The student properly represents continuous and discrete settings in each graph.
Why does the student seem to struggle with the representations for what is happening in questions 3 and 4? The defining features and parameters in the equations, tables, and graphs do not all align with each other in the exponential situations in the same way that they do align in the linear situations.
3. CCSS Alignment
The student distinguishes between linear and exponential equations in questions 1 – 3, but initially shows situation 4 as decreasing at a constant rate, but then revises the student’s thinking. Even though the chosen scale on the graphs of the exponential functions tends to make the graphs appear linear, the student still correctly identifies linear and exponential situations.
HSF-LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.
4. CCSS Alignment
The student correctly constructs linear equations in both recursive and explicit form. However, there are some issues with the exponential functions. The explicit equation on question 3 has issues with how to use the starting amount in the equation and the recursive on question 4 has issues with which number to treat as the growth factor.
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 pairs (include reading these from a table).
5. Comprehension & Application
SMP.7: Look for and make use of structure.
The student understands very well the structure of representations that are linear. There is still some work that needs to be done on looking at the structure of exponential models.