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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn a real situation into an explicit formula, recursive rule, or clear calculation process. They identify the starting value, rate of change, operations, inputs, and outputs.
What Mastery Looks Like
- Students define variables and write a formula, recursive rule, or calculation steps that fit the situation. They check sample values and explain what each number means in context.
Common Misconceptions
- Students confuse an explicit formula with a recursive rule or leave out the starting value. They may use addition when the context shows repeated multiplication, ignore units, or choose an unreasonable domain.
How to Assess It
- Exit ticket: A savings account starts with $120 and gains $15 each week. Write explicit and recursive rules, then find the balance after eight weeks.
Lesson moves
Ways to Teach It
Build tile figures for stages one through four, record the counts, then write an explicit rule and recursive instructions.
Ask students to explain when repeated addition and repeated multiplication create different models for a growing quantity.
Run a card sort matching situation cards with tables, explicit formulas, recursive rules, and calculation steps.
Use a local taxi fare with a starting fee and mileage charge to write a rule and calculate several trip costs.
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Printable HSF-BF.A.1a Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSF-BF.A.1a, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSF-IF.A.1
Writing rules from contexts uses the idea that each input has one output and can be named with function notation.
- CCSS.Math.Content.HSN-Q.A.2
Choosing relevant quantities and variables supports turning a context into an explicit formula, recursive rule, or calculation steps.
- CCSS.Math.Content.HSA-CED.A.2
Writing equations for quantity relationships supports turning contexts into function rules, including explicit formulas and calculation steps.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSF-BF.A.2
Turning a context into an explicit rule or recursive process supports modeling sequences in both formula forms.
- CCSS.Math.Content.HSF-LE.A.2
Writing explicit or recursive rules from contexts supports forming linear, exponential, arithmetic, and geometric function models from descriptions or tables.
Keep exploring
Related Standards
- CCSS.Math.Content.HSA-SSE.A.2
Use the structure of an expression to identify ways to rewrite it.
- 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...
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