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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: VertexEdge Graphs Understand and apply vertexedge 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=9
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
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, 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
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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
Microsoft Word  Front Cover Page
Glossary 43 Coordinates: A pair of numbers used to describe the location of a point on a coordinate plane. Counterexample: An example that proves a statement false. Cube: A threedimensional figure that has six square faces. Customary Systems: A measuring system used mainly in the...
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Glossary 43 Coordinates: A pair of numbers used to describe the location of a point on a coordinate plane. Counterexample: An example that proves a statement false. Cube: A threedimensional figure that has six square faces. Customary Systems: A measuring system used mainly in the United States using units such as inches and feet. Data: Information, facts, or numbers used to describe something. Data Analysis: A process of collecting and organizing data in order to identify
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http://www.doe.nv.gov/Standards/Mathematics/New_Nevada_Math_Standards_Complete_Document_6.29.06_PDF.pdf#page=50
www.doe.nv.gov/Standards/Mathematics/New_Nevada_Math_Standards_Complete_D...
Glossary 43 Coordinates: A pair <span class="highlight">of</span> numbers used to describe the location <span class="highlight">of</span> a point on a coordinate plane. Counterexample: An example that proves a statement false. Cube: A threedimensional figure that has six square faces. Customary Systems: A measuring system used mainly in the United States using units such as inches and feet. Data: <span class="highlight">Information</span>, facts, or numbers used to describe something. Data <span class="highlight">Analysis</span>: A process <span class="highlight">of</span> collecting and organizing data in order to identify
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
GRADE CWR
Concept 4: VertexEdge Graphs Understand and apply vertexedge 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: VertexEdge Graphs Understand and apply vertexedge 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 vertexedge graphs: Euler circuits, Hamilton circuits, the
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeCWR.pdf#page=6
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
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, networks, and
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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
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGradeCWR.pdf#page=15
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
and Examples Students are expected to: PO 2. Understand, analyze, and apply vertex<span class="highlight">edge</span> graphs to model and solve problems related to paths, circuits, networks, and relationships among a finite number <span class="highlight">of</span> elements, in realworld and abstract settings. Connections: MCWRS2C401, MCWR S2C403, MCWRS2C404, SSHSS4C1 03 MCWRS5C201. Analyze a problem situation, determine the question(s) to be answered, organize given <span class="highlight">information</span>, determine how to represent the problem, and identify
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 roundrobin 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=6
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
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 problems involving
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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 roundrobin 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: VertexEdge Graphs Understand and apply vertexedge graphs. In Grade 7, students use vertexedge
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade7.pdf#page=10
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
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, 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
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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>
Microsoft Word  K8 Mathematics Curriculum Framework.doc
experiment Explicit A formula whose dependent variable is defined in terms of the independent variable Ex. y = 2x – 3 Exponential form A quantity expressed as a number raised to a power (In exponential form, 32 can be written as 2 5 .) Face A twodimensional side of...
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experiment Explicit A formula whose dependent variable is defined in terms of the independent variable Ex. y = 2x – 3 Exponential form A quantity expressed as a number raised to a power (In exponential form, 32 can be written as 2 5 .) Face A twodimensional side of a threedimensional figure Ex. The faces of a cube are squares. Factor One of two or more numbers that are multiplied together to get a product (13 and 4 are both factors of 52 because 13 • 4 = 52.) Flip (Reflection) (See
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http://arkansased.org/teachers/pdf/k8_math_may05.pdf#page=70
arkansased.org/teachers/pdf/k8_math_may05.pdf#page=70
experiment Explicit A formula whose dependent variable is defined in terms <span class="highlight">of</span> the <span class="highlight">independent</span> variable Ex. y = 2x – 3 Exponential form A quantity expressed as a number raised to a power (In exponential form, 32 can be written as 2 5 .) <span class="highlight">Face</span> A twodimensional side <span class="highlight">of</span> a threedimensional figure Ex. The faces <span class="highlight">of</span> a cube are squares. Factor One <span class="highlight">of</span> two or more numbers that are multiplied together to get a product (13 and 4 are both factors <span class="highlight">of</span> 52 because 13 • 4 = 52.) Flip (Reflection) (See
GRADE 3
previously solved problems, and identify possible strategies for solving the problem. M03S5C208. Make and test conjectures based on data (or information) collected from explorations and experiments. Examples: • County map of Arizona • Map of United States...
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previously solved problems, and identify possible strategies for solving the problem. M03S5C208. Make and test conjectures based on data (or information) collected from explorations and experiments. Examples: • County map of Arizona • Map of United States PO 2. Investigate properties of vertex edge graphs • circuits in a graph, • weights on edges, and • shortest path between two vertices. Connections: M03S1C102, M03S1C2 01, M03S1C202, SS3S4C103 M03S5C202. Identify relevant
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http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade3.pdf#page=15
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
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, 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
19
0
http://www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade3.pdf#page=19
www.ade.state.az.us/standards/math/Articulated08/Gradeleveldocs/MathGrade...
previously solved problems, and identify possible strategies <span class="highlight">for</span> solving the problem. M03S5C208. Make and test conjectures based on data (or <span class="highlight">information</span>) collected from explorations and experiments. Examples: • County map <span class="highlight">of</span> Arizona • Map <span class="highlight">of</span> United States PO 2. Investigate properties <span class="highlight">of</span> vertex <span class="highlight">edge</span> graphs • circuits in a graph, • weights on edges, and • shortest path between two vertices. Connections: M03S1C102, M03S1C2 01, M03S1C202, SS3S4C103 M03S5C202. Identify relevant
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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0
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
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apply the given formula to find area and circumference of circles, area and perimeter of polygons, and volume of regular solids; use appropriate measurements in collecting data for a real world situation At Level 3, the student is able to solve real world problems given l...
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apply the given formula to find area and circumference of circles, area and perimeter of polygons, and volume of regular solids; use appropriate measurements in collecting data for a real world situation At Level 3, the student is able to solve real world problems given logarithmic and exponential formulas (e.g. Ph scale, Richter scale.). Sample Task: Construct a regular geometric solid and determine the surface area, volume, and edge length. Linkages: Science, art, construction
5
0
http://www.state.tn.us/education/ci/math/doc/MA_3134.pdf#page=5
www.state.tn.us/education/ci/math/doc/MA_3134.pdf#page=5
apply the given formula to find area and circumference <span class="highlight">of</span> circles, area and perimeter <span class="highlight">of</span> polygons, and volume <span class="highlight">of</span> regular solids; use appropriate measurements in collecting data <span class="highlight">for</span> a real world situation At Level 3, the student is able to solve real world problems given logarithmic and exponential formulas (e.g. Ph scale, Richter scale.). Sample Task: Construct a regular geometric solid and determine the surface area, volume, and <span class="highlight">edge</span> length. Linkages: Science, art, construction

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