Enhancing the teaching of problem solving involving fractions

1. Enhancing the teaching of problem solving involving fractions Cheryl McAllister Southeast Missouri State University December 2008 http://cstl-csm.semo.edu/mcallister/mainpage

2. Topics for today • Definitions • Ordering techniques • Problem solving using only the definition of fractions • Operations with fractions • Problem solving using operations with fractions

3. 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

4. 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

5. 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

6. 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

7. 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?