6-A-1-3


6.A.1.3 Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.

In a Nutshell

When presented with an expression, equation or inequality and given the value of the variable, students should be able to substitute the given number for the variable, then apply standard order of operations to solve for the equivalent expression. For example, “What is the value of x + 4 when x = 2?” Students would replace the x with the number 2, then evaluate.  Students should also be able to determine if an equation or inequality is true for a given variable. For example, “Is x + 2 > 3  true for the value x = 5?” Students would replace x with the given value of 5 and evaluate.  Students should understand there are many different values of x in an inequality that would make the inequality true.

Student Actions

Teacher Actions

  • Develop a conceptual understanding by exploring the use of  a variable as a symbol that represents a number.

  • Develop accurate procedures when using order of operations while evaluating an expression for a given value of a variable.

  • Develop procedural fluency when investigating the use of order of operations while simplifying to discover if an equation or inequality is true or false for a given variable value.

  • Use multiple representations such as number lines to develop a visual contextual concept of inequalities.

     

  • Implement numerical and real-world tasks where students explore and discuss expressions, equations, and inequalities.

  • Build procedural fluency by providing opportunities for students to use order of operations and simplifying expressions.

  • Use and connect representations (Ex: pan balance, number line), of expressions, equations and inequalities to aid in the understanding of numbers that will make an expression or inequality true or false.

  • Use evidence of student thinking to provide students with the opportunity to explore what numbers make an expression or inequality true in addition to numbers that make it false.

Key Understandings

Misconceptions

  • In order to evaluate an expression for a given variable, the variable must be replaced with the given number.  Then, perform the correct order of operations.

  • When a number is substituted for a variable in the expression 5x the number is a factor to be multiplied by 5.

  • There can be an infinite value of variables in an inequality that can make a statement true.

  • That a variable represents only one possible number.

  • Of the equal sign as a symbol that means "to calculate" rather than "is the same as."

  • That expressions, equations, or inequalities always result in whole number solutions.

  • There is only one value of a variable that makes an inequality true.

 

OKMath Framework Introduction

6th Grade Introduction