Lesson 7: Review and Assessment

How can you strategically compare the rules of two functions if one is represented as an algebraic equation and the other is given as an input-output data table?

What structural features of an equation or a coordinate graph immediately indicate whether a function's rate of change is linear or nonlinear?

When evaluating a contextual graphing story, how do you mathematically distinguish an interval where a quantity is constant from an interval where a quantity has dropped to zero?

Function, Relation, Input (x), Output (y), Domain, Range, Independent Variable, Dependent Variable, Function Notation (f(x)), Rate of Change, Slope, Initial Value (y-intercept), x-intercept, Linear, Nonlinear, Qualitative Features (Increasing, Decreasing, Constant)

8.F.A.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.A.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

8.F.A.3: Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

8.F.B.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph.

8.F.B.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

Description: A comprehensive 2-day unit culmination.

Purpose: To solidify students' graphic and algebraic conceptualization of functions, address lingering misconceptions regarding inputs/outputs, and measure final academic growth before transitioning to systems of linear equations.

DOK Level: Level 3 (Strategic Thinking)

Notation Multiplication Syntax: Attempting to multiply a function letter by its input variable when reading function notation, such as treating f(5) as f×5 rather than evaluating the output when x=5.

Coordinate Variable Inversion: Mistakenly flipping the coordinates of real-world variables on a graph grid, such as plotting the independent variable (e.g., time) along the vertical axis instead of the horizontal axis.

Constant Interval vs. Empty Space: Assuming a flat, horizontal slope interval on a qualitative graph indicates that a value has reached absolute zero, rather than recognizing that the behavior is simply continuing at an unchanging, steady rate.

Tiered Path Review Boards

Graphic Anchor Sheet Scaffolds

Formative and Summative Assessments