Let's Color
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This learning activity provided by:
Author:
Lorie White
System: Lauderdale County School: Rogers High School
General Activity Information
Activity ID:
2906
Title: Let's Color
Digital Tool/Resource: Let's Color - Graph Coloring
Web Address – URL:
Overview: Students will color the vertices of a network/graph using as many colors as possible and as few colors as possible.
Associated Standards and Objectives
Content Standard(s):
Mathematics 19. Use vertex-coloring, edge-coloring, and matching techniques to solve application-based problems involving conflict.
Examples: Use graph-coloring techniques to color a map of the western states of the United States so that no adjacent states are the same color, determining the minimum number of colors needed and why no fewer colors may be used; use vertex colorings to determine the minimum number of zoo enclosures needed to house ten animals given their cohabitation constraints; use vertex colorings to develop a time table for scenarios such as scheduling club meetings or for housing hazardous chemicals that cannot all be safely stored together in warehouses.
Unpacked Content
Evidence Of Student Attainment:
Students:
Use vertex coloring and edge coloring techniques to solve application-based problems modeled using a graph.
Provide explanations for why no fewer colors may be used to color a graph. Teacher Vocabulary:
Vertex coloring
Matching techniques
Conflict graphs
Adjacent edges
Adjacent vertices
Odd wheel graph
Proper coloring Knowledge:
Students know:
Graphing procedures and properties. Skills:
Students are able to:
Model application-based problems that may be solved using graph colorings.
Color the edges or vertices of a graph using the least number of colors so that no two adjacent vertices or edges are colored the same.
Interpret the coloring of the graph in terms of a solution for an application-based problem, such as scheduling committee meetings (vertex colorings) or class scheduling (edge-colorings).
Identify structures in a graph that require a minimum number of colors for a proper coloring. Understanding:
Students understand that:
-Techniques are used to minimize colors needed to color the vertices (edges) of a graph so that no two adjacent vertices (edges) are colored the same.
-Real-world problems such as scheduling and conflict can be modeled with graphs and solved using the minimization of the number of colors. Diverse Learning Needs:
Learning Objectives: Students should be able to identify the chromatic number of a simple graph.
Strategies, Preparations and Variations
Phase: Before/Engage
Activity: 1. Share the Google Slide "Let's Color " with the students and direct them to open the document.
2. Instruct the students to follow the prompts to color the vertices of the graph in three different ways.
3. Remind students to refer to the definition for proper coloring presented at the top of the slide.
4. The students should share the document with the teacher and the teacher should check the responses and clear up any misconceptions.
Assessment Strategies: Once the students share their responses, the teacher can assess the students' answers. The teacher should correct the students' mistakes or misunderstandings.
Advanced Preparation: The teacher will need to ensure the classroom has the following:
1) internet connection (WiFi).
2) classroom set of computers, iPads, or smart devices. (If allowed students can use their own personal devices.)
Prior to the lesson, the teacher should share the google slide "Let's Color " with the students.
The teacher should also preview the slide to anticipate problems or misconceptions.
Variation Tips (optional): The Google Slide can be downloaded as a PDF, printed, and distributed to the students as a paper copy. Please provide colored pencils for the student to use if a paper copy is used.
Notes or Recommendations (optional):
Keywords and Search Tags
Keywords and Search Tags:
Chromatic Number, Color theory
