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999 West Dundee Road
Wheeling, Illinois 60090

Phone: 847-537-8270

Superintendent: Dr. Michael Connolly

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Mathematics

Ratios and Proportional Relationships

Critical Content

Power Standards

  • Determine whether two quantities are in a proportional relationship. (7.RP.2a)
  • Use proportional relationships to solve multi-step ratio and percent problems. (7.RP.3)

 

Concepts and Skills

* Power Standard Content

  • Convert rates to equivalent unit rates (including those presented as fractions)
  • * Recognize proportional relationships
  • Find the unit rate of a proportional relationship presented in a table, graph, equation, or description
  • Write equations to represent proportional relationships
  • Interpret a point on the graph of a proportional relationship
  • * Solve multi-step ratio and percent problems
  • Set up and solve proportions that arise in applications

 

Critical Language

Language Usage

  • A student in 7th grade can demonstrate the ability to apply and comprehend critical language by developing and explaining ways to use quantitative comparison information to make larger and smaller scale models and reasoning in proportional situations.

 

Content-Specific Vocabulary

  • Unit rate
  • Fraction
  • Ratio
  • Proportional relationship
  • Proportion
  • Equations
  • Percent
  • Scale

 

Process-Specific Vocabulary

  • Relationships
  • Recognize
  • Analyze
  • Interpret
  • Set up
  • Solve
  • Equivalent

 

Concept-Based Connections

Essential Understandings

  • Proportional reasoning facilitates comparisons and problem solving.
  • Proportional relationships can be scaled up or down as determined by the situation.

 

Factual Guiding Questions

  • How do you compute ratios, percentages, and fractions?
  • How do you convert between a ratio, percent, and/or fraction?
  • How do you find a unit rate?
  • How do you write and solve proportions?
  • How can you scale a ratio up or down?

 

Conceptual Guiding Questions

  • How can you use a ratio, percent, and/or fraction to make comparisons?
  • How can you scale a ratio up or down to make an equivalent ratio?
  • How do we use unit rates to make a decision?
  • Why do we use proportions?
  • How do you write and solve proportions?
  • How do you use a proportion to solve a problem?
  • How do you know when two quantities are in a proportional relationship?

 

Engaging/Debatable Guiding Questions

  • How are unit rates useful when solving problems?
  • How can we use proportions for solving problems?
  • Where can ratios be used in daily life to find unknown quantities?
  • What purpose do ratios, percent and fractions serve?