8.PAR.3Linear Equations and Inequalities

Expectations

• 8.PAR.3.1

  Interpret expressions and parts of an expression, in context, by utilizing formulas or expressions with multiple terms and/or factors.

• 8.PAR.3.2

  Describe and solve linear equations in one variable with one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b). Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

• 8.PAR.3.3

  Create and solve linear equations and inequalities in one variable within a relevant application.

• 8.PAR.3.4

  Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.

• 8.PAR.3.5

  Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solution based on the contextual, mathematical situation.

• 8.PAR.3.6

  Use algebraic reasoning to fluently manipulate linear and literal equations expressed in various forms to solve relevant, mathematical problems.

Georgia Milestones coverage

• Mathematics Grade 8 (EOG) · Patterning & Algebraic Reasoning

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

  about 17% of the test · 10 points

What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

Beginning

Identify terms, factors, and coefficients in an expression. Solve linear equations in the form of ax + b = cx with one solution.

Developing

Interpret terms, factors, operations, and coefficients of an expression in context in binomial expressions. Solve linear equations in one variable that have infinitely many solutions or no solutions, and identify the linear equation or inequality in one variable that models a relevant application. Use relevant algebraic properties to solve one-variable equations or inequalities. Justify the steps of a one-solution equation or inequality. Solve linear equations and inequalities in one variable with coefficients represented by letters (e.g., ax + 3 = 7, solve for x).

Proficient

Interpret terms, factors, operations, and coefficients of an expression in context in multi-term expressions by using formulas. Describe situations with one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b) when solving a one-variable equation. Create and solve a linear equation or inequality in one variable that models a relevant application. Solve linear equations and inequalities, including compound inequalities, in one variable from relevant mathematical phenomena with coefficients represented by letters and describe the solution in the context of the problem. Rearrange formulas and different linear and literal mathematical equations to highlight a quantity of interest and be able to use the new formula to solve for an appropriate value.

Distinguished

Explain real-world phenomena involving linear equations and inequalities, including compound inequalities in one variable, and relate solutions or solution sets back to the contexts of the real phenomena.

The same standard across grades

1. Grade 1 · 1.PAR.3

   Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns found in real-life situations.

2. Grade 3 · 3.PAR.3

   Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole numbers within 100.

3. Grade 4 · 4.PAR.3

   Generate and analyze patterns, including those involving shapes, input/output diagrams, factors, multiples, prime numbers, and composite numbers.

4. Grade 7 · 7.PAR.3

   Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.

5. Grade 8 · 8.PAR.3 (this standard)

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