Standard: HSF.BF.A1 – Write a function that describes a relationship between two quantities.*
Grade level: High School: Functions
Subject: Mathematics
Domain: Building Functions
Teacher Overview
This standard focuses on helping students understand how to write functions that describe the relationship between two quantities. This skill is crucial as it lays the foundation for more advanced topics in mathematics and allows students to model and solve real-world problems effectively. Students should be comfortable with algebraic manipulation, graphing linear equations, and interpreting graphs. They should also understand the concept of a function and how it relates to real-world scenarios.
After mastering this standard, students will be able to construct and analyze more complex functions and apply their understanding to new mathematical and real-world contexts.
Common Misconception 1
A common misconception is that all relationships between quantities are linear. This is incorrect because relationships can also be quadratic, exponential, or take other forms depending on the context.
Intervention 1
To address this, provide students with diverse examples of functions, including quadratic and exponential functions. Use graphing activities to illustrate how these functions differ from linear ones.
Common Misconception 2
Another misconception is that the function’s formula is the only way to describe the relationship between two quantities. This is incorrect because functions can also be represented using tables, graphs, and verbal descriptions.
Intervention 2
Encourage students to represent functions in multiple ways. Use activities that require them to convert between tables, graphs, and equations to reinforce the idea that these are different representations of the same relationship.
Prerequisite Knowledge
Students should have a solid understanding of basic algebraic concepts, including variables, equations, and graphing linear equations. They should also be familiar with interpreting and creating graphs of functions.
Subsequent Knowledge
After mastering this standard, students will be able to construct more complex functions, analyze and interpret different types of functions, and apply their understanding to solve real-world problems involving exponential, logarithmic, and trigonometric functions.
Instructional Activities
- Graphing different types of functions and comparing their shapes
- Creating tables of values for given functions and plotting them
- Writing verbal descriptions of functions based on real-world scenarios
- Using graphing calculators or software to explore function behavior
- Solving real-world problems by modeling situations with functions
