CCSS.Math.Content.HSF-BF.A
The standard
Build a function that models a relationship between two quantities
Common Core State Standards for Mathematics · High School — Functions
What this standard means
Students need to choose variables, decide how quantities depend on each other, and write a function rule that fits the situation. They should use tables, graphs, words, or data to build linear, quadratic, exponential, or piecewise models when appropriate.
Mastery looks like a student explaining why their function matches the context, what the inputs and outputs mean, and what the parameters represent. Students often get stuck picking the right function type, defining variables clearly, and checking whether answers make sense in the situation.
Ways to teach it
- Give pairs a cup-stacking task, measure stack heights for different cup counts, then write and graph a function for height.
- Ask students to write: What does the slope, starting value, or growth factor mean in this situation?
- Show a small table of phone plan costs and ask students to write a rule, then test it with one new input.
- Use a local taxi fare, gym membership, or streaming subscription to build and compare cost functions.
Plan a lesson for CCSS.Math.Content.HSF-BF.A
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Related standards
- CCSS.Math.Content.HSF-BF.A.1
Write a function that describes 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.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of...
- CCSS.Math.Content.8.F.B
Use functions to model relationships between quantities.