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5.3 TeachingThe development of rational number concepts is a major goal for grades 3-5, which should lead to informal methods for calculating with fractions. NCTM Standards 2000, page 33The Standards are saying that informal methods of calculating with fractions should precede rules and algorithms for such calculations. Using the pizza model to represent fractions, illustrate each of the following operations and briefly explain how each result can be shown informally without rules and algorithms. Write a word problem for school students that can be answered by each of the following computations. 1/2 + 1/8 = 5/8 3/4 – 3/8 = 3/8 2 x 3/4 = 1 1/2 1/2 ÷ 4 = 1/8 1/2 ÷ 1/8 = 4 5.3 Concepts Students in grades 3-5 will need to be encouraged to routinely reflect on the size of an anticipated solution. If 3/8 of a cup of sugar is needed for a recipe and the recipe is doubled, will more or less than one cup of sugar be needed? NCTM Standards 2000, page 156Recipes are meaningful sources for questions involving fractions that can be understood by school students. Write a question involving recipes for each of the following situations: addition of two or more fractions; subtraction of two fractions; multiplication of a fraction times a whole number; and division of a fraction by a fraction. 5.3 Concepts The 6th national mathematics assessment found that only 25% of the eighth grade students could write a word problem involving division of a whole number and a fraction (Kouba, Zawojewski, and Strutchens, 1997). Results from the Sixth Mathematics Assessment of NAEP, page 132An understanding of division involving fractions and/or whole numbers can be enhanced by creating and solving word problems that are meaningful. Write a word problem for each of the following situations: division of a whole number by a fraction; division of a fraction by a fraction; and division of a fraction by a whole number. 5.3 Concepts The division of fractions has traditionally been quite vexing for students. Although “invert and multiply” has been a staple of conventional mathematics instruction and although it seems to be a simple way to remember how to divide fractions, students have for a long time had difficulty doing so. NCTM Standards 2000, page 219Explain the equal quotients mental calculating technique for dividing one whole number by another and give some examples. Then use this calculating technique to show and explain why the “invert and multiply” method for computing the quotient of two fractions produces the correct answer. |