Florida B.E.S.T. MA.912.LT.3.4

MathGrades 9–12Apply techniques from Election Theory and Fair Division Theory to solve problems.

The Standard

Solve problems using fair division and apportionment techniques.

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

Teacher's field guide

What Students Need to Do: Students divide goods among people using a stated fair division procedure. They apportion whole-number seats or resources from population data using a named method. They show calculations and check that everything is assigned.
What Mastery Looks Like: A student follows an appropriate method, computes shares or quotas accurately, and handles leftovers correctly. The final allocation uses the full total, and the student can explain why the procedure supports fairness.
Common Misconceptions: Students may treat equal size as fair even when participants value pieces differently. They may round every quota normally, which can assign too many or too few seats. They may switch methods midway or ignore leftover-seat rules.
How to Assess It: Exit ticket: Clubs A, B, and C have 50, 30, and 20 members. Use Hamilton’s method to assign seven seats and show each quota.

Lesson moves

Give pairs a paper pizza with labeled toppings and different point values, then use divider-chooser to split it fairly.
Ask students whether equal-sized pieces are always fair, using two people’s stated preferences as evidence.
Deal population cards to teams and award 12 council seats using Hamilton’s method, then check that every seat was assigned.
Use school club membership counts to apportion ten student council seats, then compare Hamilton and Jefferson results.

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