Mississippi Math A3.N.4
The Standard
Evaluate and apply infinite geometric series.
2025 Mississippi College- and Career-Readiness Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the first term and common ratio in a series that continues without end. They decide whether it has a finite sum and calculate that sum when the ratio is between -1 and 1.
What Mastery Looks Like
- A student can find the sum of 8 + 4 + 2 + ... and explain why it approaches 16. They can also spot a series whose terms do not shrink toward zero and explain why it has no finite sum.
Common Misconceptions
- Students may think any series with a ratio less than 1 has a finite sum, even when the ratio is -2. They may confuse the value of the next term with the sum of all remaining terms.
How to Assess It
- Exit ticket: For 12 + 6 + 3 + ... and 12 + 18 + 27 + ..., find each ratio, decide which series has a finite sum, and calculate it.
Lesson moves
Ways to Teach It
Cut paper strips 8, 4, 2, and 1 inches long, place them end to end, and predict the total with more strips.
Ask, “How can 8 + 4 + 2 + ... keep growing but never reach 17?” Have students explain in writing.
Give pairs cards with a first term and ratio; have them sort for finite sums, then calculate those sums.
A ball drops 10 feet and rebounds to half its previous height each time; calculate its total travel distance, counting each rise and fall.
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