Meaningful Distributed Practice Planning
Grade Level / Class
Big Idea(s)
9-12 Geometry
Preview
Review
Vertex Edge Graphs (Paths and Circuits)
MDP1
MDP 2
MDP3
Given the vertices {A, B, C, D, E} and
edges {AB, BD, DC, DC, DC, ED,
BE, AD} draw the graph.
List the vertices and edges in this graph.
Find a path from vertex A to vertex B.
Find a circuit.
Find a path that visits each vertex exactly once, starting and
ending at a different vertex.
Probing Questions:

What is a path?

What is a circuit?

Are there any more paths (or circuit)?

Are there 8 vertices or 6 vertices in this figure? Explain.

Where in the “real world” do edges cross without creating a
vertex?
Probing Questions:

Is there only one way to draw this graph?

Are there any “parallel” edges in this graph?
Anticipated Student Responses:

Vertices = {A, B, C, D, E, F}

Edges = {AC, AD, AB, BD, CE, CF, DE}

Paths & Circuits = (Multiple Answers)

What is a path?

What is a circuit?

Some of the “vertices” are not labeled (i.e. intersections).

Edge ABD (as arc ABD)
Anticipated Student Responses:

One possible solution:

7031 a Vertex Edge Graphs
How many edges are there from D to C?
Find a circuit that visits each vertex exactly once, starting and
ending at the same vertex.
Probing Questions:

Are your solutions unique?

Is there a path that visits each vertex exactly once, starting
and ending at a different vertex that includes F?

Is there a circuit that visits each vertex exactly once, starting
and ending at the same vertex that includes F?

How does removing F change this problem?
Anticipated Student Responses:
Hamiltonian Path = {FCEDBA}
Hamiltonian Circuits = { }
Hamiltonian Paths = {ABDEC, BDECA, DECAB, ECABD,
CABDE}
Hamiltonian Circuits = {ABDECA, BDECAB, DECABD, ECABDE,
CABDEC}
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7031 a Vertex Edge Graphs
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