CCSS.Math.Content.HSF-LE.A.1
The standard
Distinguish between situations that can be modeled with linear functions and with exponential functions.
Common Core State Standards for Mathematics
What this standard means
Students need to tell whether a situation changes by adding the same amount each step or multiplying by the same factor each step. They should connect that pattern to linear or exponential functions, using tables, graphs, equations, and words.
Mastery looks like spotting constant difference versus constant ratio, then explaining why the model fits. Students often get stuck when both patterns increase, or when data is messy. They may also confuse a steep line with exponential growth, so push them to check changes between equal input intervals.
Ways to teach it
- Hands-on activity: Give groups card sets with tables, graphs, equations, and scenarios, then have them sort into linear or exponential piles with reasons.
- Writing prompt: Explain whether a phone plan with a flat monthly fee plus per-gigabyte charges is linear or exponential, and justify your answer.
- Quick assessment: Show three tables and ask students to mark constant difference, constant ratio, or neither in two minutes.
- Real-world connection: Compare hourly wages to a bacteria culture doubling every hour, then ask which model fits each situation and why.
Plan a lesson for CCSS.Math.Content.HSF-LE.A.1
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Related standards
- CCSS.Math.Content.HSF-LE.A.1a
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
- CCSS.Math.Content.HSF-LE.B.5
Interpret the parameters in a linear or exponential function in terms of a context.
- CCSS.Math.Content.HSF-LE.A
Construct and compare linear, quadratic, and exponential models and solve problems
- CCSS.Math.Content.HSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pa...