Georgia 8.PAR.4
Georgia Standard (Expectation Cluster)
Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph.
Georgia's K-12 Mathematics Standards
Cluster contents
Expectations in This Standard
8.PAR.4 is a Georgia mathematics standard. These are the expectations under it.
- 8.PAR.4.1
Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for a line intersecting the vertical a...
- 8.PAR.4.2
Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate p...
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students connect tables, graphs, equations, and real situations that show linear relationships. They distinguish proportional relationships with zero initial value from non-proportional linear relationships. They create graphs and explain rates, starting values, and points in context.
What Mastery Looks Like
- A student can match a linear situation with its table, graph, and equation. They can identify the rate of change and initial value in each form. They explain what the slope, intercept, and selected points mean in context.
Common Misconceptions
- Students may think every straight-line graph shows a proportional relationship. They may confuse slope with the starting value or ignore whether the line passes through the origin. They may also describe points without using the quantities and units from the situation.
How to Assess It
- Use this exit ticket: “A gym charges $12 to join and $5 per visit. Write an equation, sketch the graph, and explain why the relationship is not proportional.”
Lesson moves
Ways to Teach It
Have pairs measure water added to an empty cup and a cup starting with 100 milliliters, then graph and compare both data sets.
Ask students to explain how changing the initial value affects a graph, equation, and real situation while the rate stays constant.
Give groups cards showing tables, graphs, equations, and situations, then have them match each set and label it proportional or non-proportional.
Compare a taxi fare with a starting fee to an hourly wage with no starting amount, then graph and interpret both models.
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Printable 8.PAR.4 Worksheet
A ready-to-print activity worksheet aligned to 8.PAR.4, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Related Standards
- 7.PAR.4
Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.
- 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.
- 7.PAR.4.8
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in differen...
- 7.PAR.4.4
Identify, represent, and use proportional relationships.
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