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6.2 TeachingMultiplying and dividing fractions and decimals can be challenging for many students because of problems that are primarily conceptual rather than procedural. From their experience with whole numbers, many students appear to develop the belief that “multiplication makes bigger and division makes smaller." NCTM Standards 2000, page 218Write an explanation with diagrams that would convince school students that when multiplying two decimals, both of which are less than 1, the product will be smaller than either decimal. 6.2 Concepts In the 16th century, several different notations were used to represent decimals. One of these involved writing a small numeral to indicate the number of decimal places. As examples, 4.85 was written as 485 . . . 2 and 15.6 as 156 . . . 1 . Use this notation to show an addition and multiplication algorithm for computing the sum and product of these two numbers and describe how these algorithms work. 6.2 Concepts Estimation serves as an important companion to computation. It provides a tool for judging the reasonableness of calculator, mental, and paper-and-pencil computations. NCTM Standards 2000, page 155When estimating a product by rounding one decimal up to the nearest whole number and one decimal down to the nearest whole number, the estimation might be larger or smaller than the actual product (see section 6.2). Devise a method, without computing the actual product, for determining if the estimation from rounding is too large or too small. Use the base-ten grid model to explain and illustrate why your method works. |