Florida B.E.S.T. MA.912.LT.2.5

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

The Standard

Apply spanning trees, rooted trees, binary trees and decision trees to solve problems.

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

Teacher's field guide

What Students Need to Do: Students represent networks, hierarchies, and choices with tree diagrams. They select a suitable tree structure, then use paths, branches, and weights to minimize cost, organize information, or make decisions.
What Mastery Looks Like: Given a weighted network, a student builds a spanning tree with no cycles and finds its minimum total weight. They identify roots, parents, children, and leaves, and check whether a tree is binary. They build and follow decision paths to justify an outcome.
Common Misconceptions: Students may leave a vertex disconnected, include a cycle, or assume choosing the smallest edge always gives a valid minimum tree. They often think every binary tree node must have exactly two children, rather than at most two. They may stop along a decision path before reaching a leaf.
How to Assess It: Exit ticket: Using edges AB = 2, AC = 5, BC = 1, BD = 4, and CD = 3, draw the minimum spanning tree, root it at A, label parents and children, and state whether it is binary. Then draw a decision tree using “Is it raining?” and “Is it below 50°F?” to choose indoor or outdoor recess.

Lesson moves

Give groups labeled location cards and weighted yarn edges, then have them build the lowest-cost connected network without cycles.
Show two rooted versions of the same family tree and ask students to explain how changing the root changes parent and child relationships.
Deal edge cards with endpoints and weights, then have teams connect all vertices at minimum total weight without forming a cycle.
Use a school laptop troubleshooting list to build a yes-or-no decision tree, then test it on three fault scenarios.

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