Big Idea:

Big Idea 3

Rate of change describes how one quantity changes with respect to another.

1 week

Evidence of Understanding

  • use the rate of change to extend a pattern, sequence, table, or graph
    • identify and justify the rate at which the independent and dependent quantities/variables are changing in relation to each other
      • describe rate of change with its attached units (e.g., miles per hour)
      • calculate the rate of change between pairs of values
         
  • 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
    • convert one or both units for a given relationship, including the use of proportions and unit rate
      • Ex: convert a situation relating distance to time from miles per hour to feet per second
      • understand unit conversion is a unit rate that is proportional and is linear when graphed
    • 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
         
  • compare linear, quadratic, and exponential functions using the rate of change
    • recognize the second difference (“rate of change of the rate of change”) for quadratic functions is constant
    • recognize exponential functions grow by equal factors over equal intervals
      • rate of change for exponential growth increases over the domain
      • rate of change for exponential decay decreases over the domain
    • match a situation with a graph or table using the function’s rate of change

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

Core Resource
A core resource supports multiple days of instruction. COMING SOON!