6.EE.3 - About the Math, Learning Targets, and Increasing Rigor

Grade 5AGL Expressions and Equations

6.EE.3

About the Math

Full Standard

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

 

Learning Target (I can)

  • Explain why two or more expressions are equivalent using properties of operations.
  • Generate equivalent expressions using properties of operations.

 

About the Math

  • Explain why two or more expressions are equivalent using properties of operations.
  • Generate equivalent expressions using properties of operations.

Students use the distributive property to write equivalent expressions. Using their understanding of area models from elementary students illustrate the distributive property with variables. Properties are introduced throughout elementary grades (3.OA.5); however, there has not been an emphasis on recognizing and naming the property. In 6th grade students are able to use the properties and identify the properties by name as used when justifying solution methods. Students interpret y as referring to one y. Thus, they can reason that one y plus one y plus one y must be 3y. They also use the distributive property, the multiplicative identity property of 1, and the commutative property for multiplication to prove that y + y + y = 3y.

 

Essential vocabulary for this standard includes: numerical expressions, algebraic expressions, evaluate, sum, equivalent expressions, variables, and distributive property. 

 

 

Progression of Standard within 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 or more expressions are equivalent using properties of operations.
  • Generate equivalent expressions using properties of operations.

 

 

 

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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Instructional Tasks

TASKS

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

  • Is 5v = v + 5 true or false? If false, what can you do to make the expression true?
  • Write two expressions equivalent to 30x + 20y.
  • How does knowing factors of numbers help you find equivalent expressions for 24b - 36t? Use examples as you explain your thinking.
  • Anthony wrote the expression 4(s +7) where s = 6 and Bettina wrote the expression 6(s + 2) where s = 6. Bettina thinks that her expression and Anthony’s expression are equivalent. Is Bettina correct? Explain your thinking.
  • Where could you insert parentheses to make this number sentence true?
    • 80 ÷ 8 x 5 + 4 = 90
  • Which expressions are true when the same number is used to replace the variable?
    • 12 + a = a + 12
    • a - 5 = 5 - a
    • 6 + (5 +a) = (6 + 5) + a
    • 0 x a = a
    • 7 x (4 + a) = (7 x4 ) + a
    • a = 0 + a

 

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.

Module 5 • Expressions

Use Properties to Determine if Expressions are Equivalent:

 

 

Additional Tasks 

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

 

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

 

6-8

Open Sentences, Activity 12.5, Page 230
Writing True/False Sentences, Activity 12.6, Page 231
Conjecture Creation, Activity 12.10, Page 241

 

 

 

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Independent Work

Centers

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

 

 

 

 

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.

 

 

 

 

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Assessment

Learning Targets

  • Explain why two or more expressions are equivalent using properties of operations.
  • Generate equivalent expressions using properties of operations.

 

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

Download Rubric for Tasks (3-5)

(pdf)

 

 

 

 

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.