.pdf#page=107 education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_wri...

W9 Grade 6 Writing Conventions W6:2 In independent writing, students demonstrate command of appropriate English conventions by… • Applying rules of standard English usage to correct grammatical errors EXAMPLES: subject-verb agreement, nonstandard usage, irregular plurals, sentence fragments and run-ons • Applying basic capitalization rules • Using punctuation to clarify meaning W6:3 In independent writing, students demonstrate command of conventional English spelling by… • Independently applying

108 0 http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_writing.pdf#page=108 education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_wri...

independent writing, students demonstrate command of conventional English spelling by… • Independently applying spelling knowledge in proofreading and editing of writing • Correctly spelling grade-appropriate, high-frequency words and applying conventional spelling patterns/rules EXAMPLES: consonant doubling, consonant patterns, units of meaning—common roots, base words, pre/suffi xes W–7–9.5 • Correctly spelling grade-appropriate word groups that share a common root (e.g., “structure,” “construction

109 0 http://education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_writing.pdf#page=109 education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_wri...

command of conventional English spelling by… • Independently applying spelling knowledge in proofreading and editing of writing • Correctly spelling grade-appropriate, high-frequency words, including homonyms, homophones, and homographs • Correctly spelling grade-appropriate word groups that share a common root (e.g., “inspire,” “respiration,” “conspire,” “perspire”) • Recognizing spelling-meaning connections EXAMPLES: “sign/signal,” “defi ne/defi nition,” “critic/criticize” • Applying conventional and

education.vermont.gov/new/pdfdoc/pubs/grade_expectations/math_reading_wri...

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SBEinsideCovTitleIX.qxd

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describe and use recursively-defined relationships to solve problems. Objective 3.01 Use recursion to model and solve problems. a) Find the sum of a finite sequence. b) Find the sum of an infinite sequence. c) Determine whether a given series converges or diverges. d) Write explicit definitions using iterative processes, including finite differences and arithmetic and geometric formulas. e) Verify an explicit definition with inductive proof.

63 0 http://www.dpi.state.nc.us/docs/curriculum/mathematics/scos/math2003.pdf#page=63 www.dpi.state.nc.us/docs/curriculum/mathematics/scos/math2003.pdf#page=63

describe and use recursively-defined relationships to solve problems. Objective 3.01 Use recursion to model and solve problems. a) Find the sum of a finite sequence. b) Find the sum of an infinite sequence. c) Determine whether a given series converges or diverges. d) Write explicit definitions using iterative processes, including finite differences and arithmetic and geometric formulas. e) Verify an explicit definition with inductive proof.

75 0 http://www.dpi.state.nc.us/docs/curriculum/mathematics/scos/math2003.pdf#page=75 www.dpi.state.nc.us/docs/curriculum/mathematics/scos/math2003.pdf#page=75

Revised 2003 71 Mathematics 4.02 Use recursively-defined functions to model and solve problems. a) Find the sum of a finite sequence. b) Find the sum of an infinite sequence. c) Determine whether a given series converges or diverges. d) Translate between recursive and explicit representations. 4.03 Use the composition and inverse of functions to model and solve problems. 4.04 Use trigonometric and inverse trigonometric functions to model and solve problems. a) Solve using graphs and algebraic properties. b

www.dpi.state.nc.us/docs/curriculum/mathematics/scos/math2003.pdf#page=63

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GRADE HS

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Integration Explanations and Examples Students are expected to: Example: • In finding the diagonal of a square whose perimeter is 24 a student explains that while the original problem contains natural numbers (6 and 24), the use of the Pythagorean theorem dictates the square root of a natural number (72) is calculated, causing the solution to the equation to be an irrational number ( 26 ). PO 2. Sort sets of numbers as finite or infinite, and justify the sort. MHS-S5C2-08. Use inductive reasoning

2 0 http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeHS.pdf#page=2 www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

Integration Explanations and Examples Students are expected to: Example: • In finding the diagonal of a square whose perimeter is 24 a student explains that while the original problem contains natural numbers (6 and 24), the use of the Pythagorean theorem dictates the square root of a natural number (72) is calculated, causing the solution to the equation to be an irrational number ( 26 ). PO 2. Sort sets of numbers as finite or infinite, and justify the sort. MHS-S5C2-08. Use inductive reasoning

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Mathematics Content Standards - Curriculum Frameworks (CA Dept of Education)

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probabilities. 20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers. 21.0 Students apply the method of mathematical induction to prove general state ments about the positive integers. 22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series. 23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series. 24.0 Students solve

55 0 http://www.cde.ca.gov/be/st/ss/documents/mathstandard.pdf#page=55 www.cde.ca.gov/be/st/ss/documents/mathstandard.pdf#page=55

probabilities. 20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers. 21.0 Students apply the method of mathematical induction to prove general state ments about the positive integers. 22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series. 23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series. 24.0 Students solve

62 0 http://www.cde.ca.gov/be/st/ss/documents/mathstandard.pdf#page=62 www.cde.ca.gov/be/st/ss/documents/mathstandard.pdf#page=62

complementation to solve for probabilities of particular events in finite sample spaces. 2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces. 3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses. 4.0 Students are familiar with the standard distributions (normal, binomial, and

63 0 http://www.cde.ca.gov/be/st/ss/documents/mathstandard.pdf#page=63 www.cde.ca.gov/be/st/ss/documents/mathstandard.pdf#page=63

54 GRADES EIGHT THROUGH TWELVE—ADVANCED PLACEMENT PROBABILITY AND STATISTICS Advanced Placement Probability and Statistics This discipline is a technical and in-depth extension of probability and statistics. In particular, mastery of academic content for advanced placement gives students the background to succeed in the Advanced Placement examination in the subject. 1.0 Students solve probability problems with finite sample spaces by using the rules for addition, multiplication, and complementation

www.cde.ca.gov/be/st/ss/documents/mathstandard.pdf#page=55

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Microsoft Word - ALGEBRA III.doc

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Define and discriminate, with and without appropriate technology, between arithmetic and geometric sequences and series SS.4.AIII.3 Solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and series SS.4.AIII.4 Determine, with and without appropriate technology, the n th term of a sequence given a rule or specific terms SS.4.AIII.5 Use, with and without appropriate technology, sequences and series to

6 0 http://arkansased.org/teachers/pdf/algebra3.pdf#page=6 arkansased.org/teachers/pdf/algebra3.pdf#page=6

Define and discriminate, with and without appropriate technology, between arithmetic and geometric sequences and series SS.4.AIII.3 Solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and series SS.4.AIII.4 Determine, with and without appropriate technology, the n th term of a sequence given a rule or specific terms SS.4.AIII.5 Use, with and without appropriate technology, sequences and series to

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Speaking Standard 3

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and multiplication properties of equality • Addition and multiplication properties of inequalities Building upon knowledge and skills gained in preceding grades, by the end of Grade 12, students will: 4.3.12 A. Patterns 1. Use models and algebraic formulas to represent and analyze sequences and series. • Explicit formulas for nth terms • Sums of finite arithmetic series • Sums of finite and infinite geometric series 2. Develop an informal notion of limit. 3. Use inductive reasoning to form

34 0 http://www.nj.gov/education/cccs/2004/s4_math.pdf#page=34 www.nj.gov/education/cccs/2004/s4_math.pdf#page=34

and multiplication properties of equality • Addition and multiplication properties of inequalities Building upon knowledge and skills gained in preceding grades, by the end of Grade 12, students will: 4.3.12 A. Patterns 1. Use models and algebraic formulas to represent and analyze sequences and series. • Explicit formulas for nth terms • Sums of finite arithmetic series • Sums of finite and infinite geometric series 2. Develop an informal notion of limit. 3. Use inductive reasoning to form

www.nj.gov/education/cccs/2004/s4_math.pdf#page=34

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Standard 1: Number and Operation

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for example, 3/4 or .75. Finite decimals, repeating decimals, and mixed numbers all represent rational numbers. Real numbers - All rational and irrational numbers. Real-world problems (also called real-world experiences) - Quantitative problems that arise from a wide variety of human experiences which may take into consideration contributions from various cultures (for example, Mayan or American pioneers), problems from abstract mathematics, and applications to various careers (for example, making

92 0 http://www.dpi.state.nd.us/standard/content/math/math.pdf#page=92 www.dpi.state.nd.us/standard/content/math/math.pdf#page=92

for example, 3/4 or .75. Finite decimals, repeating decimals, and mixed numbers all represent rational numbers. Real numbers - All rational and irrational numbers. Real-world problems (also called real-world experiences) - Quantitative problems that arise from a wide variety of human experiences which may take into consideration contributions from various cultures (for example, Mayan or American pioneers), problems from abstract mathematics, and applications to various careers (for example, making

www.dpi.state.nd.us/standard/content/math/math.pdf#page=92

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