Content Area: Math

 

Index: 4.4D Grade 2 CPI 4

 

Standard: 4.4 - Data Analysis, Probability, and Discrete Mathematics

 

Strand: D - Discrete Mathematics--Vertex-Edge Graphs and Algorithms

 

Cumulative Progress Indicator: 4 -  The student will explore concrete models of vertex-edge graphs (e.g. vertices as "islands" and edges as "bridges")

·        Paths from one vertex to another

 

Grade: 2

 

Sample Activities:

 

·        Students find a way of getting from one island to another, in the graph described in the K-2 Overview laid out on the classroom floor with masking tape, by crossing exactly four bridges. They make their own graphs, naming each of the islands, and make a "from-to" list of islands for which they have found a four-bridge-route. (Note: it may not always be possible to find four-bridge-routes.)

 

·        Students count the number of edges at each vertex (called the degree of the vertex) of a network and construct graphs where all vertices have the same degree, or where all the vertices have one of two specified degrees.

 

·        On a pattern of islands and bridges laid out on the floor, students try to find a way of visiting each island exactly once; they can leave colored markers to keep track of islands already visited. Note that for some patterns this may not be possible! Students can be challenged to find a way of visiting each island exactly once which returns them to their starting point. Similar activities can be found in Inside, Outside, Loops, and Lines by Herbert Kohl.