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.
    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.