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Enhancing the teaching of problem solving involving fractions. Cheryl McAllister Southeast Missouri State University December 2008 http://cstl-csm.semo.edu/mcallister/mainpage. Topics for today. Definitions Ordering techniques Problem solving using only the definition of fractions

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enhancing the teaching of problem solving involving fractions

Enhancing the teaching of problem solving involving fractions

Cheryl McAllister

Southeast Missouri State University

December 2008

http://cstl-csm.semo.edu/mcallister/mainpage

topics for today
Topics for today
  • Definitions
  • Ordering techniques
  • Problem solving using only the definition of fractions
  • Operations with fractions
  • Problem solving using operations with fractions
definitions
Definitions
  • There is no one standard definition for the term ‘fraction’.
  • There are a variety of ways to conceptualize fractions:
    • Part/whole: ¾ means 3 parts out of 4 equal sized parts that make a whole or unit
    • Quotient: ¾ means 3 divided by 4
    • Ratio or Rate: ¾ means 3 parts compared to 4 parts
ordering techniques
Ordering techniques
  • Standard method – find a common denominator
  • Intuitive methods
    • Same denominator – compare numerators
    • Same numerator – compare denominators
    • One away from a whole
    • Benchmarking by 1/2
problem solving using only the definition of fractions
Problem solving using only the definition of fractions
  • Problem solving that emphasizes the importance of identifying the ‘whole’ or ‘unit’ that is the reference for the fraction
  • Problem solving that emphasizes the definition of a fraction – equal sized parts of a whole
operations with fractions
Operations with fractions
  • Using manipulatives to reinforce what it means to add, subtract, multiply and divide fractions.
  • Addition – joining two sets
  • Subtraction – take-away or comparison of two sets
  • Multiplication – area of a rectangle or scaling
  • Division – partitive or measurement
problem solving using operations with fractions
Problem solving using operations with fractions
  • Examples of problems using different contexts
  • Have students write their own problems, then trade with other students
  • Encourage students to draw diagrams to better understand word problems. What is the whole? What operation does the word problem describe? Does the answer make sense?