Mississippi Math C.N.3

MathGrades 9–12Number and Quantity (N) Compute and Determine the Reasonableness of Results in Mathematical and Real-world Situations

The Standard

Prove statements using mathematical induction.

2025 Mississippi College- and Career-Readiness Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students prove a formula works for every integer from a stated starting value. They check the first value, assume it works at k, then use that assumption to prove it works at k+1.
What Mastery Looks Like: A student can prove the sum of the first n positive integers is n(n+1)/2. They show the first case, then add k+1 to the assumed sum and simplify to the formula for k+1.
Common Misconceptions: Students may think checking several numbers proves a formula for all numbers. Some skip the first case or assume the formula works at k+1 instead of proving it.
How to Assess It: Exit ticket: Prove 1+3+...+(2n−1)=n² for every positive integer n. Show the first case and the step from k to k+1.

Lesson moves

Build square patterns with tiles, adding an L-shaped strip of 2n+1 tiles to turn an n-by-n square into the next square.
Ask students to write why checking the odd-number sum for n=1, 2, and 3 does not prove it for every n.
Give pairs four proof-step cards to sort into first case, assumption, valid next step, and unsupported claim.
Show a photo of cans stacked in rows of 1, 2, 3, and more; ask students to prove the total for n rows.

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