6.EE.9 - About the Math, Learning Targets, and Increasing Rigor

Grade 5AGL Expressions and Equations

6.EE.9

About the Math

Full Standard

Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

 

Learning Targets (I can)

  • Describe a dependent variable.
  • Describe an independent variable. 
  • Use variables to represent quantities that change in relation to one another.
  • Write an equation to express a dependent variable in terms of an independent variable.
  • Use a function to generalize the relationship between the dependent and independent variables 
  • Graph ordered pairs resulting from a function.
  • Analyze the relationship between the dependent and independent variables using graphs and tables.
  • Make predictions or assumptions about relationships and use graphs and tables to prove or disprove the prediction.

 

About the Math 

Students can use many forms to represent relationships between quantities. Multiple representations include describing the relationship using language, a table, an equation, or a graph. Translating between multiple representations helps students understand that each form represents the same relationship and provides a different perspective on the function. Essential vocabulary for this standard includes: dependent, independent, variables, quantity, ordered pairs, equation, constant speed, distance, and time. 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 6 (5 AGL)

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

Print Resources
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Describe a dependent variable.
  • Describe an independent variable. 
  • Use variables to represent quantities that change in relation to one another.
  • Write an equation to express a dependent variable in terms of an independent variable.
  • Use a function to generalize the relationship between the dependent and independent variables 
  • Graph ordered pairs resulting from a function.
  • Analyze the relationship between the dependent and independent variables using graphs and tables.
  • Make predictions or assumptions about relationships and use graphs and tables to prove or disprove the prediction.

 

 

 

 

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 

Graph two patterns/rules on coordinate plane (5.OA.3)

This concept is not taught after grade 6.  Students are expected to apply the standard proficiently.

 

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Instructional Tasks

TASKS

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

  • The following equation shows Jen’s babysitting earnings: e = 12h. Jen babysat for 3 hours for 7 days straight. Create a function table show how much she earned in the 7 days.
  • The PTA is making pompoms for the school pep rally. The supplies cost $4, and they plan to sell the pompoms for $1 each. Let x = the number of pompoms sold. Let y = the profit. Graph the equation y = x - 4 to show the relationship between x and y
  • You are considering whether to start buying organic eggs at the grocery store. A carton of a dozen organic eggs costs $0.75 more than a regular carton. You buy about one carton per week. Write an equation to represent the additional cost of buying organic eggs over time. Create a graph to show the increase in price over time for a month.
  • The two function tables (pictured to the right) show Karen and Jerry’s run times. Karen and Jerry are arguing about who ran 7 miles faster. Use what you know about variable and expressions to explain who ran the 7 miles faster.

 

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 7 • Inequalities

Use Dependent and Independent Variables:

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

 

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 Sketch A Graph, Activity 12.14, Page 251
Bottles and Volume Graphs, Activity 12.15, Page 252
How Many Gallons Left, Activity 12.16, Page 256

 

 

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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.[NOTE: NCTM membership required for access to Illuminations lessons.]

 

 

 

 

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

  • Describe a dependent variable.
  • Describe an independent variable. 
  • Use variables to represent quantities that change in relation to one another.
  • Write an equation to express a dependent variable in terms of an independent variable.
  • Use a function to generalize the relationship between the dependent and independent variables 
  • Graph ordered pairs resulting from a function.
  • Analyze the relationship between the dependent and independent variables using graphs and tables.
  • Make predictions or assumptions about relationships and use graphs and tables to prove or disprove the prediction.

 

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.