Georgia 8.FGR.5
Georgia Standard (Expectation Cluster)
Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.
Georgia's K-12 Mathematics Standards
Cluster contents
Expectations in This Standard
8.FGR.5 is a Georgia mathematics standard. These are the expectations under it.
- 8.FGR.5.1
Show and explain that a function is a rule that assigns to each input exactly one output.
- 8.FGR.5.2
Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of ...
- 8.FGR.5.3
Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.
- 8.FGR.5.4
Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, ...
- 8.FGR.5.5
Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y₁) = m(x - x₁) (point-slope form) as defining a linear...
- 8.FGR.5.6
Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- 8.FGR.5.7
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...
- 8.FGR.5.8
Explain the meaning of the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of va...
- 8.FGR.5.9
Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students identify inputs, outputs, domain, range, initial value, and rate of change from tables, graphs, equations, and descriptions. They evaluate functions for given inputs, compare relationships across representations, and explain what graph features mean in context.
What Mastery Looks Like
- A student can use function notation, calculate outputs, and decide whether a relationship is linear or nonlinear. The student can compare two functions using rate of change and initial value, then use a graph to support a claim about a real situation.
Common Misconceptions
- Students may treat f(x) as multiplication, confuse input with output, or read a graph’s height as its rate of change. They may compare functions using only one point, assume every relationship is linear, or ignore units and realistic domain limits.
How to Assess It
- Give Function A as y = 3x + 4 and Function B as the points (0, 7) and (2, 11). Ask students to find A(5), identify each initial value and rate of change, and explain which function grows faster.
Lesson moves
Ways to Teach It
Use toy cars, ramps, meter sticks, and stopwatches to collect distance and time data, then graph and compare each car’s movement.
Ask students to write which graph shows faster growth and defend their answer using slope, points, and labels.
Run a card sort matching equations, tables, graphs, and descriptions that represent the same function.
Compare two taxi fare rules, then graph each cost and decide which company is cheaper for several trip distances.
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