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G6 m1-c-lesson 21-t

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Oct. 31, 2013

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G6 m1-c-lesson 21-t

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G6 m1-c-lesson 21-t

Lesson 21 NYS COMMON

CORE MATHEMATICS CURRICULUM 6•1 Lesson 21:Getting the Job Done—Speed, Work, and Measurement Units Student Outcomes Students use rates between measurements to convert measurement in one unit to measurement in another unit. They manipulate and transform units appropriately when multiplying or dividing quantities. Lesson Notes Prior to this lesson, a measurement center should be made available to students. By allowing all students to handle all of the various items, they gain a real sense of each measure and its relationship to the others. Measurement Center materials:rulers (centimeter and inches), meter sticks, yard sticks, measuring tapes; kilogram, gram and milligram masses; liter box, liter bottle, or liter graduated cylinder, eyedropper (for milliliter);ounce and pound weights; cup, pint, quart, and gallon containers Materials:copies of conversion charts, calculators Vocabulary:Length, Mass, Weight, Capacity, Metric System, U.S. Customary system, kilo-, deci-, centi-, milliConversion tables contain ratios that can be used to convert units of length, weight or capacity. You must multiply the given number by the ratio that compares the two units. Classwork It may be helpful to copy the vocabulary terms on one side of a handout and the conversion charts on the other. Distribute these to each student.Pair the students for the first two exercises. Exercise 1 (4 minutes) Exercise 1 Identify the ratios that are associated with conversions between feet, inches, and yards. inches = foot; the ratio of inches to feet is foot= inches; the ratio of feet to inches is . . feet= yard; the ratio of feet to yards is . yard= feet; the ratio of yards to feet is . Lesson 21: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Getting the Job Done—Speed, Work, and Measurement Units 10/31/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 165

Lesson 21 NYS COMMON

CORE MATHEMATICS CURRICULUM 6•1 Exercise 2 (10 minutes) Conversion tables are really ratio tables that can be used to convert units of length, weight or capacity (and other units, too). You must multiply the given number by the ratio that compares the two units. Work with your partner to find out how many feet are in inches. Use the conversion rate of inches. Make a ratio table that compares feet and inches per foot or foot per inch. Allow students to solve the problem using the conversion chart. When all groups finish, make clear that they can multiply by , or divide by . The result is feet either way. Exercise 2 Work with your partner to find out how many feet are in Use the conversion rate of inches per foot, or inches. Make a ratio table that compares feet and inches. foot per inch. inches equals feet. Exercise 3 (5 minutes) Exercise 3 How many grams are in kilograms? Again, make a record of your work before using the calculator. The rate would be grams per kg. The unit rate would be . There are grams in kilograms. Examples 1–2 (10 minutes) Example 1 How many cups are in There are cups in quarts? As always, make a record of your work before using the calculator. quarts. Lesson 21: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Getting the Job Done—Speed, Work, and Measurement Units 10/31/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 166

Lesson 21 NYS COMMON

CORE MATHEMATICS CURRICULUM 6•1 Example 2 How many quarts are in cups? Closing (5 minutes) In Example 2, what if it was set up this way: set up? cups × ( cups / quart) = quarts. What is wrong with that If the conversion factor is flipped upside down, the units will not cancel and the number won’t make sense. Lesson Summary Conversion tables contain ratios that can be used to convert units of length, weight, or capacity. You must multiply the given number by the ratio that compares the two units. Exit Ticket (5 minutes) Lesson 21: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Getting the Job Done—Speed, Work, and Measurement Units 10/31/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 167

Lesson 21 NYS COMMON

CORE MATHEMATICS CURRICULUM Name ___________________________________________________ 6•1 Date____________________ Lesson 21: Getting the Job Done—Speed, Work, and Measurement Units Exit Ticket Jill and Erika make gallons of lemonade for their lemonade stand. How many quarts will they be able to sell? If they charge $ per quart, how much money will they make if they sell it all? Lesson 21: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Getting the Job Done—Speed, Work, and Measurement Units 10/31/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 168

Lesson 21 NYS COMMON

CORE MATHEMATICS CURRICULUM 6•1 Exit Ticket Sample Solutions The following solutions indicate an understanding of the objectives of this lesson: Jill and Erika make gallons of lemonade for their lemonade stand. How many quarts will they be able to sell? If they charge $ per quart, how much money will they make if they sell it all? The conversion rate is 4 quarts per gallon. qt/gal.• gal. = $ /qt.• quarts qt. = $ Problem Set Sample Solutions 1. 7 ft. = 84 in. 2. 100 yd. = 300 ft. 3. 25 m = 2,500 cm 4. 5 km = 5,000 m 5. 96 oz. = 16 lb. 6. 2 mi. = 10,560 ft. 7. 2 mi. = 3,520 yd. 8. 32 fl. oz. = 4 c. 9. 1,500 ml = 1.5 l 10. 6 g = 6,000 mg 11. Beau buys a 3 pound bag of trail mix for a hike. He wants to make one-ounce bags for his friends with whom he is hiking. How many one-ounce bags can he make? 48 bags 12. The maximum weight for a truck on the New York State Thruway is 40 tons. How many pounds is this? 80,000 lb. 13. Claudia’s skis are 150 centimeters long. How many meters is this? 1.5 m 14. Claudia’s skis are 150 centimeters long. How many millimeters is this? 1,500 mm 15. Write your own problem and solve it. Be ready to share the question tomorrow. Answers will vary. Lesson 21: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Getting the Job Done—Speed, Work, and Measurement Units 10/31/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 169

Lesson 21 NYS COMMON

CORE MATHEMATICS CURRICULUM U.S. Customary Length Conversion Inch (in.) in. = Foot (ft.) ft. = in. yd. = ft. yd. = in. mi. = yd. mi. = ft. Yard (yd.) Mile (mi.) U.S. Customary Weight Pound (lb.) Ton (T.) 6•1 ft. Conversion lb. = oz. T. = lb. U.S. Customary Capacity Cup (c.) Pint (pt.) Quart (qt.) Gallon (gal.) c. = pt. = qt. = qt. = qt. = gal. = gal. = gal. = gal. = Lesson 21: Date: ©2013CommonCore,Inc. Some rights reserved.commoncore.org Conversion fluid ounces c. c. pt. fluid ounces qt. pt. c. fluid ounces Metric Length Centimeter (cm) Meter (m) Kilometer (km) Conversion cm = mm m = cm m = mm km = m Metric Capacity Liter (L) Kiloliter Conversion L= ml kL = L Metric Mass Gram (g) Kilogram (kg) Conversion g= mg kg = g Getting the Job Done—Speed, Work, and Measurement Units 10/31/13 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 170