Florida B.E.S.T. MA.912.LT.2.2

MathGrades 9–12Apply optimization and techniques from Graph Theory to solve problems.

The Standard

Solve problems involving paths in graphs.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students represent locations or choices as vertices and connections as edges. They trace valid paths, calculate total weights, and choose a route that meets stated constraints.
What Mastery Looks Like: Students can list valid routes between two vertices and find each route's total weight. They select the best route and explain why it meets the problem's conditions.
Common Misconceptions: Students may count vertices instead of adding edge weights. They may repeat an edge, skip a needed connection, or assume the path with the fewest edges has the lowest total weight.
How to Assess It: Give a graph with edges A-B 4, A-C 2, C-B 1, B-D 3, and C-D 7. Ask students to find and justify the shortest path from A to D.

Lesson moves

Use string and labeled cards to build a weighted floor graph, then have students walk the shortest valid route between two vertices.
Ask students to explain whether the route with the fewest edges must also have the lowest weight, using a counterexample.
Play a route challenge where pairs draw weighted graph cards and earn points for finding the least-cost path first.
Map bus stops as vertices and travel times as edge weights, then choose the quickest route from school to a local landmark.

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