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

Lesson 21 S.92 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 21 S.92 Vocabulary: Length Mass Weight Capacity Metric System kilo- deci- centi- milli- U.S. Customary system

Lesson 21 S.92 Rotate through the measurement displays. Refer to the conversion chart, S.95, as you handle each measurement tool.

Lesson 21 Exercise 1 S.92 Refer to S.95 to assist you in completing Exercise 1. Exercise 1 Identify the ratios that are associated with conversions between feet, inches, and yards.   12 inches = foot; the ratio of inches to feet is . 1 foot = inches; the ratio of feet to inches is . 3 feet = yard; the ratio of feet to yards is . 1 yard = feet; the ratio of yards to feet is

Lesson 21 Exercise 1 Answers S.92 Identify the ratios that are associated with conversions between feet, inches, and yards. 𝟏𝟐 inches = 𝟏 foot; the ratio of inches to feet is 𝟏𝟐:𝟏 . 𝟏 foot = 𝟏𝟐 inches; the ratio of feet to inches is 𝟏:𝟏𝟐 . 𝟑 feet = 𝟏 yard; the ratio of feet to yards is 𝟑:𝟏 . 𝟏 yard = 𝟑 feet; the ratio of yards to feet is 𝟏:𝟑 .

Lesson 21 Exercise 2 Pair Work S.92 Work with your partner to find out how many feet are in 48 inches. Use a ratio table to compare feet and inches. Use the conversion rate of 12 inches per foot, or 1 12 foot per inch. After completing the table, think and use dimensional analysis to check your answer.

Lesson 21 Exercise 2 Pair Work Answer S.92 Feet 1 2 3 4 inches 12 24 36 48 Use the conversion rate of 𝟏𝟐 inches per foot, or 𝟏 𝟏𝟐 foot per inch. 𝟒𝟖𝒊𝒏𝒄𝒉𝒆𝒔 𝟏 × 𝟏 𝒇𝒐𝒐𝒕 𝟏𝟐𝒊𝒏𝒄𝒉𝒆𝒔 = 𝟒𝟖 ×𝟏 𝒇𝒐𝒐𝒕 𝟏 ×𝟏𝟐 = 𝟒𝟖 𝟏𝟐 =𝟒 𝒇𝒆𝒆𝒕 𝟒𝟖 inches equals 𝟒 feet

Lesson 21 Exercise 3 Pair Work S.93 How many grams are in 6 kilograms? Again, make a written record of your work before using the calculator. The rate would be 1,000 grams per kg. The unit rate would be 1,000. Make a table and use dimensional analysis.

Lesson 21 Exercise 3 Pair Work Answer S.93 6 1 × 𝟏𝟎𝟎𝟎 𝟏 = 𝟔 ×𝟏𝟎𝟎𝟎 𝟏 × 𝟏 =𝟔𝟎𝟎𝟎 𝟔 𝒌𝒊𝒍𝒐𝒈𝒓𝒂𝒎𝒔 𝟏 × 𝟏𝟎𝟎𝟎 𝒈𝒓𝒂𝒎𝒔 𝟏 𝒌𝒊𝒍𝒐𝒈𝒓𝒂𝒎 = 𝟔 ×𝟏𝟎𝟎𝟎 𝒈𝒓𝒂𝒎𝒔 𝟏 × 𝟏 =𝟔𝟎𝟎𝟎 𝒈𝒓𝒂𝒎𝒔 There are 𝟔𝟎𝟎𝟎 grams in 𝟔 kilograms. Grams 1000 2000 3000 4000 kilograms 1 2 3 4 5000 6000 5 6

Lesson 21 Example 1 S.93 How many cups are in 5 quarts? As always, make a record of your work before using the calculator.

Lesson 21 Example 1 Answer S.93 𝟓 𝟏 × 𝟒 𝟏 = 𝟓 × 𝟒 𝟏 × 𝟏 =𝟐𝟎 𝟓 𝒒𝒖𝒂𝒓𝒕𝒔 𝟏 × 𝟒 𝒄𝒖𝒑𝒔 𝟏𝒒𝒖𝒂𝒓𝒕 = 𝟓 ×𝟒 𝒄𝒖𝒑𝒔 𝟏 ×𝟏 =𝟐𝟎 𝒄𝒖𝒑𝒔 There are 𝟐𝟎 cups in 𝟓 quarts.

Lesson 21 Example 2 S.94 How many quarts are in 10 cups? As always, make a record of your work before using the calculator.

Lesson 21 Example 2 Answer S.94 𝟏𝟎 𝒄𝒖𝒑𝒔• 𝟏 𝒒𝒖𝒂𝒓𝒕 𝟒 𝒄𝒖𝒑𝒔 = 𝟏𝟎 𝟒 𝒒𝒖𝒂𝒓𝒕𝒔= 𝟓 𝟐 𝒒𝒖𝒂𝒓𝒕𝒔= 𝟐 𝟏 𝟐 𝒒𝒖𝒂𝒓𝒕𝒔

Lesson 21 Closing In Example 2, what if it was set up this way: 10 cups × (4 cups / 1 quart) = 40 quarts. What is wrong with that set up?

Lesson 21 Closing Answer In Example 2, what if it was set up this way: 10 cups × (4 cups / 1 quart) = 40 quarts. What is wrong with that set up?   If the conversion factor is flipped upside down, the units will not cancel and the number won’t make sense.

Lesson 21 Summary S.96 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.

Lesson 21 Exit Ticket Jill and Erika make 4 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 21 Exit Ticket Answer Jill and Erika make 𝟒 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? The conversion rate is 4 quarts per gallon. 𝟒 qt/gal. • 𝟒 gal. = 𝟏𝟔 quarts $𝟐.𝟎𝟎/qt. • 𝟏𝟔 qt. = $𝟑𝟐   𝟒 𝒒𝒖𝒂𝒓𝒕𝒔 𝟏 𝒈𝒂𝒍𝒍𝒐𝒏 • 𝟒 𝒈𝒂𝒍𝒍𝒐𝒏𝒔 𝟏 = 𝟒 𝒒𝒖𝒂𝒓𝒕𝒔 •𝟒 𝟏 •𝟏 =𝟏𝟔 𝒒𝒖𝒂𝒓𝒕𝒔 𝟏𝟔 𝒒𝒖𝒂𝒓𝒕𝒔× $𝟐.𝟎𝟎 𝒒𝒖𝒂𝒓𝒕 =$𝟑𝟐 𝒊𝒏 𝒔𝒂𝒍𝒆𝒔

Lesson 21 Problem Set S.96 7 ft. = in. 100 yd. = ft. 25 m = cm   7 ft. = in. 100 yd. = ft. 25 m = cm 5 km = m 96 oz. = lb. 2 mi. = ft. 2 mi. = yd. 32 fl. oz. = c. 1,500 ml = l 6 g = 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? The maximum weight for a truck on the New York State Thruway is 40 tons. How many pounds is this? Claudia’s skis are 150 centimeters long. How many meters is this? Claudia’s skis are 150 centimeters long. How many millimeters is this? Write your own problem and solve it. Be ready to share the question tomorrow.

Lesson 21 Problem Set Answers S.96 7 ft. = 84 in. 100 yd. = 300 ft. 25 m = 2,500 cm 5 km = 5,000 m 96 oz. = 16 lb. 2 mi. = 10,560 ft. 2 mi. = 3,520 yd. 32 fl. oz. = 4 c. 1,500 ml = 1.5 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? 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. Students, let’s hear from you.