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?