CCSS.Math.Content.HSF-BF.A.1
The Standard
Write a function that describes a relationship between two quantities
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the input and output quantities in a situation. They write a function rule using the given rate, starting value, pattern, or operations.
What Mastery Looks Like
- Students define variables and write a function that matches every given condition. They test values and explain how each part of the rule connects to the situation.
Common Misconceptions
- Students may switch the input and output variables or use the rate with the wrong quantity. They may omit an initial value or write a rule that fits only one data pair.
How to Assess It
- Give this exit ticket: “A bike rental costs $8 plus $3 per hour. Write C(h), find C(5), and explain each number in your rule.”
Lesson moves
Ways to Teach It
Stack identical cups, measure the height of stacks from one to six cups, then write a function for stack height.
Show two proposed rules for a tile pattern and ask students to explain which rule matches every figure.
Run a card sort matching situation cards, input and output labels, tables, and function rules.
Use a school fundraiser with a fixed setup cost and profit per item to write a function for total earnings.
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Printable HSF-BF.A.1 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSF-BF.A.1, 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 a function requires knowing inputs, outputs, f(x) notation, and that each input has exactly one output.
- CCSS.Math.Content.8.F.A.1
Writing functions requires understanding a function as an input-output rule, so formulas and graphs represent assigned outputs for inputs.
- CCSS.Math.Content.8.F.B.4
Constructing linear models from tables, graphs, and contexts supports writing broader functions to describe relationships between quantities.
Keep exploring
Related Standards
- CCSS.Math.Content.HSF-BF.A
Build a function that models a relationship between two quantities
- CCSS.Math.Content.HSF-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs show...
- CCSS.Math.Content.8.F.B
Use functions to model relationships between quantities.
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