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GRADE CWR

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and Examples Students are expected to: PO 2. Understand, analyze, and apply vertex-edge graphs to model and solve problems related to paths, circuits, networks, and relationships among a finite number of elements, in real-world and abstract settings. Connections: MCWR-S2C4-01, MCWR- S2C4-03, MCWR-S2C4-04, SSHS-S4C1- 03 MCWR-S5C2-01. Analyze a problem situation, determine the question(s) to be answered, organize given information, determine how to represent the problem, and identify

15 0 http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeCWR.pdf#page=15 www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

and Examples Students are expected to: PO 2. Understand, analyze, and apply vertex-edge graphs to model and solve problems related to paths, circuits, networks, and relationships among a finite number of elements, in real-world and abstract settings. Connections: MCWR-S2C4-01, MCWR- S2C4-03, MCWR-S2C4-04, SSHS-S4C1- 03 MCWR-S5C2-01. Analyze a problem situation, determine the question(s) to be answered, organize given information, determine how to represent the problem, and identify

16 0 http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeCWR.pdf#page=16 www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

Arizona Mathematics Standard Articulated by Grade Level The bulleted items within a performance objective indicate the specific content to be taught. The performance objectives highlighted in italics have been identified as core to an Algebra II course. Explanations and Examples Updated 4.06.09 CWR (Grades 11 and 12) Arizona Department of Education: Standards and Assessment Division 16 Approved 6.24.08 Performance Objectives Process Integration Explanations

www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

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Microsoft Word - mathsol2009.doc

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will be used. *DM.4 The student will apply algorithms, such as Kruskal’s, Prim’s, or Dijkstra’s, relating to trees, networks, and paths. Appropriate technology will be used to determine the number of possible solutions and generate solutions when a feasible number exists. *DM.5 The student will use algorithms to schedule tasks in order to determine a minimum project time. The algorithms will include critical path analysis, the list-processing algorithm, and student-created algorithms. *DM.6 The student

45 0 http://www.doe.virginia.gov/VDOE/Superintendent/Sols/mathsol2009.pdf#page=45 www.doe.virginia.gov/VDOE/Superintendent/Sols/mathsol2009.pdf#page=45

will be used. *DM.4 The student will apply algorithms, such as Kruskal’s, Prim’s, or Dijkstra’s, relating to trees, networks, and paths. Appropriate technology will be used to determine the number of possible solutions and generate solutions when a feasible number exists. *DM.5 The student will use algorithms to schedule tasks in order to determine a minimum project time. The algorithms will include critical path analysis, the list-processing algorithm, and student-created algorithms. *DM.6 The student

www.doe.virginia.gov/VDOE/Superintendent/Sols/mathsol2009.pdf#page=45

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GRADE HS

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algorithm for equivalence is analyzing the multiple ways to find the slope of a line. • An example for analyzing an algorithm for validity is comparing an algorithm for finding the distance between two points using the distance formula, to an algorithm finding the square root of the sum of the horizontal distance and vertical distance between two points on a coordinate grid. 22 21 21 ()()dxx yy=−+−

50 0 http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeHS.pdf#page=50 www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

algorithms to solve problems. Students deepen these analysis skills in grades 11 and 12. Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 1. Select an algorithm that explains a particular mathematical process; determine the purpose of a simple mathematical algorithm. Connections: MHS-S2C1-02, MHS- S2C3-01, MHS-S2C3-02, MHS-S2C3-03, MHS-S3C3-12, MHS-S3C3-13, MHS- S3C4-01, MHS-S4C1-10, MHS-S4C1-11, MHS-S4C3-01, MHS-S4C3-02, MHS- S4C3-03, MHS-S4C4

51 0 http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeHS.pdf#page=51 www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

algorithm for equivalence is analyzing the multiple ways to find the slope of a line. • An example for analyzing an algorithm for validity is comparing an algorithm for finding the distance between two points using the distance formula, to an algorithm finding the square root of the sum of the horizontal distance and vertical distance between two points on a coordinate grid. 22 21 21 ()()dxx yy=−+−

www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

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STANDARDS.05

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54 PERFORMANCE STANDARDS (Grade Level Expectations) 55PERFORMANCE STANDARDS (Grade Level Expectations) *Assumes a variety of text and increasing complexity READING GRADES 7—10 GRADE 7 GRADE 8 GRADE 9 GRADE 10 The student analyzes and evaluates conventions and techniques of genres by [10] 4.5.1 Analyzing the characteristics and the effect on the reader of nonfiction and the four major structural genres: poetry, drama, novel, short story* [10] 4.5.2 Analyzing the use of literary devices appropriate to

19 0 http://www.eed.state.ak.us/standards/pdf/standards.pdf#page=19 www.eed.state.ak.us/standards/pdf/standards.pdf#page=19

18 ALASKA CONTENT STANDARDS 19 A student who meets the content standard should: 1) know that the need for people to exchange goods, services, and ideas creates population centers, cultural interaction, and transportation and communication links; 2) explain how and why human networks, including networks for communications and for transportation of people and goods, are linked globally; 3) interpret population characteristics and distributions; 4) analyze how changes in technology, transportation

55 0 http://www.eed.state.ak.us/standards/pdf/standards.pdf#page=55 www.eed.state.ak.us/standards/pdf/standards.pdf#page=55

[3] 1.7.1 Distinguishing between fiction/ nonfiction, prose/poetry, short story/ drama (L) [3] 1.7.2 Identifying use of dialogue or rhyme in common forms of text The student analyzes content and structure of genres by [4] 2.7.1 Identifying the four major genres of fiction: short story, drama (plays), novel, and poetry (L) [4] 2.7.2 Identifying or explaining the characteristics of fiction and nonfiction (L) [4] 2.7.3 Identifying use of literary elements and devices (i.e., dialogue, rhyme, alliteration

56 0 http://www.eed.state.ak.us/standards/pdf/standards.pdf#page=56 www.eed.state.ak.us/standards/pdf/standards.pdf#page=56

54 PERFORMANCE STANDARDS (Grade Level Expectations) 55PERFORMANCE STANDARDS (Grade Level Expectations) *Assumes a variety of text and increasing complexity READING GRADES 7—10 GRADE 7 GRADE 8 GRADE 9 GRADE 10 The student analyzes and evaluates conventions and techniques of genres by [10] 4.5.1 Analyzing the characteristics and the effect on the reader of nonfiction and the four major structural genres: poetry, drama, novel, short story* [10] 4.5.2 Analyzing the use of literary devices appropriate to

www.eed.state.ak.us/standards/pdf/standards.pdf#page=56

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Core Content For Mathematics Assessment

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to-text - e.g., novel, short story, song, film, website, etc.). RD-O7-4.0.1 Students will connect information from a passage to students’ lives (text-to-self), real world issues (text-to-world) and other texts (text-to-text - e.g., novel, short story, song, film, website, etc.). RD-O8-4.0.1 Students will connect information from a passage to students’ lives (text-to-self), real world issues (text-to-world) and other texts (text-to-text - e.g., novel, short story, song, film, website, etc

146 0 http://www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=146 www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=146

text - e.g., novel, short story, song, film, website, etc.). RD-04-4.0.1 Students will connect information from a passage to students’ lives (text-to-self), real world issues (text-to-world) or other texts (text- to-text - e.g., novel, short story, song, film, website, etc.). RD-05-4.0.1 Students will connect information from a passage to students’ lives (text-to-self), real world issues (text-to-world) or other texts (text- to-text - e.g., novel, short story, song, film, website, etc.).

154 0 http://www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=154 www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=154

to-text - e.g., novel, short story, song, film, website, etc.). RD-O7-4.0.1 Students will connect information from a passage to students’ lives (text-to-self), real world issues (text-to-world) and other texts (text-to-text - e.g., novel, short story, song, film, website, etc.). RD-O8-4.0.1 Students will connect information from a passage to students’ lives (text-to-self), real world issues (text-to-world) and other texts (text-to-text - e.g., novel, short story, song, film, website, etc

www.education.ky.gov/users/OTL/CCA%204%201%20FINAL/CCA_41.pdf#page=154

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GRADE 8

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Integration Explanations and Examples Students are expected to: PO 1. Create an algorithm to solve problems involving indirect measurements, using proportional reasoning, dimensional analysis, and the concepts of density and rate. Connections: M08-S1C3-01, M08-S3C2- 05, M08-S4C4-01 M08-S5C2-05. Apply a previously used problem-solving strategy in a new context. M08-S5C2-08. Describe when to use proportional reasoning to solve a problem. Dimensional analysis uses ratios to simplify the

30 0 http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade8.pdf#page=30 www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

Coordinate Geometry Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands. In Grade 8, students develop algorithms and investigate midpoint and distance calculations using the coordinate plane. Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 1. Make and test a conjecture about how to find the midpoint between any two points in the coordinate plane

33 0 http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade8.pdf#page=33 www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

Integration Explanations and Examples Students are expected to: PO 1. Create an algorithm to solve problems involving indirect measurements, using proportional reasoning, dimensional analysis, and the concepts of density and rate. Connections: M08-S1C3-01, M08-S3C2- 05, M08-S4C4-01 M08-S5C2-05. Apply a previously used problem-solving strategy in a new context. M08-S5C2-08. Describe when to use proportional reasoning to solve a problem. Dimensional analysis uses ratios to simplify the

www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

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GRADE 5

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Arizona Mathematics Standard Articulated by Grade Level The bulleted items within a performance objective indicate the specific content to be taught. Explanations and Examples Updated 1.19.09 Grade 5 Arizona Department of Education: Standards and Assessment Division 29 Approved 6.24.08 Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 2. Develop an algorithm or formula to calculate areas and perimeters of

9 0 http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade5.pdf#page=9 www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

and the study of graphs. This prepares students for the study of discrete functions as well as to make valid inferences, decisions, and arguments. Discrete mathematics is a branch of mathematics that is widely used in business and industry. Combinatorics is the mathematics of systematic counting. Vertex-edge graphs are used to model and solve problems involving paths, networks, and relationships among a finite number of objects. Concept 1: Data Analysis (Statistics) Understand and apply data

29 0 http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade5.pdf#page=29 www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

Arizona Mathematics Standard Articulated by Grade Level The bulleted items within a performance objective indicate the specific content to be taught. Explanations and Examples Updated 1.19.09 Grade 5 Arizona Department of Education: Standards and Assessment Division 29 Approved 6.24.08 Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 2. Develop an algorithm or formula to calculate areas and perimeters of

www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...

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or develop algorithms using modular arithmetic or congruence relations such as creating error detection codes, calculating greatest common factor, and solving simple coin-change problems. D.4 Graph theory: Understand how graphs of vertices joined by edges can model relationships and be used to solve a wide variety of problems. D.4.1 Use graphs to model and solve problems such as shortest paths, vertex coloring, critical paths, routing, and scheduling problems. D.4.2

4 0 http://www.ode.state.or.us/teachlearn/real/documents/maaks.pdf#page=4 www.ode.state.or.us/teachlearn/real/documents/maaks.pdf#page=4

or develop algorithms using modular arithmetic or congruence relations such as creating error detection codes, calculating greatest common factor, and solving simple coin-change problems. D.4 Graph theory: Understand how graphs of vertices joined by edges can model relationships and be used to solve a wide variety of problems. D.4.1 Use graphs to model and solve problems such as shortest paths, vertex coloring, critical paths, routing, and scheduling problems. D.4.2

5 0 http://www.ode.state.or.us/teachlearn/real/documents/maaks.pdf#page=5 www.ode.state.or.us/teachlearn/real/documents/maaks.pdf#page=5

interest. D.7.2 Use finite differences to solve problems and to find explicit formulas for recurrence relations. D.7.3 Use mathematical induction to prove recurrence relations and concepts in number theory such as sums of infinite integer series, divisibility statements, and parity statements. D.7.4 Use mathematical induction to analyze the validity of an iterative algorithm. D.7.5 Describe arithmetic and geometric sequences recursively. D.7.6 Use understanding of

www.ode.state.or.us/teachlearn/real/documents/maaks.pdf#page=4

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CONTENts.PDF

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Content Standard 10: Discrete Mathematics Students will use the concepts and processes of discrete mathematics to analyze and model a variety of real-world situations that involve recurring relationships, sequences, networks, combinations and permutations. Educational experiences in Grades K-4 will assure that students: • classify data according to attributes; • solve simple counting problems; • use diagrams and models of simple networks that represent everyday situations; • identify and

5 0 http://www.sde.ct.gov/sde/lib/sde/PDF/DEPS/Career/STC/contents_standards.pdf#page=5 www.sde.ct.gov/sde/lib/sde/PDF/DEPS/Career/STC/contents_standards.pdf#pag...

and share examples of events from the novel that illustrate inconsistencies between characters’ words and actions. • interpret the text by using prior knowledge and experiences; K-4: Students will use what they know to identify or infer important characters, settings, themes, events, ideas, relationships or details within a work. Example: Students read Encyclopedia Brown, then use their experience to role play a scene in which Encyclopedia solves a problem for a character from another story

9 0 http://www.sde.ct.gov/sde/lib/sde/PDF/DEPS/Career/STC/contents_standards.pdf#page=9 www.sde.ct.gov/sde/lib/sde/PDF/DEPS/Career/STC/contents_standards.pdf#pag...

family’s life had been like before the events described in the novel, supporting their inferences with references to the novel. 9-12: Students will use the literary elements of a text (theme, symbolism, imagery, conflict, etc.) to draw conclusions about a text. Example: Students meet in groups to share their interpretations of the symbolism in Maya Angelou’s poem, “Caged Bird,” then report the group’s findings to the class. K-12 PERFORMANCE STANDARDS • understand that a single text may elicit a

32 0 http://www.sde.ct.gov/sde/lib/sde/PDF/DEPS/Career/STC/contents_standards.pdf#page=32 www.sde.ct.gov/sde/lib/sde/PDF/DEPS/Career/STC/contents_standards.pdf#pag...

Content Standard 10: Discrete Mathematics Students will use the concepts and processes of discrete mathematics to analyze and model a variety of real-world situations that involve recurring relationships, sequences, networks, combinations and permutations. Educational experiences in Grades K-4 will assure that students: • classify data according to attributes; • solve simple counting problems; • use diagrams and models of simple networks that represent everyday situations; • identify and

www.sde.ct.gov/sde/lib/sde/PDF/DEPS/Career/STC/contents_standards.pdf#pag...

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