



Grade 2  

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• Explanation of the fact that only four colors are needed to color a map or picture with different sections • Definition of Edge and Vertex • The use of odd and even vertices to determine whether only 2 colors are needed or if 3 or 4 colors are required • Interactive practice coloring complex figures in a strategic manner 






Grade 3 – Part 1 

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Description of Lesson • Review and continuation of methods for coloring complex figures • Edge verses Perimeter 





Grade 3 – Part 2 

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Description of Lesson • Review and continuation of methods for coloring complex figures • The importance of Edges separating conflicting color areas in a picture or map • Creation of a VertexEdge Graph from a color picture. • Creation of a VertexEdge Graph from a map • Definition and examples of a Path on a VertexEdge Graph; interactive practice • Weights (time and distance) on the Edges of a VertexEdge graph; interactive practice • Definition and examples of a Circuit on a VertexEdge graph 





Grade 4 – Part 1  
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Description
of
Lesson • Review and continuation of methods for coloring complex figures • The importance of Edges separating conflicting color areas in a picture or map • Creation of a VertexEdge Graph from a color picture. • Creation of a VertexEdge Graph from a map • Definition and examples of a Path on a VertexEdge Graph; interactive practice • Weights (time and distance) on the Edges of a VertexEdge graph; interactive practice • Definition and examples of a Circuit on a VertexEdge graph • Definition of an Euler Path and Circuit; interactive practice 





Grade
4 – Part 2 

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Homework User Instructions Note: Lesson file is very large and may take a few minutes to download depending on your connect speed. 
Description
of
Lesson • Review of the derivation of a VertexEdge Graph from a picture, emphasizing the role of Edges. • Conflict Resolution using VertexEdge Graphs; interactive practice: ○ After School Activities
–
determining the minimum number of meeting times for
all
students to attend all their desired extracurricular
activities
○ Habitat Problem – The minimum number of habitats needed to house 8 animals some of which cannot live in the same habitat. ○ Bat Project– The minimum number of days needed so that students can meet in two groups, each studying a particular type of bat. ○ Movies  The number of visits to the movie theater so all 5 students can each see their two favorite movie. 





Grade 5 – Part 1 


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Description
of
Lesson
• Creation of a VertexEdge Graph from a color picture or map. • Definition and examples of Paths and Circuits on a VertexEdge Graph • Weights (time and distance) on the Edges of a VertexEdge graph • Definition of Euler Paths and Euler Circuits • Interactive practice problems 





Grade 5 – Part 2 

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Description
of Lesson • Review of Euler Paths and Euler Circuits • The Degree of a Vertex • The rules for determining Euler Paths and Circuits • Interactive problem solving using Euler Paths and Circuits 





Grade 6 


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Description
of Lesson
• The rules for determining Hamilton Paths and Circuits • Interactive problem solving using Hamilton Paths and Circuits • Solving shortest route problems 





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2009
Amphitheater Public Schools 

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