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

Grade 4 G/T Expressions and Equations

6.EE.6

About the Math

Full Standard

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

 

Learning Targets (I can)

  • Use variables to represent numbers.
  • Determine if a variable represents a single unknown or a set of unknowns (i.e. in x + 7 > 10, x represents more than one unknown, in x + 7 = 10, x represents a single unknown).
  • Write expressions to solve real-world problems.

 

About the Math 

  • Use variables to represent numbers.

Students write expressions to represent various real-world situations. Given a contextual situation, students define variables and write an expression to represent the situation. No solving is expected with this standard. Students should understand the inverse relationships that can exist between two variables. Connecting writing expressions with story problems and/or drawing pictures will give students a context for this work. It is important for students to read algebraic expressions in a manner that reinforces that the variable represents a number.

  • Determine if a variable represents a single unknown or a set of unknowns (i.e. in x + 7 > 10, x represents more than one unknown, in x + 7 = 10, x represents a single unknown).

Variables can represent one or more unknowns dependent upon the equation or inequality. Often, students think a variable represents a specific value that they have to find. They recognize that it is unknown but they don't necessarily recognize that it could represent more than one value. 

  • Write expressions to solve real-world problems.

Expressions, equations, and inequalities can represent real-world problems. These tools can then be used to model the contexts and find solutions. Students have been working with creating expressions and equations for real-world problems since primary grades.

 

Essential vocabulary for this standard includes: inequalities, equations, and variable. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

 

 

Progression of Standard within Grade 4 G/T

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

 

 

 
  • Use variables to represent numbers.
  • Determine if a variable represents a single unknown or a set of unknowns (i.e. in x + 7 > 10, x represents more than one unknown, in x + 7 = 10, x represents a single unknown).
  • Write expressions to solve real-world problems.

 

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)
  • Graph two patterns/rules on coordinate plane (5.OA.3)
  • Use equations and inequalities to solve problems by reasoning about the quantities. (7.EE.4)

 

 

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Instructional Tasks

TASKS

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

  • A carpenter charges $25 per hour plus the cost of materials. It takes the carpenter h hours to build a bookcase and $50 in materials. Write an expression to show the cost of the bookcase.
  • Tommy runs 3 times faster than Mikayla. Both Tommy and Mikayla ran the 100-yard dash. Write 2 expressions to show that Tommy ran the 100-yard dash 3 times faster than Mikayla.
  • Using 3 as the value for b, create two equations that equal a total of 42.
  • You are on a square called s on the 100 chart. Write expressions to describe these locations in terms of s:
    • 31 less than s
    • 37 more than s
    • 18 more than s

 

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 10 • Using Expressions and Equations

Write Expressions with Variables to Solve Problems:

 

 

Additional Tasks

These links provide instructional ideas connected to this standard. 

brachiosaurus

 

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 Open Sentences, Activity 12.5, Page 230
Number Tricks, Activity 12.9, Page 235

Hands-On Standards

 

 5-6 108 (Expressions with a Variable)
110 (Equations with a Variable)

Nimble with Numbers

6-7

 126-128 (Modeling Equations)
132-133 (Creating Equations)
140-141 (Solve and Travel)
143 (Symbolizing Number Riddles)

Groundworks: Algebraic Thinking

 5 55 (Weight Scales)

Problem-Driven Math

 6

94-96 (Problem #25)

 

 

 

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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

rubric

  • Use variables to represent numbers.
  • Determine if a variable represents a single unknown or a set of unknowns (i.e. in x + 7 > 10, x represents more than one unknown, in x + 7 = 10, x represents a single unknown).
  • Write expressions to solve real-world problems.

 

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

 

 

 

 

 

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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.