Evidence of Understanding

**determine and apply the rate of change from a graph, table, sequence, or pattern**- describe how independent and dependent quantities/variables change in relation to each other
- describe
**rate of change**with its attached units (Example: miles per hour) - calculate the rate of change between pairs of values
- use the rate of change to extend a pattern, sequence, table, or graph
- use the
**common difference**or**common ratio**to find terms in an**arithmetic**or**geometric**sequence

- use the

**interpret a mathematical representation using the rate of change**- calculate and articulate the usefulness of the
**average rate of change**in relation to context- recognize when the average rate of change is zero and describe its meaning

- analyze and compare rates of change within the context of situations
- recognize how scale or units impact a comparison

- convert one or both units for a given relationship, including the use of
**proportions**and unit rate*Example: convert miles per hour to feet per second*- understand unit conversion is a unit rate that is proportional and is linear when graphed

- calculate and articulate the usefulness of the

**compare linear, quadratic, and exponential functions using the rate of change**- recognize a
**constant rate of change**in a table of values, graph, or situation- explain why a
**line**results when graphing a constant rate of change

- explain why a
- recognize the second difference for quadratic functions is constant
- recognize
**exponential functions**grow by equal factors over equal intervals- distinguish e
**xponential growth**from**exponential decay**

- distinguish e
- match a situation with a graph or table using the function’s rate of change

- recognize a

Develop conceptual understanding:

rate, rate of change, average rate of change, proportion, constant rate of change, line, exponential function, exponential growth, exponential decay

Supporting terms to communicate:

function, f(x), axes, units, scale, coordinate point, ordered pair, table of values, interval, increasing, decreasing, positive, negative, turning point, maximum, minimum, intercept, dependent, independent, domain, range