ALGRZ.MATH.7.D

Determine an appropriate function model, including linear, quadratic, and exponential functions, for a set of data arising from real-world situations using finite differences and average rates of change; and October 2015 Update Page 33 §111.C. High School.

Algebraic Reasoning · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

AI-generated as a starting point — sign in to edit.
Vocabulary
function modellinear functionquadratic functionexponential functionset of datareal-world situationsfinite differencesaverage rates of change
Skills
  • determine (appropriate function model for a data set) #dok2
  • use (finite differences to analyze data) #dok2
  • use (average rates of change to analyze data) #dok2
  • select (linear, quadratic, or exponential model for real-world situations) #dok2
  • analyze (data arising from real-world situations) #dok2
Learning Targets
  • I can identify finite differences in a data set arising from a real-world situation. #dok1
  • I can identify average rates of change in a data set. #dok1
  • I can recognize linear, quadratic, and exponential patterns in data. #dok1
  • I can use finite differences to analyze patterns in real-world data. #dok2
  • I can use average rates of change to analyze patterns in a data set. #dok2
  • I can determine the most appropriate function model for a set of real-world data. #dok2
  • I can justify my choice of function model based on the analysis of data. #dok3
  • I can explain how the characteristics of the data relate to the chosen model. #dok3
  • I can evaluate the effectiveness of different models in representing a given set of data. #dok3
Big Ideas
  • Real-world data can be modeled using different types of functions, and choosing the appropriate model depends on patterns observed through finite differences and average rates of change.
  • The selection and justification of a function model are grounded in mathematical analysis of data, linking concrete real-world situations to abstract mathematical concepts.
Essential Questions
  • How can you determine whether a set of data best fits a linear, quadratic, or exponential function?
  • What role do finite differences and average rates of change play in selecting a function model?
  • Why is it important to choose the most appropriate function model for a real-world situation?
  • How can analyzing a data set help you justify your choice of a particular function model?
  • In what ways do mathematical models help us understand and predict real-world phenomena?