Georgia 6.PAR.7.1
The Standard
Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable.
Georgia's K-12 Mathematics Standards · Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find an unknown in a one-step equation or describe the values that make a one-step inequality true. They use addition, subtraction, multiplication, or division to isolate the variable. They substitute a given number and compare both sides to decide whether the statement holds.
What Mastery Looks Like
- A student can solve x − 8 = 13 and show the same operation on both sides. The student can solve 4x > 20, state x > 5, and verify that 5 is false while 6 is true.
Common Misconceptions
- Students may use an inverse operation on only one side or choose the wrong inverse. They may read < as ≤, including a boundary value that should be excluded. When checking a value, they may substitute incorrectly or compare before evaluating both sides.
How to Assess It
- Exit ticket: Solve x + 7 = 19. Then decide whether x = 11 makes x + 7 ≤ 19 true, and show the substitution.
Lesson moves
Ways to Teach It
Use cups and counters to model x + 4 = 11, remove four counters from both sides, then check the value in the original equation.
Ask, “Is 5 a solution to 3x < 18?” Students calculate both sides, choose true or false, and defend their choice.
Give pairs a card deck with equations, inequalities, and candidate values; they race to sort each match into true or false.
Plan a class party with a $60 limit: write c + 18 ≤ 60 for food and supplies, then test possible food costs.
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Printable 6.PAR.7.1 Worksheet
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Related Standards
- 6.PAR.7
Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations.
- 7.PAR.3
Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.
- 8.PAR.3.3
Create and solve linear equations and inequalities in one variable within a relevant application.
- 6.PAR.7.2
Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number or any number in a specified ...
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