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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—VertexEdge 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=18
www.nj.gov/education/cccs/2004/s4_math.pdf#page=18
dimensional shapes. • Vertex, <span class="highlight">edge</span>, <span class="highlight">face</span>, side • 3D figures – cube, rectangular prism, sphere, cone, cylinder, and pyramid • 2D figures – square, rectangle, circle, triangle • Relationships between three and twodimensional shapes (i.e., the <span class="highlight">face</span> <span class="highlight">of</span> a 3D shape is a 2D shape) 3. Describe, identify and create instances <span class="highlight">of</span> line symmetry. 4. Recognize, describe, extend and create designs and patterns with geometric objects <span class="highlight">of</span> different shapes and colors. 4.2.2 B. Transforming Shapes 1. Use simple shapes to
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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 2digit 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=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=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 • Boxandwhisker plot
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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., whoeatswhom 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
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8. Draw conclusions and inferences from texts. 9. Recognize firstperson “I” point of view. 10. Compare and contrast story plots, characters, settings, and themes. 11. Participate in creative responses to texts (e.g., dramatizations, oral presentations). 12. Read regularly in mate...
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8. Draw conclusions and inferences from texts. 9. Recognize firstperson “I” point of view. 10. Compare and contrast story plots, characters, settings, and themes. 11. Participate in creative responses to texts (e.g., dramatizations, oral presentations). 12. Read regularly in materials appropriate for their independent reading level. 13. Read and comprehend both fiction and nonfiction that is appropriately designed for grade level. 14. Use information and reasoning to examine bases of hypotheses and
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http://www.nj.gov/education/cccs/2004/s3_lal.pdf#page=12
www.nj.gov/education/cccs/2004/s3_lal.pdf#page=12
in silent <span class="highlight">independent</span> reading <span class="highlight">for</span> specific purposes. 3.1.1 H. Inquiry and Research 1. Ask and explore questions related to a topic <span class="highlight">of</span> interest. 2. Draw conclusions from <span class="highlight">information</span> and data gathered. 3. Be exposed to and read a variety <span class="highlight">of</span> fiction and nonfiction, and produce evidence <span class="highlight">of</span> reading. Building upon knowledge and skills gained in preceding grades, by the end <span class="highlight">of</span> Grade 2, students will: 3.1.2 A. Concepts About Print/Text 1. Use titles, tables <span class="highlight">of</span> contents, and chapter headings to locate <span class="highlight">information</span>. 2
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http://www.nj.gov/education/cccs/2004/s3_lal.pdf#page=14
www.nj.gov/education/cccs/2004/s3_lal.pdf#page=14
8. Draw conclusions and inferences from texts. 9. Recognize firstperson “I” point <span class="highlight">of</span> view. 10. Compare and contrast story plots, characters, settings, and themes. 11. Participate in creative responses to texts (e.g., dramatizations, oral presentations). 12. Read regularly in materials appropriate <span class="highlight">for</span> their <span class="highlight">independent</span> reading level. 13. Read and comprehend both fiction and nonfiction that is appropriately designed <span class="highlight">for</span> grade level. 14. Use <span class="highlight">information</span> and reasoning to examine bases <span class="highlight">of</span> hypotheses and
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http://www.nj.gov/education/cccs/2004/s3_lal.pdf#page=18
www.nj.gov/education/cccs/2004/s3_lal.pdf#page=18
features (e.g., paragraphs, topic, sentence, index, glossary, table <span class="highlight">of</span> contents) and graphic features, (e.g., charts, maps, diagrams) to comprehend <span class="highlight">information</span>. 2. Develop an understanding <span class="highlight">of</span> the organizational structure <span class="highlight">of</span> printed material (e.g. chronological, sequential, procedural text). 3.1.7 B. Phonological Awareness No additional indicators at this grade level. 3.1.7 C. Decoding and Word <span class="highlight">Recognition</span> 1. Distinguish among the spellings <span class="highlight">of</span> homophones (e.g. cite, site, sight). 2. Apply spelling rules and

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