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K–12 teaching and learning · from the UNC School of Education

Fair division

http://www.sciencenetlinks.com/sci_update.cfm?DocID=20

A lesson plan for grades 6–8 Mathematics and Science

Provider: American Association for the Advancement of Science


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In this Science Update, students explore the idea that disagreements can be solved with math. Mathematician Francis Su at Harvey Mudd College has written a computer program that he says will guarantee what thinks will solve the problem of dividing rooms and rent among roommates. The Rental Harmony Theorem helps uses an interactive algorithm to decide how to modify and figure the price of rent. Science NetLinks provides a link to the audio file, a written transcript, and questions to engage students in a discussion about the theorem, how it can be put into practice, and what other kinds of disputes might be resolved using similar fairness programs. This activity also contains links to two follow up lessons from Science NetLinks.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 6

  • Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
    • Objective 1.04: Develop fluency in addition, subtraction, multiplication, and division of non-negative rational numbers.
      • Analyze computational strategies.
      • Describe the effect of operations on size.
      • Estimate the results of computations.
      • Judge the reasonableness of solutions.

Grade 7

  • Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
    • Objective 1.02: Develop fluency in addition, subtraction, multiplication, and division of rational numbers.
      • Analyze computational strategies.
      • Describe the effect of operations on size.
      • Estimate the results of computations.
      • Judge the reasonableness of solutions.

Science (2005)

Grade 6

  • Goal 1: The learner will design and conduct investigations to demonstrate an understanding of scientific inquiry.
    • Objective 1.01: Identify and create questions and hypotheses that can be answered through scientific investigations.
    • Objective 1.05: Analyze evidence to:
      • Explain observations.
      • Make inferences and predictions.
      • Develop the relationship between evidence and explanation.
    • Objective 1.08: Use oral and written language to:
      • Communicate findings.
      • Defend conclusions of scientific investigations.
    • Objective 1.09: Use technologies and information systems to:
      • Research.
      • Gather and analyze data
      • Visualize data.
      • Disseminate findings to others.
    • Objective 1.10: Analyze and evaluate information from a scientifically literate viewpoint by reading, hearing, and/or viewing:
      • Scientific text.
      • Articles.
      • Events in the popular press.

Grade 7

  • Goal 1: The learner will design and conduct investigations to demonstrate an understanding of scientific inquiry.
    • Objective 1.01: Identify and create questions and hypotheses that can be answered through scientific investigations.
    • Objective 1.05: Analyze evidence to:
      • Explain observations.
      • Make inferences and predictions.
      • Develop the relationship between evidence and explanation.
    • Objective 1.08: Use oral and written language to:
      • Communicate findings.
      • Defend conclusions of scientific investigations.
    • Objective 1.09: Use technologies and information systems to:
      • Research.
      • Gather and analyze data.
      • Visualize data.
      • Disseminate findings to others.
    • Objective 1.10: Analyze and evaluate information from a scientifically literate viewpoint by reading, hearing, and/or viewing:
      • Scientific text.
      • Articles.
      • Events in the popular press.