Florida B.E.S.T. MA.912.LT.1.3

MathGrades 9–12Apply recursive methods to solve problems.

The Standard

Apply mathematical induction in a variety of applications.

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

Teacher's field guide

What Students Need to Do: Students prove that a claim holds for every positive integer. They verify a starting case, assume the claim holds for one integer, and prove it holds for the next.
What Mastery Looks Like: Students organize a proof into a base case, inductive hypothesis, and inductive step. They use the hypothesis correctly to prove the next case. They can apply the method to sums, divisibility claims, inequalities, and recursive patterns.
Common Misconceptions: Students may check several examples and treat that as proof. They may assume the claim for n + 1 instead of n, or forget to prove the base case. Some complete algebra without showing how the inductive hypothesis is used.
How to Assess It: On an exit ticket, prove that 1 + 3 + ... + (2n − 1) = n² for every positive integer n. Label the base case, hypothesis, and inductive step.

Lesson moves

Set up a row of dominoes, then label the first falling domino as the base case and the chain reaction as the inductive step.
Discuss why checking a claim for n = 1, 2, and 3 does not prove it for every positive integer.
Sort mixed proof cards into base case, inductive hypothesis, inductive step, and conclusion, then repair any missing reasoning.
Model a culture starting with 50 cells that doubles hourly, then use induction to prove its population formula after n hours.

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