Enhancing the teaching of problem solving involving fractions

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# Enhancing the teaching of problem solving involving fractions - PowerPoint PPT Presentation

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

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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
• Operations with fractions
• Problem solving using operations with fractions
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
• 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 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
• 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
• 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?