Mississippi Math C.A.8
The Standard
Calculate limits using algebraic methods.
2025 Mississippi College- and Career-Readiness Standards for Mathematics · Evaluate the Limits and Communicate an Understanding of the Limiting Process
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find what an expression approaches as the input gets close to a number. They try substitution first, then simplify if substitution gives 0/0.
What Mastery Looks Like
- A student can factor and cancel (x²−9)/(x−3) to find its limit as x approaches 3. They can explain why the limit is 6 even though the expression is undefined at 3.
Common Misconceptions
- Students may treat 0/0 as an answer or assume the limit does not exist. Some cancel terms that are not factors, such as canceling x from x+3.
How to Assess It
- Exit ticket: Find the limit of (x²−4)/(x−2) as x approaches 2. Show the algebra and explain why substituting 2 does not give the limit.
Lesson moves
Ways to Teach It
Hand out factor cards labeled x−3 and x+3; have students build (x²−9)/(x−3), cancel matching factors, and find its limit near 3.
Ask students to write why (x²−25)/(x−5) approaches 10 as x approaches 5, even though substituting 5 fails.
Match limit cards to answer cards for (x²−16)/(x−4) near 4 and (√x−3)/(x−9) near 9; require written algebra.
For a toy car with distance s(t)=t² meters, simplify [s(2+h)−s(2)]/h and find its speed as h approaches 0.
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