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6.3 TeachingAs with fractions and decimals, computational difficulties [with percents] need to be carefully addressed in instruction. In particular percents less than 1 percent and greater than 100 percent are often challenging . . . NCTM Standards 2000, page 217Sketch Decimal Squares to illustrate percents less than 1 percent, such as .5%, .1%, and .25%, and write a word problem involving this type of percent. Explain how Decimal Squares can be used to illustrate percents greater than 100 percent and write a word problem for such a percent. 6.3 Concepts If the ratio of girls to boys in a school is 2 to 3, this ratio also can be written as, “the ratio of girls to boys is the fraction 2/3”. However, 2/3 of the students are not girls. Write an explanation with diagrams to explain what fraction of the students are girls and what fraction are boys. Then write a general statement about the fraction of girls and the fraction of boys in a school, if the ratio of girls to boys is K to H. 6.3 Concepts If the price of an object rises from $4 to $6, the price has increased 50% and the new cost is 150% of the old cost. However, if the price decreases from $6 to $4, this is not a 50% decrease. Explain why. What is the percent decrease? In this case, the new price is what percent of the original price? Generalize this example by explaining why an increase in price from P dollars to K dollars and a decrease in price from K dollars to P dollars does not result in the same percentage increase and decrease. |