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 GRADE 5
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 16 Approved 6.24.08 St...
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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 16 Approved 6.24.08 Strand 2: Data Analysis, Probability, and Discrete Mathematics Concept 4: Vertex-Edge Graphs Understand and apply vertex-edge graphs. In Grade 5, students continue to develop their
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade5.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. Explanations and Examples Updated 1.19.09 Grade 5 Arizona Department <span class="highlight">of</span> Education: Standards and Assessment Division 16 Approved 6.24.08 Strand 2: Data <span class="highlight">Analysis</span>, Probability, and Discrete Mathematics Concept 4: Vertex-<span class="highlight">Edge</span> Graphs Understand and apply vertex-<span class="highlight">edge</span> graphs. In Grade 5, students continue to develop their
GRADE CWR
Concept 4: Vertex-Edge Graphs Understand and apply vertex-edge graphs. In Grades 11 and 12, students extend their understanding of networks to devise, analyze, and apply algorithms for solving problems related to circuits, shortest paths, minimum weight spanning trees,...
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Concept 4: Vertex-Edge Graphs Understand and apply vertex-edge graphs. In Grades 11 and 12, students extend their understanding of networks to devise, analyze, and apply algorithms for solving problems related to circuits, shortest paths, minimum weight spanning trees, and adjacency matrices. Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 1. Study the following topics related to vertex-edge graphs: Euler circuits, Hamilton circuits, the
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeCWR.pdf#page=14
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Concept 4: Vertex-<span class="highlight">Edge</span> Graphs Understand and apply vertex-<span class="highlight">edge</span> graphs. In Grades 11 and 12, students extend their understanding <span class="highlight">of</span> networks to devise, analyze, and apply algorithms <span class="highlight">for</span> solving problems related to circuits, shortest paths, minimum weight spanning trees, and adjacency matrices. Performance Objectives Process Integration Explanations and Examples Students are expected to: PO 1. Study the following topics related to vertex-<span class="highlight">edge</span> graphs: Euler circuits, Hamilton circuits, the
Speaking Standard 3
shirts and 4 skirts). 4.4.5 D. Discrete Mathematics—Vertex-Edge Graphs and Algorithms 1. Devise strategies for winning simple games (e.g., start with two piles of objects, each of two players in turn removes any number of objects from a single pile, and the...
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shirts and 4 skirts). 4.4.5 D. Discrete Mathematics—Vertex-Edge Graphs and Algorithms 1. Devise strategies for winning simple games (e.g., start with two piles of objects, each of two players in turn removes any number of objects from a single pile, and the person to take the last group of objects wins) and express those strategies as sets of directions. Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will: 4.4.6 A. Data Analysis 1. Collect
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http://www.nj.gov/education/cccs/2004/s4_math.pdf#page=36
www.nj.gov/education/cccs/2004/s4_math.pdf#page=36
mathematical perspectives on everyday phenomena and with important examples <span class="highlight">of</span> how mathematics is used in the modern world. Two important areas <span class="highlight">of</span> discrete mathematics are addressed in this standard; a third area, iteration and recursion, is addressed in Standard 4.3 (Patterns and Algebra). Data <span class="highlight">Analysis</span> (or Statistics). In today’s <span class="highlight">information</span>-based world, students need to be able to read, understand, and interpret data in order to make informed decisions. In the early grades, students should be involved in
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http://www.nj.gov/education/cccs/2004/s4_math.pdf#page=38
www.nj.gov/education/cccs/2004/s4_math.pdf#page=38
describe practical sets <span class="highlight">of</span> directions (e.g., to add two 2-digit numbers). 2. Explore vertex-<span class="highlight">edge</span> graphs • Vertex, <span class="highlight">edge</span> • Path 3. Find the smallest number <span class="highlight">of</span> colors needed to color a map. Building upon knowledge and skills gained in preceding grades, by the end <span class="highlight">of</span> Grade 4, students will: 4.4.4 A. Data <span class="highlight">Analysis</span> 1. Collect, generate, organize, and display data in response to questions, claims, or curiosity. • Data collected from the school environment 2. Read, interpret, construct, analyze
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http://www.nj.gov/education/cccs/2004/s4_math.pdf#page=40
www.nj.gov/education/cccs/2004/s4_math.pdf#page=40
shirts and 4 skirts). 4.4.5 D. Discrete Mathematics—Vertex-<span class="highlight">Edge</span> Graphs and Algorithms 1. Devise strategies <span class="highlight">for</span> winning simple games (e.g., start with two piles <span class="highlight">of</span> objects, each <span class="highlight">of</span> two players in turn removes any number <span class="highlight">of</span> objects from a single pile, and the person to take the last group <span class="highlight">of</span> objects wins) and express those strategies as sets <span class="highlight">of</span> directions. Building upon knowledge and skills gained in preceding grades, by the end <span class="highlight">of</span> Grade 6, students will: 4.4.6 A. Data <span class="highlight">Analysis</span> 1. Collect
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http://www.nj.gov/education/cccs/2004/s4_math.pdf#page=42
www.nj.gov/education/cccs/2004/s4_math.pdf#page=42
shortest network connecting specified sites • Finding the shortest route on a map from one site to another • Finding the shortest circuit on a map that makes a tour <span class="highlight">of</span> specified sites Building upon knowledge and skills gained in preceding grades, by the end <span class="highlight">of</span> Grade 8, students will: 4.4.8 A. Data <span class="highlight">Analysis</span> 1. Select and use appropriate representations <span class="highlight">for</span> sets <span class="highlight">of</span> data, and measures <span class="highlight">of</span> central tendency (mean, median, and mode). • Type <span class="highlight">of</span> display most appropriate <span class="highlight">for</span> given data • Box-and-whisker plot
GRADE HS
find Hamilton paths, and discuss implications for ranking the players in the tournament. In grades 9 and 10, students can expand their initial methods of analysis to now include a matrix method to rank the players in the tournament. Grade 8 Example: • Four players (Dom, N...
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find Hamilton paths, and discuss implications for ranking the players in the tournament. In grades 9 and 10, students can expand their initial methods of analysis to now include a matrix method to rank the players in the tournament. Grade 8 Example: • Four players (Dom, Nate, Ryan, & Zach) are playing in a round-robin tennis tournament, where every player plays every other player. Dom beats Nate and Ryan, Nate beats Zach, Ryan beats Nate and Zach, and Zach beats Dom. o Represent this
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeHS.pdf#page=18
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
find Hamilton paths, and discuss implications <span class="highlight">for</span> ranking the players in the tournament. In grades 9 and 10, students can expand their initial methods <span class="highlight">of</span> <span class="highlight">analysis</span> to now include a matrix method to rank the players in the tournament. Grade 8 Example: • Four players (Dom, Nate, Ryan, & Zach) are playing in a round-robin tennis tournament, where every player plays every other player. Dom beats Nate and Ryan, Nate beats Zach, Ryan beats Nate and Zach, and Zach beats Dom. o Represent this
GRADE 7
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 7 Arizona Department of Education: Standards and Assessment Division 18 Approved 6.24.08...
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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 7 Arizona Department of Education: Standards and Assessment Division 18 Approved 6.24.08 Strand 2: Data Analysis, Probability, and Discrete Mathematics Concept 4: Vertex-Edge Graphs Understand and apply vertex-edge graphs. In Grade 7, students use vertex-edge
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade7.pdf#page=18
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 7 Arizona Department <span class="highlight">of</span> Education: Standards and Assessment Division 18 Approved 6.24.08 Strand 2: Data <span class="highlight">Analysis</span>, Probability, and Discrete Mathematics Concept 4: Vertex-<span class="highlight">Edge</span> Graphs Understand and apply vertex-<span class="highlight">edge</span> graphs. In Grade 7, students use vertex-<span class="highlight">edge</span>
Illinois Mathematics Assessment Framework PSAE Grade 11
10C 1% 2% 0% Note: The mathematics portion of the PSAE is a combination of the ACT Assessment Mathematics component and the WorkKeys Applied Mathematics Assessment component. Note Added on 3/18/08: A new scoring methodology was announced that affects only reading and ma...
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10C 1% 2% 0% Note: The mathematics portion of the PSAE is a combination of the ACT Assessment Mathematics component and the WorkKeys Applied Mathematics Assessment component. Note Added on 3/18/08: A new scoring methodology was announced that affects only reading and mathematics. For more information, please see Probability http://www.isbe.net/assessment/listserv/2008/mar14.htm. *These percents are typical, based on an analysis of forms from multiple years. These percents in this chart were derived
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http://www.isbe.state.il.us/assessment/pdfs/iaf_math_PSAEFINAL.pdf#page=10
www.isbe.state.il.us/assessment/pdfs/iaf_math_PSAEFINAL.pdf#page=10
10C 1% 2% 0% Note: The mathematics portion <span class="highlight">of</span> the PSAE is a combination <span class="highlight">of</span> the ACT Assessment Mathematics <span class="highlight">component</span> and the WorkKeys Applied Mathematics Assessment <span class="highlight">component</span>. Note Added on 3/18/08: A new scoring methodology was announced that affects only reading and mathematics. <span class="highlight">For</span> more <span class="highlight">information</span>, please see Probability http://www.isbe.net/assessment/listserv/2008/mar14.htm. *These percents are typical, based on an <span class="highlight">analysis</span> <span class="highlight">of</span> forms from multiple years. These percents in this chart were derived
GRADE K
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 K Arizona Department of Education: Standards and Assessment Division 7 Approved 6.24.08 S...
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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 K Arizona Department of Education: Standards and Assessment Division 7 Approved 6.24.08 Strand 2: Data Analysis, Probability, and Discrete
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeK.pdf#page=7
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 K Arizona Department <span class="highlight">of</span> Education: Standards and Assessment Division 7 Approved 6.24.08 Strand 2: Data <span class="highlight">Analysis</span>, Probability, and Discrete
STANDARDS.05
102 PERFORMANCE STANDARDS (Grade Level Expectations) 103PERFORMANCE STANDARDS (Grade Level Expectations) GRADE 7 GRADE 8 GRADE 9 GRADE 10 Analysis and Central Tendency The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, des...
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102 PERFORMANCE STANDARDS (Grade Level Expectations) 103PERFORMANCE STANDARDS (Grade Level Expectations) GRADE 7 GRADE 8 GRADE 9 GRADE 10 Analysis and Central Tendency The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions) by [10] S&P-2 using information from a display to solve a problem or analyzing the validity of statistical conclusions (M6.4.1 & M6.4.4) [10] S
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http://www.eed.state.ak.us/standards/pdf/standards.pdf#page=103
www.eed.state.ak.us/standards/pdf/standards.pdf#page=103
102 PERFORMANCE STANDARDS (Grade Level Expectations) 103PERFORMANCE STANDARDS (Grade Level Expectations) GRADE 7 GRADE 8 GRADE 9 GRADE 10 <span class="highlight">Analysis</span> and Central Tendency The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions) by [10] S&P-2 using <span class="highlight">information</span> from a display to solve a problem or analyzing the validity <span class="highlight">of</span> statistical conclusions (M6.4.1 & M6.4.4) [10] S
GRADE 4
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 4 Arizona Department of Education: Standards and Assessment Division 18 Approved 6.24.08 St...
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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 4 Arizona Department of Education: Standards and Assessment Division 18 Approved 6.24.08 Strand 2: Data Analysis
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade4.pdf#page=18
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 4 Arizona Department <span class="highlight">of</span> Education: Standards and Assessment Division 18 Approved 6.24.08 Strand 2: Data <span class="highlight">Analysis</span>
GRADE 6
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 6 Arizona Department of Education: Standards and Assessment Division 19 Approved 6.24.08 St...
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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 6 Arizona Department of Education: Standards and Assessment Division 19 Approved 6.24.08 Strand 2: Data Analysis, Probability, and Discrete Mathematics Concept 4: Vertex-Edge Graphs Understand and apply vertex-edge graphs. In Grade 6
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade6.pdf#page=19
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 6 Arizona Department <span class="highlight">of</span> Education: Standards and Assessment Division 19 Approved 6.24.08 Strand 2: Data <span class="highlight">Analysis</span>, Probability, and Discrete Mathematics Concept 4: Vertex-<span class="highlight">Edge</span> Graphs Understand and apply vertex-<span class="highlight">edge</span> graphs. In Grade 6
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