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 Speaking Standard 3
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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...
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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
39 0 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. &bull; Venn diagrams &bull; 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. &bull; Organized lists, charts, tree diagrams &bull; 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&mdash;Vertex-<span class="highlight">Edge</span> Graphs and Algorithms 1. Follow, devise, and
40 0 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&mdash;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
41 0 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&rsquo;s hand once). 4.4.6 D. Discrete Mathematics&mdash;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
44 0 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. &bull; Circuits that include every <span class="highlight">edge</span> in a graph &bull; Circuits that include every vertex in a graph &bull; Scheduling problems (e.g., when project meetings should be scheduled to avoid conflicts) using graph coloring &bull; Applications to science (e.g., who-eats-whom graphs, genetic trees, molecular structures) 2. Explore strategies <span class="highlight">for</span> making fair decisions. &bull; Combining individual preferences into a group decision (e.g., determining winner <span class="highlight">of</span> an election or selection process