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


  • define variables within a situation and describe how they relate to each other
    • describe quantities as values that include a sign, the number, and the unit in a situation
      • convert between units within a single measurement system (Example: inches to feet)
    • identify dependent and independent variables for a given situation/context
      • justify which quantities in a situation are the most important
    • function relationships in a given situation from other relations(Note: this is a introduction explored in depth in Unit 1, Big Idea 2)
      • Example: If “grapes are $2 a pound, and turkey is $7 a pound,” then pounds of grapes to cost of grapes is a function, and pounds of grapes to cost of turkey is a relation
    • determine appropriate domain and range values of a function for a given situation
      • state restrictions of a function’s domain and range
      • select appropriate units and round as indicated by the context
    • describe the quantities in the domain and range using the terms whole, integer, rational, irrational, etc.


  • analyze graphs to describe the relationship between quantities in a context/situation
    • interpret the graph of a function by identifying key features and describing what those features represent 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 them to make predictions about outputs of a function in a situation (include 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.