Florida B.E.S.T. MA.912.AR.10.6
The Standard
Given a mathematical or real-world context, find the domain of a given sequence defined recursively or explicitly.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide which integer index values belong to a sequence. They use the starting index, rule restrictions, and contextual endpoint to write a finite or infinite domain.
What Mastery Looks Like
- A student identifies the first valid index and states whether the sequence stops or continues. The student uses initial conditions, undefined inputs, and context limits to justify a domain such as {0, 1, ..., 12}.
Common Misconceptions
- Students often give an interval of real numbers instead of separate integer indices. They may assume every sequence begins at 1, overlook an undefined formula value, or continue beyond a contextual limit.
How to Assess It
- Exit ticket: A training log starts at week 0 and records results through week 12 using a₀ = 18 and aₙ = aₙ₋₁ + 3. Write the domain and justify both endpoints.
Lesson moves
Ways to Teach It
Give pairs index cards labeled 0 through 15 and a 10-day recursive plant growth rule; students keep only cards representing valid days.
Ask students to explain why a sequence for 24 monthly payments cannot have all real numbers as its domain.
Run a card sort matching six sequence rules, starting conditions, contexts, and domain sets; pairs defend one match.
Show a bus timetable with stops numbered 0 through 14; students write the domain and explain why fractional stop numbers fail.
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Related Standards
- MA.912.AR.10.2
Given a mathematical or real-world context, write and solve problems involving geometric sequences.
- MA.912.AR.10.1
Given a mathematical or real-world context, write and solve problems involving arithmetic sequences.
- MA.912.F.1.2
Given a function represented in function notation, evaluate the function for an input in its domain. For a real-world context, interpret the output.
- MA.912.AR.10.5
Given a mathematical or real-world context, write a sequence using function notation, defined explicitly or recursively, to represent relationships between quan...
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