CCSS.Math.Content.HSF-BF.A.1a
The standard
Determine an explicit expression, a recursive process, or steps for calculation from a context.
Common Core State Standards for Mathematics · Build a function that models a relationship between two quantities
What this standard means
Students need to turn a situation into a rule for finding outputs. They may write a formula, describe a repeated process, or list clear calculation steps. The focus is choosing a structure that fits the context, such as linear growth, doubling, adding a fixed amount, or using a percent change.
Mastery looks like reading a scenario, naming the quantities, choosing variables, and writing a usable rule with correct units. Students often get stuck deciding whether the pattern is explicit or recursive, mixing up starting value and rate, or writing steps that work for one case but not any input.
Ways to teach it
- Hands-on: Use stacking cups, record heights for 1 to 6 cups, then write both a formula and a step-by-step rule.
- Prompt: Explain whether a phone plan with a start fee and monthly charge is better modeled by one formula or repeated adding.
- Quick assessment: Give three contexts and ask students to write one explicit rule, one recursive rule, and one calculation procedure.
- Real-world connection: Use a paycheck with hourly pay, tax percent, and a bonus to build a clear calculation rule.
Plan a lesson for CCSS.Math.Content.HSF-BF.A.1a
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Related standards
- CCSS.Math.Content.HSA-SSE.A.2
Use the structure of an expression to identify ways to rewrite it.
- 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.7.EE.A.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
- CCSS.Math.Content.6.EE.A.2b
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a singl...