Unpacked Content
Knowledge
Students know:
- Characteristics of a geometric series.
- Techniques for performing algebraic manipulations and justifications for the equivalence of the resulting expressions.
Skills
Students are able to:
- Identify the regularity that exists in a series as being that which defines it as a geometric series.
- Accurately perform the procedures involved in using geometric series to solve contextual problems,
- Explain with mathematical reasoning why each step in the derivation of the formula for the sum of a finite geometric series is legitimate, including explaining why the formula does not hold for a common ratio of 1.
Understanding
Students understand that:
- When each term of a geometric series is multiplied by a value, the result is a new geometric series.
- When many problems exist with the same mathematical structure, formulas are useful generalizations for efficient solution of problems, (e.g., mortgage payment calculation with geometric series).
Vocabulary
- Geometric series (finite and infinite)
- Common ratio
