Big Idea:

Big Idea 1

The relationship between the variables of a function can be represented visually by a graph.

1 week

Evidence of Understanding

  • identify variables within a situation and describe how they relate to each other
    • identify dependent and independent variables given a situation/context
      • grapple with several possible relationships and distinguish the difference between a relation and a function
    • analyze quantities and their units in a situation to justify which ones are the most important
      • use units to describe quantities with precision
    • determine appropriate domain and range values of a function based on a given situation
      • state restrictions on a function’s domain and range within a given situation
      • select appropriate units and round as indicated by the context or direction
    • think flexibly about the relationship between quantities by converting among different-sized standard measurement units within a given measurement system (ie. inches to feet)
  • recognize the graph of a function as one way to represent all of the solutions between two quantities in a context/situation (NOTE: no equations!)
    • explain how two axes of a graph are related to each other and describe specific coordinate points that define that relationship
    • interpret the graph of a function by identifying its most important features and describing what those features mean within the context of the situation
      • key features include: intervals where the function is increasing or decreasing, positive or negative, intercepts, turning points/maximums and minimums, symmetries
    • analyze patterns within a function’s graph and use it to make predictions about outputs of a function in a situation (including piecewise and step functions)
      • recognize how restrictions on a function’s domain or range can cause a graph to be continuous or discrete

Develop conceptual understanding:

dependent, independent, function, relation, units, domain, range, interval, continuous, discrete

Supporting terms to communicate:

convert, ordered pair, axes, x-axis, y-axis, coordinate point, increasing, decreasing, positive, negative, turning point, maximum, minimum, intercept, piecewise function, step function

Core Resource
A core resource supports multiple days of instruction.
  • Studying Situations
    A multiple-day resource that supports students in grappling with quantities, relationships, functions, and graphs.
    Studying Situations

    The goal of these activities are to leverage students’ prior experiences to describe how the qualities and units belonging to variables in a situation impact the shape, direction, and features of graphs.  

    All Resources From:
Instructional Routine: Connecting Representations
These tasks are embedded within the instructional routine called Connecting Representations.