Maryland Math A.SSE.B.5
The Standard
Determine the sum, if it exists, of an infinite geometric series.
Maryland College and Career Ready Standards for Mathematics (2025) · Write expressions in equivalent forms to solve problems.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the common ratio between terms of a geometric series. They decide whether the series has a finite sum and, if it does, calculate that sum.
What Mastery Looks Like
- A student can tell that 8 + 4 + 2 + ... has a ratio of 1/2 and a sum of 16. They can explain why 8 + 16 + 32 + ... has no finite sum.
Common Misconceptions
- Students may use the difference between terms instead of the ratio. They may assume every infinite series has a sum, or that a series with a negative ratio cannot have one.
How to Assess It
- Exit ticket: Does 12 + 6 + 3 + ... have a finite sum? Give its ratio and sum, then explain whether 12 + 24 + 48 + ... has a finite sum.
Lesson moves
Ways to Teach It
Give students a paper strip to shade one half, one quarter, and one eighth, then predict how much will eventually be shaded.
Ask: Why does 8 + 4 + 2 + ... approach 16, while 8 + 16 + 32 + ... does not?
Give pairs series cards to sort into finite sum or no finite sum, then have them calculate each finite sum.
A ball drops from 2 meters and rebounds to half its previous height; have students calculate its total vertical travel.
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