Mississippi Math A3.S.46

MathGrades 9–12Statistics and Probability (S) Explore and Apply Fundamental Principles of Probability

The Standard

Prove statements using mathematical induction.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Apply Trigonometry to General Triangles

Teacher's field guide

What Students Need to Do: Students prove a claim for every positive integer by checking the first case. They assume it holds for k, then use that assumption to prove it holds for k+1.
What Mastery Looks Like: A student states the starting case and the assumption clearly. Their algebra shows how the k case leads to the k+1 case.
Common Misconceptions: Some students think checking n=1, 2, and 3 proves a claim for all n. Others write the k+1 case but never show why the k case makes it true.
How to Assess It: Give this exit ticket: Prove that 1+3+⋯+(2n−1)=n² for every positive integer n. Label the starting case and the step from k to k+1.

Lesson moves

Build square arrays with counters, adding an L-shaped border of 2n+1 counters to show how n² becomes (n+1)².
Ask, 'Why don't five successful cases prove a formula holds for every positive integer?' Have pairs write a response.
Give pairs shuffled cards for a proof of 1+2+⋯+n=n(n+1)/2; have them order the cards and justify each step.
Use a seating chart with 10 seats in row one and one more per row; prove the total after n rows is n(n+19)/2.

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