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.
    Resource:
    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.