Content Area: Math

 

Index: 4.4D Grade 4 CPI 3

 

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

 

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

 

Cumulative Progress Indicator: 3 -   The student will explore vertex-edge graphs and tree diagrams.

·        Vertex, edge, neighboring/adjacent, number of neighbors

·        Path, circuit (i.e., path that ends at its starting point)

 

Grade: 4

 

Sample Activities:

 

·        Students create "human graphs" where they themselves are the vertices and they use pieces of yarn (several feet long) as edges; each piece of yarn is held by two students, one at each end. They might create graphs with specified properties; for example, they might create a human graph with four vertices of degree 2, or, as with six vertices of which four have degree 3 and two have degree 2. (The degree of a vertex is the total number of edges that meet at the vertex.) They might count the number of different shapes of human graphs they can form with four students (or five, or six).

 

·        Students use a floor plan of their school to map out alternate routes from their classroom to the school's exits, and discuss whether the fire drill route is in fact the shortest route to an exit.

 

·        Students draw graphs of their own neighborhoods, with edges representing streets and vertices representing locations where roads meet. Can you find a route for the mail carrier in your neighborhood which enables her to walk down each street, without repeating any streets, and which ends where it begins? Can you find such a route if she needs to walk up and down each street in order to deliver mail on both sides of the street?

 

·        Additional Framework Activities