CCSS.Math.Content.HSF-IF.A.3
The standard
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Common Core State Standards for Mathematics
What this standard means
Students need to see a sequence as a function where the input is a term number, usually 1, 2, 3, and so on, and the output is the term value. They should connect tables, graphs, explicit rules, and recursive rules.
Mastery means students can find terms from a recursive rule, write the domain correctly, and explain how each term depends on earlier terms. Common trouble spots are mixing up term number and term value, starting at the wrong index, and expecting every function graph to be continuous.
Ways to teach it
- Give pairs index cards with term numbers and values, then have them arrange, table, and graph an arithmetic or Fibonacci-like sequence.
- Ask students to explain in writing how a recursive rule is like giving directions for making the next term.
- Show a short recursive rule and ask students to write the first five terms and the domain values used.
- Use stair-step savings, where week numbers are inputs and total saved is output, then compare explicit and recursive descriptions.
Plan a lesson for CCSS.Math.Content.HSF-IF.A.3
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Related standards
- CCSS.Math.Content.HSF-BF.A.2
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
- CCSS.Math.Content.HSF-IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
- CCSS.Math.Content.HSF-TF.B.6
(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
- CCSS.Math.Content.HSF-BF.B.4d
(+) Produce an invertible function from a non-invertible function by restricting the domain.