Mississippi Math A3.A.16

MathGrades 9–12Algebra (A) Analyze and Manipulate Functions

The Standard

Add, subtract, multiply and divide rational expressions.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Perform Operations on Expressions, Equations, Inequalities, and Polynomials

Teacher's field guide

What This Standard Means

What Students Need to Do: Students add and subtract rational expressions using common denominators. They multiply and divide by factoring, canceling shared factors, and checking which values make the original expressions undefined.
What Mastery Looks Like: A student simplifies 1/x - 1/(x+1) to 1/[x(x+1)] and excludes x=0 and x=-1. They cancel factors, not terms, in products and quotients and keep restrictions even when factors cancel.
Common Misconceptions: Students may add denominators, turning 1/x + 1/(x+1) into 2/(2x+1), or cancel x from (x+2)/x. They may forget that a canceled denominator factor or a zero divisor still excludes a value.
How to Assess It: Exit ticket: Simplify (x+1)/(x-2) + 3/(x-2) and (x^2-1)/(x+2) ÷ (x-1)/(x+2). List excluded values for each.

Lesson moves

Ways to Teach It

Give pairs index cards labeled 1/x, 1/(x+1), x, and x+1; have them arrange a common denominator and rewrite both fractions.
Ask: Why can x cancel in x(x+2)/x but not in (x+2)/x, and what happens at x=0?
Play four-corner relay: post 1/x + 1/(x+1), 1/x - 1/(x+1), 1/x · (x+1)/x, and 1/x ÷ (x+1)/x; teams simplify and list exclusions.
A faucet fills a tank in x minutes; a second takes x+2 minutes. Have students calculate their combined tank-per-minute rate.

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