Big Idea:

Big Idea 3

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

1 week

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

 

  • 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

 

  • 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
    • recognize the second difference for quadratic functions is constant
    • recognize exponential functions grow by equal factors over equal intervals
      • distinguish exponential growth from exponential decay 
    • 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
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