Lesson 21: Getting the Job Done Speed, Work, and Measurement Units

Transcription

1 Lesson 2 6 Lesson 2: Getting the Job Done Speed, Work, and Measurement 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-, milli- 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 ( minutes) Exercise Lesson 2: Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

2 Lesson 2 6 Identify the ratios that are associated with conversions between feet, inches, and yards. 2 inches = foot; the ratio of inches to feet is 2:. foot = 2 inches; the ratio of feet to inches is :2. 3 feet = yard; the ratio of feet to yards is 3:. yard = 3 feet; the ratio of yards to feet is : 3. Exercise 2 (0 minutes) 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 8 inches. Make a ratio table that compares feet and inches. Use the conversion rate of 2 inches per foot or 2 foot per inch. Allow students to solve the problem using the conversion chart. When all groups finish, make clear that they can multiply 8 by 2, or divide 8 by 2. The result is feet either way. Exercise 2 Work with your partner to find out how many feet are in 8 inches. Make a ratio table that compares feet and inches. Use the conversion rate of 2 inches per foot, or 2 foot per inch. 8inc hes foot 2inc hes = 8 foot 2 = 8 = feet 2 8 inches equals feet. Exercise 3 (5 minutes) Exercise 3 Lesson 2: 2

3 Lesson 2 6 How many grams are in 6 kilograms? Again, make a record of your work before using the calculator. The rate would be 000 grams per kg. The unit rate would be = = kilograms 000 grams kilogram grams = =6000 grams There are 6000 grams in 6 kilograms. Examples 2 (0 minutes) Example How many cups are in 5 quarts? As always, make a record of your work before using the calculator. 5 = 5 =20 5quarts cups quart = 5 cups =20 cups There are 20 cups in 5 quarts. Example 2 How many quarts are in 0 cups? 0cups quart cups = 0 quarts= 5 2 quarts=2 2 quarts Closing (5 minutes) Lesson 2: 3

4 Lesson 2 6 In Example 2, what if it was set up this way: is wrong with that set up? 0 cups ( cups / quart) = 0 quarts. What. If the conversion factor is flipped upside down, the units will not cancel and the number won t make sense. Lesson Summary 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) Name Date Lesson 2: Getting the Job Done Speed, Work, and Measurement Lesson 2:

5 Lesson 2 6 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 $ 2.00 per quart, how much money will they make if they sell it all? 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 $ 2.00 per quart, how much money will they make if they sell it all? Lesson 2: 5

6 Lesson 2 6 The conversion rate is quarts per gallon. qt/gal. gal. = 6 quarts $ 2.00 /qt. 6 qt. = $ 32 quarts gallon gallons 6quarts $ 2.00 quart =$32 sales = quarts =6 quarts Problem Set Sample Solutions 7 ft. = 8 in. 00 yd. = 300 ft. 25 m = 2,500 cm 5 km = 5,000 m 96 oz. = 6 lb. 2 mi. = 0,560 ft. 2 mi. = 3,520 yd. 32 fl. oz. = c.,500 ml =.5 l 6 g = 6,000 mg 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? 8 bags The maximum weight for a truck on the New York State Thruway is 0 tons. How many pounds is this? 80,000 lb. Claudia s skis are 50 centimeters long. How many meters is this?.5 m Claudia s skis are 50 centimeters long. How many millimeters is this?,500 mm Write your own problem and solve it. Be ready to share the question tomorrow. Answers will vary. U.S. Customary Length Lesson 2: 6

7 Lesson 2 6 Inch (in.) in. = 2 ft. Foot (ft.) ft. = 2 in. yd. = 3 ft. Yard (yd.) Mile (mi.) yd. = 36 mi. = 760 mi. = 5280 in. yd. ft. Metric Length Centimeter (cm) cm = 0 Meter (m) m = 00 m = 000 Kilometer (km) km = 000 mm cm mm m Metric Capacity Liter (L) L = 000 ml Kiloliter kl = 000 L Lesson 2: 7

8 Lesson 2 6 U.S. Customary Weight Pound (lb.) lb. = 6 oz. Ton (T.) T. = 2000 lb. Metric Mass Gram (g) g = 000 mg Kilogram (kg) kg = 000 g U.S. Customary Capacity Cup (c.) c. = 8 fluid ounces Pint (pt.) pt. = 2 Quart (qt.) qt. = qt. = 2 c. c. pt. Lesson 2: 8

9 Lesson 2 6 qt. = 32 ounces Gallon (gal.) gal. = fluid qt. gal. = 8 pt. gal. = 6 c. gal. = 28 fluid ounces Lesson 2: 9