CCSS.Math.Content.HSF-BF.A.2
The standard
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Common Core State Standards for Mathematics
What this standard means
Students need to write rules for number patterns that grow by adding or multiplying. They should describe a sequence using a starting value and a step rule, and also write a formula for any term. They also need to move between those two forms without changing the pattern.
Mastery means students can tell whether a situation is arithmetic or geometric, choose the right form, and explain what each number means. Students often mix up term number and term value, start with the wrong first term, or use multiplication for a constant difference.
Ways to teach it
- Give pairs pattern cards like 3, 7, 11, 15 and have them write both recursive and explicit rules on mini whiteboards.
- Ask students to explain which rule is better for finding the 5th term and which is better for finding the 100th term.
- Use an exit ticket with one sequence table and ask for the type, recursive rule, explicit rule, and 12th term.
- Model phone plan costs or bacteria growth, then have students decide if the pattern adds or multiplies each step.
Plan a lesson for CCSS.Math.Content.HSF-BF.A.2
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Related standards
- CCSS.Math.Content.HSA-SSE.B.4
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
- CCSS.Math.Content.3.OA.D.9
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.
- CCSS.Math.Content.HSF-BF.A.1a
Determine an explicit expression, a recursive process, or steps for calculation from a context.
- CCSS.Math.Content.HSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pa...