ALGRZ.MATH.7.C

Determine the accuracy of a prediction from a function that models a set of data compared to the actual data using comparisons between average rates of change and finite differences such as gathering data from an emptying tank and comparing the average rate of change of the volume or the second differences in the volume to key attributes of the given model.

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

Standard Unwrapping

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Vocabulary
accuracypredictionfunctionset of dataactual datacomparisonsaverage rates of changefinite differencesemptying tankvolumesecond differenceskey attributesmodel
Skills
  • determine (accuracy of a prediction from a function compared to actual data) #dok2
  • compare (average rate of change and finite differences of data to key attributes of a model) #dok2
  • gather (data from real-world contexts, such as an emptying tank) #dok1
  • analyze (differences between predictions and actual outcomes using rates of change or finite differences) #dok3
Learning Targets
  • I can gather data from a real-world context, such as the volume of an emptying tank. #dok1
  • I can compare the average rate of change or finite differences in a set of data to the key attributes of a function model. #dok2
  • I can determine the accuracy of a prediction from a model by comparing it to actual data. #dok2
  • I can analyze how closely a mathematical model fits actual data using quantitative comparisons such as average rates of change or second differences. #dok3
Big Ideas
  • Comparing predicted values from models to actual data helps us evaluate how well a model fits real-world situations.
  • Average rates of change and finite differences are essential tools for measuring and explaining the fit between data and mathematical models.
Essential Questions
  • How can we tell if a function provides accurate predictions for a real-world data set?
  • What role do average rates of change and finite differences play in evaluating models?
  • Why might a model’s prediction differ from actual data, and how can we measure that difference?
  • How do we use key attributes of a function to compare predictions and actual observations?
  • In what ways can analyzing second differences help us assess the validity of a model?