1. CCSS Alignment
The student is working toward proficiency in HSF-LE.B.5 as shown in the student’s ability to interpret the parameters of a linear or exponential function given a context. The student was clearly able to create a linear function from the context given, but initially struggled to interpret the percent rate of change correctly as an exponential function.
HSF-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.
Because this is a special education student, when the work is compared to task 1, it appears that number size is obscuring the student’s ability to demonstrate proficiency in explicit and recursive equations. There is evidence of this by the revision marks on the student’s paper.
3. Comprehension & Application
SMP.7: Look for and make use of structure.
The student uses the table as a tool to reconsider the student’s initial interpretation of the context. The student was looking at the structure of the table with common factors and common differences, which allowed the student to look back and revise the interpretation.
4. CCSS Alignment
The intent of standard HSF-LE.A.3 is to recognize that exponential functions will eventually exceed a linear function. The student did make this observation. There is evidence that the table helped make this connection, even though there is no graphical evidence.
HSF-LE.A.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.