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

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 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.

TASKS

These tasks can be used with small group or whole group instruction.

• Mykia and Amari have equal amounts of play money in two piles. Mykia has $1 and 1 quarter in her pile. Amari has 5 quarters in his pile. Are the two piles equal? Write expressions to express the relationship. 1 + 4(.25) = 5(.25)
• If 10 x 3 = 30, does 10 x 3 + 4 = 30 + 4? Explain your reasoning.
• What value in the “blank” makes this a true statement? 6(x + 6y) = 12x - 6x + 3y + ___
• You use a $20 bill to pay for a DVD that cost $18.60. The cashier gives you two $1 bills and 4 dimes back. Were you given the correct change? Why or why not? 

SLIDE-BASED TASKS 

  These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Additional Tasks 

  These links provide instructional ideas connected to this standard.  [NOTE: NCTM membership required for access to Illuminations lessons.] 

• Lesson 6.8 - Equal and Equivalent Links to an external site. (Illustrative Math)
• Equivalent Expressions Links to an external site. (Illustrative Math)
• Rectangle Perimeter 2 Links to an external site.(Illustrative Math)
• Equivalent Expressions 1 Links to an external site. (Open Middle)
• Equivalent Expressions 2 Links to an external site. (Open Middle)
• Equivalent Expressions 3 Links to an external site. (Open Middle) 
• Combining Terms Download Combining Terms (HCPSS Lesson Collection)
• Deep Sea Dual Links to an external site.(NCTM Illuminations Lesson)

Tasks From Print Resources

  These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	5-8	Tilt or Balance, Activity 12.3, Page 228 True or False, Activity 12.4, Page 229
	Hands-On Standards	5-6	112 (Addition/Subtraction Equations) 114 (Multiplication/Division Equations)
	Brain Compatible Lessons for Mathematics	4-5	121-126
	Problem-Driven Math	5	109 (Tabletop Tiles)

Centers

  These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

• Grocery Store Links to an external site. (print resource)
• Expressions Match Game Download Expressions Match Game
   (print resource)
• Station Activity Download Station Activity
  (print resource) 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

  These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

• Equivalent Expressions A Links to an external site.
• Equivalent Expressions B Links to an external site.
• Identify and Generate Equivalent Expressions a Links to an external site.
• Identify and Generate Equivalent Expressions b Links to an external site.
• Identify and Generate Equivalent Expressions c Links to an external site.
• Identify and Generate Equivalent Expressions d Links to an external site.
• Identify and Generate Equivalent Expressions e Links to an external site.
• Identify and Generate Equivalent Expressions f Links to an external site.

• Evaluate Expressions for Equivalence Links to an external site.
• Evaluate Expressions for Equivalence_2 Links to an external site.
• Evaluate Expressions for Equivalence_3 Links to an external site.
• Generate and Explain Equivalent Expressions Links to an external site.

Learning Targets

• 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.

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

Rubric for Tasks Links to an external site.