6.EE.4 - About the Math, Learning Targets, and Increasing Rigor

Grade 5AGL Expressions and Equations

6.EE.4

Full Standard

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

 

Learning Targets (I can)

  • Explain why two expressions are equivalent.
  • Explain why two expressions are not equivalent though they generate the same value (i.e. 3y and 2y are not equivalent even though both equal zero when y equals zero; 3x is not always equivalent to 3y).
  • Generate equivalent expressions.

 

About the Math

  • Explain why two expressions are equivalent.

Expressions are equivalent when they always generate the same value regardless of the value being used for the unknown. For example, 3y and y + y + y are equivalent because both always generate the same value.

  • Explain why two expressions are not equivalent though they generate the same value (i.e. 3y and 2y are not equivalent even though both equal zero when y equals zero; 3x is not always equivalent to 3y). 

Expressions may generate the same value though they are not equivalent. This is a common misconception for many students. 3y and 4y are not equivalent even though they both generate 0 when 0 is used as the value for y. There are countless other examples of expressions that are not equivalent though they occasionally produce the same value. Students should be able to articulate this clearly.

  • Generate equivalent expressions.

Using what they know about equivalent expressions, students should be able to generate equivalent expressions. They should also be able to explain why the expressions are equivalent - aligned to the information provided above. 

 These learning targets are connected to student understanding of like terms. Students demonstrate an understanding of like terms as quantities being added or subtracted with the same variables and exponents. For example, 3x + 4x are like terms and can be combined as 7x; however, 3x + 4 x 2 are not like terms since the exponents with the x are not the same. This concept can be illustrated by substituting in a value for x. For example, 9x – 3x = 6x not 6. Choosing a value for x, such as 2, can prove non-equivalence. Students can also generate equivalent expressions using the associative, commutative, and distributive properties. They can prove that the expressions are equivalent by simplifying each expression into the same form.

Essential vocabulary for this standard includes: algebraic expressions, like terms, equivalent expressions, and variables. 

 

 

Development of the Standard in Grade 6 (5 AGL)

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Explain why two expressions are not equivalent though they generate the same value (i.e. 3y and 2y are not equivalent even though both equal zero when y equals zero; 3x is not always equivalent to 3y).
  • Generate equivalent expressions.

 

 

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 5 Grade 7
  • Write simple expressions (5.OA.2)
  • Apply properties if operations to linear expressions (7.EE.1)

 

 

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