|
Education
Web
 GRADE 2
colored using the same color. Many students believe a point is considered an edge. Realizing that a point is not an edge does not happen without exploration and discussion. Students should have multiple opportunities to color a variety of simple pictures and maps. The goal is ...
1
0
colored using the same color. Many students believe a point is considered an edge. Realizing that a point is not an edge does not happen without exploration and discussion. Students should have multiple opportunities to color a variety of simple pictures and maps. The goal is for students to use the fewest number of colors; some possible strategies that young children may use include a guess-and-check strategy, use many colors and try to eliminate one color at a time; or use few colors and insert
15
0
http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade2.pdf#page=15
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
colored using the same color. Many students believe a point is considered an <span class="highlight">edge</span>. Realizing that a point is not an <span class="highlight">edge</span> does not happen without exploration and discussion. Students should have multiple opportunities to color a variety <span class="highlight">of</span> simple pictures and maps. The goal is <span class="highlight">for</span> students to use the fewest number <span class="highlight">of</span> colors; some possible strategies that young children may use include a guess-and-check strategy, use many colors and try to eliminate one color at a time; or use few colors and insert
17
0
http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade2.pdf#page=17
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Explanations and Examples Students are expected to: PO 2. Build vertex-<span class="highlight">edge</span> graphs using concrete materials and explore simple properties <span class="highlight">of</span> vertex-<span class="highlight">edge</span> graphs • number <span class="highlight">of</span> vertices and edges, • neighboring vertices, and • paths in a graph. Connections: M02-S2C4-03 A vertex-<span class="highlight">edge</span> graph is a collection <span class="highlight">of</span> vertices and edges. A vertex is a point/dot that represents an object or location. An <span class="highlight">edge</span> connects two vertices and represents some relationship between them. The vertex-<span class="highlight">edge</span> graph below has 4
GRADE 1
Mathematics This strand requires students to use data collection, data analysis, statistics, probability, systematic listing and counting, and the study of graphs. This prepares students for the study of discrete functions as well as to make valid inferences, decisions, a...
1
0
Mathematics This strand requires students to use data collection, data analysis, statistics, probability, systematic listing and counting, 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
8
0
http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade1.pdf#page=8
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Mathematics This strand requires students to use data collection, data <span class="highlight">analysis</span>, statistics, probability, systematic listing and counting, and the study <span class="highlight">of</span> graphs. This prepares students <span class="highlight">for</span> the study <span class="highlight">of</span> discrete functions as well as to make valid inferences, decisions, and arguments. Discrete mathematics is a branch <span class="highlight">of</span> mathematics that is widely used in business and industry. Combinatorics is the mathematics <span class="highlight">of</span> systematic counting. Vertex-<span class="highlight">edge</span> graphs are used to model and solve problems involving paths
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...
1
0
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
7
0
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...
1
0
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
103
0
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...
1
0
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
11
0
http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade4.pdf#page=11
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
Probability, and Discrete Mathematics This strand requires students to use data collection, data <span class="highlight">analysis</span>, statistics, probability, systematic listing and counting, and the study <span class="highlight">of</span> graphs. This prepares students <span class="highlight">for</span> the study <span class="highlight">of</span> discrete functions as well as to make valid inferences, decisions, and arguments. Discrete mathematics is a branch <span class="highlight">of</span> mathematics that is widely used in business and industry. Combinatorics is the mathematics <span class="highlight">of</span> systematic counting. Vertex-<span class="highlight">edge</span> graphs are used to model and solve
18
0
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 8
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 s...
1
0
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 collection
7
0
http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade8.pdf#page=7
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
<span class="highlight">of</span> graphs. This prepares students <span class="highlight">for</span> the study <span class="highlight">of</span> discrete functions as well as to make valid inferences, decisions, and arguments. Discrete mathematics is a branch <span class="highlight">of</span> mathematics that is widely used in business and industry. Combinatorics is the mathematics <span class="highlight">of</span> systematic counting. Vertex-<span class="highlight">edge</span> graphs are used to model and solve problems involving paths, networks, and relationships among a finite number <span class="highlight">of</span> objects. Concept 1: Data <span class="highlight">Analysis</span> (Statistics) Understand and apply data collection
Microsoft Word - 2007 MS Math Framework Competencies and Objectives 9-18-07.doc
graphing. A variety of problem-solving techniques and technology will be used when applying these concepts, which will enable students to solve real-life application, routine word, and non- routine problems. Technology should be a component of the instruction. The instruction...
1
0
graphing. A variety of problem-solving techniques and technology will be used when applying these concepts, which will enable students to solve real-life application, routine word, and non- routine problems. Technology should be a component of the instruction. The instructional approach should provide opportunities for students to work together collaboratively and cooperatively as they solve routine and non-routine problems. Communication strategies should include reading, writing, speaking, and critical
39
0
http://www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math%20Framework%20Competencies%20and%20Objectives%209-18-07.pdf#page=39
www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math...
a <span class="highlight">component</span> <span class="highlight">of</span> the instruction. The instructional approach should provide opportunities <span class="highlight">for</span> students to work together collaboratively and cooperatively as they solve routine and non-routine problems. Communication strategies should include reading, writing, speaking, and critical listening as students present and evaluate mathematical arguments, proofs, and explanations about their reasoning. Physical materials should continue to be part <span class="highlight">of</span> the development <span class="highlight">of</span> mathematical understanding. The
43
0
http://www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math%20Framework%20Competencies%20and%20Objectives%209-18-07.pdf#page=43
www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math...
graphing. A variety <span class="highlight">of</span> problem-solving techniques and technology will be used when applying these concepts, which will enable students to solve real-life application, routine word, and non- routine problems. Technology should be a <span class="highlight">component</span> <span class="highlight">of</span> the instruction. The instructional approach should provide opportunities <span class="highlight">for</span> students to work together collaboratively and cooperatively as they solve routine and non-routine problems. Communication strategies should include reading, writing, speaking, and critical
46
0
http://www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math%20Framework%20Competencies%20and%20Objectives%209-18-07.pdf#page=46
www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math...
about the characteristics <span class="highlight">of</span> graphs and their associated equations, expanding the techniques used to solve equations, and applying properties in real-world applications, routine word, and non-routine problems. Technology should be a <span class="highlight">component</span> <span class="highlight">of</span> the instruction. The instructional approach should provide opportunities <span class="highlight">for</span> students to work together collaboratively and cooperatively as they solve routine and non-routine problems. Communication strategies should include reading, writing, speaking, and
49
0
http://www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math%20Framework%20Competencies%20and%20Objectives%209-18-07.pdf#page=49
www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math...
equations. Concepts and computations with matrices are introduced. The <span class="highlight">analysis</span> <span class="highlight">of</span> graphs includes scatter plots. Written and oral justifications to support solution methods and solutions are required. Technology should be a <span class="highlight">component</span> <span class="highlight">of</span> the instruction. The instructional approach should provide opportunities <span class="highlight">for</span> students to work together collaboratively and cooperatively as they solve routine and non-routine problems. Communication strategies should include reading, writing, speaking, and critical
52
0
http://www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math%20Framework%20Competencies%20and%20Objectives%209-18-07.pdf#page=52
www.mde.k12.ms.us/acad/id/curriculum/math/2007_framework/2007%20MS%20Math...
representations should be included across all objectives. Students should be given an opportunity to develop spatial sense and an understanding <span class="highlight">of</span> a variety means <span class="highlight">of</span> providing reasoning, mathematical arguments, and proofs. The justifications used in geometry should include a variety <span class="highlight">of</span> techniques including paragraph and algebraic proofs. Technology should be a <span class="highlight">component</span> <span class="highlight">of</span> the instruction. The instructional approach should provide opportunities <span class="highlight">for</span> students to work together collaboratively and cooperatively as
Microsoft Word - mathsol2009.doc
solutions exist (counting problems), and focus on finding the best solution (optimization problems). Connections will be made to other disciplines. The importance of discrete mathematics has been influenced by computers. Modern technology (graphing calculators and/or computers) will be an int...
1
0
solutions exist (counting problems), and focus on finding the best solution (optimization problems). Connections will be made to other disciplines. The importance of discrete mathematics has been influenced by computers. Modern technology (graphing calculators and/or computers) will be an integral component of this course. *DM.1 The student will model problems, using vertex-edge graphs. The concepts of valence, connectedness, paths, planarity, and directed graphs will be investigated. Adjacency matrices and
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
solutions exist (counting problems), and focus on finding the best solution (optimization problems). Connections will be made to other disciplines. The importance <span class="highlight">of</span> discrete mathematics has been influenced by computers. Modern technology (graphing calculators and/or computers) will be an integral <span class="highlight">component</span> <span class="highlight">of</span> this course. *DM.1 The student will model problems, using vertex-<span class="highlight">edge</span> graphs. The concepts <span class="highlight">of</span> valence, connectedness, paths, planarity, and directed graphs will be investigated. Adjacency matrices and
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...
1
0
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
19
0
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
|
