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 Speaking Standard 3
slate of officers from a class (e.g., if there are 23 students and 3 officers, the number is 23 x 22 x 21) 3. List the possible combinations of two elements chosen from a given set (e.g., forming a committee of two from a group of 12 students, finding how many handshakes...
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slate of officers from a class (e.g., if there are 23 students and 3 officers, the number is 23 x 22 x 21) 3. List the possible combinations of two elements chosen from a given set (e.g., forming a committee of two from a group of 12 students, finding how many handshakes there will be among ten people if everyone shakes each other person’s hand once). 4.4.6 D. Discrete Mathematics—Vertex-Edge Graphs and Algorithms 1. Devise strategies for winning simple games (e.g., start with two piles of objects
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http://www.nj.gov/education/cccs/2004/s4_math.pdf#page=39
www.nj.gov/education/cccs/2004/s4_math.pdf#page=39
as shape or color, and relationships. • Venn diagrams • Numerical and alphabetical order 2. Represent all possibilities <span class="highlight">for</span> a simple counting situation in an organized way and draw conclusions from this representation. • Organized lists, charts, tree diagrams • Dividing into categories (e.g., to find the total number <span class="highlight">of</span> rectangles in a grid, find the number <span class="highlight">of</span> rectangles <span class="highlight">of</span> each size and add the results) 4.4.4 D. Discrete Mathematics—Vertex-<span class="highlight">Edge</span> Graphs and Algorithms 1. Follow, devise, and
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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=41
www.nj.gov/education/cccs/2004/s4_math.pdf#page=41
slate <span class="highlight">of</span> officers from a class (e.g., if there are 23 students and 3 officers, the number is 23 x 22 x 21) 3. List the possible combinations <span class="highlight">of</span> two elements chosen from a given set (e.g., forming a committee <span class="highlight">of</span> two from a group <span class="highlight">of</span> 12 students, finding how many handshakes there will be among ten people if everyone shakes each other person’s hand once). 4.4.6 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
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http://www.nj.gov/education/cccs/2004/s4_math.pdf#page=44
www.nj.gov/education/cccs/2004/s4_math.pdf#page=44
represent and solve practical problems. • Circuits that include every <span class="highlight">edge</span> in a graph • Circuits that include every vertex in a graph • Scheduling problems (e.g., when project meetings should be scheduled to avoid conflicts) using graph coloring • Applications to science (e.g., who-eats-whom graphs, genetic trees, molecular structures) 2. Explore strategies <span class="highlight">for</span> making fair decisions. • Combining individual preferences into a group decision (e.g., determining winner <span class="highlight">of</span> an election or selection process
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...
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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
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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
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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
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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
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...
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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
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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
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