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 GRADE 3
previously solved problems, and identify possible strategies for solving the problem. M03-S5C2-08. 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. M03-S5C2-08. 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: M03-S1C1-02, M03-S1C2- 01, M03-S1C2-02, SS3-S4C1-03 M03-S5C2-02. Identify relevant
15
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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
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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. M03-S5C2-08. 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: M03-S1C1-02, M03-S1C2- 01, M03-S1C2-02, SS3-S4C1-03 M03-S5C2-02. Identify relevant
GRADE 2
Explanations and Examples Students are expected to: PO 2. Build vertex-edge graphs using concrete materials and explore simple properties of vertex-edge graphs • number of vertices and edges, • neighboring vertices, and • paths in a graph. Connections: M...
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Explanations and Examples Students are expected to: PO 2. Build vertex-edge graphs using concrete materials and explore simple properties of vertex-edge graphs • number of vertices and edges, • neighboring vertices, and • paths in a graph. Connections: M02-S2C4-03 A vertex-edge graph is a collection of vertices and edges. A vertex is a point/dot that represents an object or location. An edge connects two vertices and represents some relationship between them. The vertex-edge graph below has 4
17
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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...
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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 4
Probability, and Discrete 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 vali...
1
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Probability, and Discrete 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
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
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