Georgia 8.FGR.7

8.FGR.7 is a Georgia mathematics standard. These are the expectations under it.

• 8.FGR.7.1

  Interpret and solve relevant mathematical problems leading to two linear equations in two variables.

• 8.FGR.7.2

  Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of...

• 8.FGR.7.3

  Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection

• 8.FGR.7.4

  Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.

• 8.FGR.7.5

  Create and compare the equations of two lines that are either parallel to each other, perpendicular to each other, or neither parallel nor perpendicular.

01

What Students Need to Do

Students turn a realistic situation into two linear equations and find the values that make both equations true. They use graphing, substitution, or elimination, then justify their choice and explain what the solution means.

02

What Mastery Looks Like

Students write two linear equations from a situation and solve the system accurately. They choose an efficient method and explain why it works. They check the solution in both equations and interpret it using the situation.

03

Common Misconceptions

Students may solve each equation separately instead of finding values that satisfy both. They often make sign errors during elimination or substitute into only one equation. Some confuse no solution with an incorrect method and infinitely many solutions with one solution.

04

How to Assess It

Exit ticket: Adult tickets cost $8, student tickets cost $5, and 20 tickets bring in $130. Write a system, solve it, justify your method, and explain the answer.

1. 01

   Use algebra tiles to model two equations, then combine rows to show how elimination removes one variable.

2. 02

   Ask students to compare graphing, substitution, and elimination for one system, then defend which method is most efficient.

3. 03

   Set up method-match cards where students pair each system with graphing, substitution, or elimination and solve to confirm the match.

4. 04

   Compare two phone plans with different fees and rates, then find when their total costs are equal.

• 6.PAR.7

  Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations.

• 8.PAR.3

  Create and interpret expressions within relevant situations. Create, interpret, and solve linear equations and linear inequalities in one variable to model and ...