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3.3 Lesson 3.3 Solving Conversion Problems Objectives ● 3.3.1 Explain what happens when a measurement is multiplied by a conversion factor. ● 3.3.2 Describe the kinds of problems that can be easily solved using dimensional analysis. Lesson Links Ch. 3 Core TR: Section 3 Review 3.3 Chemistry Tutorial: Using Dimensional Analysis 3.3 Lesson Overview (PowerPoint file) 3.3 Chemistry Tutorial: Using Density as a Conversion Factor 3.3 Kinetic Art: Conversion Factors Chapter 3 Online Student Edition Study WB Chapter 3 Lesson 3 Overview/Materials Pacing Overview Standard In this lesson you will cover how to use conversion factors and dimensional analysis to solve problems in chemistry. Classroom Materials Conversion Factors: copies of a recipe, lists of equivalents and conversions among the following measurements: teaspoon, tablespoon, 1 /4 cup, 1/2 cup, and 1 cup Dimensional Analysis: Internet access or copies of media guides containing vital statistics, such as heights and weights of players on a sports team (These guides are available from local sports franchises.) Standard There are no items. Chemistry & You page 1 of 7 2 Block 1 Description Engage Resources Content Pacing Chapter 3 Online Student Edition Have students examine the Chemistry & You feature on p. 84. Ask Has anyone ever noticed a chart or table in a bank or in the newspaper relating the values of foreign currency to the U.S. dollar? (yes or no) Explain that these tables are called currency conversion tables. These are the daily values that allow people to relate one currency to another. Ask How could you know for certain which amount of money is worth more—75 euros or 75 British pounds? (Convert these values to a familiar currency—U.S. dollars.) Activate Prior Knowledge Description Resources Pacing Resources Pacing Engage Provide various types of measuring devices to the class. Tell students to select one device and record the length of their shoe. Then ask them to create a chart and record the length of their shoe in inches, feet, yards, millimeters, centimeters, and meters. As a class, discuss how students determined the measurements. Begin a list of conversion factors on the word wall. Conversion Factors Description Explain Have students inspect Figure 3.12. Emphasize that a conversion factor relates two equivalent measurements. Ask What two parts does every measurement have? (a number and a unit) Point out that if this is so, then every conversion factor must contain two numbers and two units so that one number and its unit equal another number and its unit. Have students complete the 3.3 Kinetic Art: Conversion Factors activity on PearsonChem.com. page 2 of 7 Content 3.3 Kinetic Art: Conversion Factors Content Figure 3.12 Conversion Factors Description Resources Pacing Resources Pacing Extend The conversion of chemical units is similar to the exchange of currency. Americans who travel outside the United States must exchange U.S. dollars for foreign currency at a given rate of exchange. These exchange rates vary from day to day. The daily exchange rates affect all international monetary transactions. Each time one type of money is exchanged for another, the current exchange rate serves as a conversion factor. International currency traders keep track of exchange rates 24 hours a day through a linked computer network. Challenge students to choose a country to which they would like to travel. Have them research the exchange rate and then estimate how much money they would need, both in American dollars and the foreign currency, to travel for a week in that country. They might include things like airfare, hotel costs, food, and entertainment. Conversion Factors Description Explore Use a short class activity to allow students to use dimensional analysis to convert common units. Distribute copies of a recipe and a list of conversion factors to pairs of students. Explain that they must rewrite the recipe so that it can feed six times the number of serving sizes suggested by the recipe. Point out that it would be tedious to have to measure out a particular ingredient (pick out one) in teaspoons or tablespoons six times, so students must rewrite the recipe in appropriately larger units. After students have rewritten the recipe, have student pairs exchange and compare recipes. Materials: copies of a recipe, lists of equivalents and conversions among the following measurements: teaspoon, tablespoon, 1/4 cup, 1/2 cup, and 1 cup page 3 of 7 Dimensional Analysis Description Resources Pacing Resources Pacing Explain Explain that dimensional analysis is an extremely powerful problem-solving tool. Learning this method requires extra effort on the part of students. They must often use multiple conversion factors. The extra effort can be justified because the proper manipulation of the units assures accurate manipulation of the numbers. Emphasize that students should use dimensional analysis as a tool for solving all of the problems they encounter in chemistry. Their first question about any quantity should be, "What are the units of this quantity?" By comparing the units of various quantities in a problem, students can discover whether they need to perform any unit conversions before proceeding. Dimensional Analysis Description Explain Explain that measurements are often made using one unit and then converted into a related unit before being using in calculations. For example, students might measure volume in liters or milliliters in the laboratory, but express it as cubic centimeters in a calculation. Explain to the students that conversions are done using conversion factors. Emphasize that these conversion factors are ratios of equivalent physical quantities, such as 1 mL/1 cm3. Reassure students that they are more familiar with conversions than they may realize. Point out examples of everyday conversions, such as converting money from cents to dollars and converting time from minutes to hours. Start out by giving them practice with everyday examples. Ask A chicken needs to be cooked 20 minutes for each pound it weighs. How long should the chicken be cooked if it weighs 4.5 pounds? (4.5 lb × 20 min/lb = 90 min; 90 min × 1 h/60 min = 1.5 h. Most students will automatically relate 90 minutes to 1.5 hours. This may help them become comfortable with the process.) If students are having difficulty with conversion factors, provide a more tactile environment for students to discover these relationships. page 4 of 7 Content 3.3 Chemistry Tutorial: Using Density as a Conversion Factor Content 3.3 Chemistry Tutorial: Converting Ratios of Units Have students complete 3.3 Chemistry Tutorial: Using Density as a Conversion Factor and 3.3 Chemistry Tutorial: Converting Ratios of Units on PearsonChem.com. Dimensional Analysis Description Resources Pacing Explore Have students use dimensional analysis to convert between English and metric units. Distribute the media guides (if necessary) and assign each group of students a set of players. Ask the group to convert heights and weights into heights and masses expressed in meters and kilograms, respectively. Have students document their approach, including dimensional analysis expressions, conversion factors, and calculations. Materials: Internet access or copies of media guides containing vital statistics, such as heights and weights of players on a sports team (These guides are available from local sports franchises.) Assess and Remediate Description Evaluate To determine students' grasp of conversion factors, ask students to orally explain the relationship between the numerator and the denominator of any measurement conversion factor. (They are equivalent so that the ratio of numerator to denominator equals 1.) Then, have students complete the 3.3 Lesson Check. Remediate Model the conversion of 2 L to 2000 mL. Suggest that students check the answer by explaining that when using a conversion factor, such as 1 L = 1000 mL, the measurement expressed with the smaller unit (mL) should have a larger number associated with it than the measurement page 5 of 7 Resources Content Pacing Chapter 3 Online Student Edition expressed with the larger unit (L). Chapter 3 Review Description Resources Choose from the chapter review and assessment resources for Chapter 3: Scientific Measurement listed at the right. Pacing Content Ch. 3 Math Tutorial A: Converting Units Content Ch. 3 Math Tutorial B: Scientific Notation Content Ch. 3 Problem Set Content Ch. 3 Core TR: Chapter Quiz Content Ch. 3 Core TR: Chapter Test A Content Ch. 3 Core TR: Chapter Test B Differentiated Instruction Description Resources Less Proficient Readers Students may benefit from a reminder that certain key words and phrases in each word problem indicate the unknown quantity and its units. Some of these phrases are: how much, what is, how long, determine, and find. Struggling Students When writing problems on the board, assign a different color to each unique unit of measurement in the problem. This will assist students in understanding that a unit in the numerator can only be cancelled by an equivalent unit in the denominator. Advanced Students Direct students' attention to Tables 3.3, 3.4, and 3.5. Have students express the ratio in scientific notation between the largest and smallest units listed in each table. (Table 3.3: 12 6 1 × 10 ; Table 3.4: 1 × 10 ; Table 3.5: 1 × 109) Focus on ELL page 6 of 7 Pacing Content Table 3.3 Content Table 3.4 Content Table 3.5 Content Study WB Chapter 3 Lesson 3 Content Ch. 3 Core TR: Section 3 Review Description Content and Language Present academic vocabulary for this lesson, such as analyze, calculate, and evaluate. Pronounce the words and have students repeat them. Provide explanations, examples, and visuals of each word so students are aware of what tasks lie ahead when they encounter these words. My Notes page 7 of 7 Resources Pacing Content Study WB Chapter 3 Lesson 3 Content Ch. 3 Core TR: Section 3 Review Homework