Grade 8: Freestyle 200 – Functions


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8. F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8. F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph.  (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Standards for Mathematical Practice

MP.1       Make sense of problems and persevere in solving them.

MP.2       Reason abstractly and quantitatively.

MP.3       Construct viable arguments and critique the reasoning of others.

MP.4       Model with Mathematics.

MP.6       Attend to precision.


This unit “Freestyle 200 – Functions” from the NYC Department of Education is focused on the introduction to a precise definition of functions. The unit is paced to 2 to 3 weeks, depending on students’ prior knowledge. Prerequisite knowledge includes using tables and graphs to represent the values of proportional and non-proportional relationships, interpreting and evaluating linear equations, and solving systems of linear equations. The unit includes an outline with formative assessments and suggested learning activities. A performance task with a rubric and scored student work is included.


Connecticut teachers should be aware that this unit is actually an outline with links to multiple sources. Teachers who are not using the comprehensive Algebra I Curriculum may need to select some of the resources and adapt them to fit student needs during the transition to full implementation of the CCSS-M.


  • The multiple links to lessons provide a balanced approach for instruction as well as opportunities for differentiation.
  • The performance task requires that students analyze graphs of functions and interpret rates of change, intersections, and points on the curves of different functions.