1. CCSS Alignment
The student is not demonstrating proficiency in HSF-LE.A.2. The student can construct recursive equations for linear tables. However, the student is not consistent in writing a correct explicit linear equation from a linear table and graph, as shown in question 3. Although the student incorrectly decides that question 3 is a linear situation, the student does not write a correct explicit linear equation to match the table. Because the student incorrectly identifies the situation in question 3 as linear, there is no evidence that the student can write an exponential equation.
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).
2. Comprehension & Application
SMP.7: Look for and make use of structure.
In the two linear graphs in question 1 and 3, it appears that all linear graphs pass through the origin, since the student labels the y-coordinate of the origin with the value of the starting amount. This is problematic in distinguishing linear situations that are proportional to linear situations that are not proportional. The student uses the graph to show the mapping between the input and output values of the function, relating the structure of the graph to the structure of the table.
3. CCSS Alignment
The student is below proficient in HSF-LE.A.1. The student is unable to distinguish between linear and exponential contexts.
HSF-LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.