Unit 4. Day 8.

Please get out paper for today’s lesson Name Date Period -------------------------------------------------------- Topic: Unit Rates 7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Today’s Lesson 1) Review Unit Rate 2) Using Unit Rate to compare. 3) Introduction to proportions

Example A. : Popeye’s chicken sells an 8-piece chicken for $13. 75 Example A*: Popeye’s chicken sells an 8-piece chicken for $13.75. How much is one piece of chicken? Example B*: A woman rides 7 8 mile in 1 2 hour. What is her rate of speed?

$ 1 𝑝𝑖𝑒𝑐𝑒 1.72 $13.75 8 𝑝𝑖𝑒𝑐𝑒𝑠 8 𝑝𝑖𝑒𝑐𝑒𝑠 $13.75 𝑜𝑟 1.71875 . Example Aº: Popeye’s chicken sells an 8-piece chicken for $13.75. How much is one piece of chicken? $13.75 8 𝑝𝑖𝑒𝑐𝑒𝑠 8 𝑝𝑖𝑒𝑐𝑒𝑠 $13.75 $ 1 𝑝𝑖𝑒𝑐𝑒 1.72 ÷8 𝑜𝑟 ÷8 1.71875 . 1 1 7 8 7 5 8 1 3 . 7 5 7 5 − 8 5 − 56 1 − 8 7 − 64 Dependent 6 − Independent 56 4

Example B. : A woman rides 7 8 mile in 1 2 hour Example B*: A woman rides 7 8 mile in 1 2 hour. What is her rate of speed? 7 8 ÷ 1 2 7 8 𝑚𝑖 1 2 ℎ ℎ𝑟 𝑚𝑖 𝑚𝑖 1 ℎ 𝑚𝑖 ℎ 𝑜𝑟 1 2 ÷ 1 2 Dependent Independent 7 8 ÷ 1 2 7 8 ∙ 2 1 14 8 2∙7 2∙2∙2 7 4 1 3 4 1 3 4 = = = = =

𝑚𝑖 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 61∙8=1288 161=7∙23 𝑚 2 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚 2 𝑜𝑟 Example C*: A car uses 2 7 8 of a gallon to drive 40 1 4 miles. What is the mileage of the car? 𝑚𝑖 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 61∙8=1288 161=7∙23 Example D*: Winston used 2 1 2 gallons of paint to cover a wall that is 12 1 4 square meters. How much area will one gallon of paint cover? 𝑚 2 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚 2 𝑜𝑟

𝑚𝑖 1 𝑔𝑎𝑙 40 1 4 161 4 𝑚𝑖 23 8 𝑔𝑎𝑙 𝑚𝑖 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 = 2 7 8 = = = = 14 Example C*: A car uses 2 7 8 of a gallon to drive 40 1 4 miles. What is the mileage of the car? 40 1 4 ÷ 23 8 161 4 𝑚𝑖 23 8 𝑔𝑎𝑙 𝑚𝑖 1 𝑔𝑎𝑙 𝑚𝑖 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚𝑖 𝑜𝑟 = 2 7 8 ÷ 23 8 161 4 ÷ 23 8 14 1 161 4 ∙ 8 23 1288 92 2∙2∙2∙7∙23 = = = = 14 14 = 2∙2∙23

Example D*: Winston used 2 1 2 gallons of paint to cover a wall that is 12 1 4 square meters. How much area will one gallon of paint cover? 12 1 4 ÷ 5 2 49 4 𝑚 2 5 2 𝑔𝑎𝑙 𝑚 2 1 𝑔𝑎𝑙 𝑚 2 𝑔𝑎𝑙 𝑔𝑎𝑙 𝑚 2 𝑜𝑟 = 2 1 2 ÷ 5 2 49 4 ÷ 5 2 49 10 49 4 ∙ 2 5 98 20 2∙7∙7 4 9 10 4 9 10 = = = = = 2∙2∙5

Today’s Lesson 1) Review Unit Rate 2) Using Unit Rate to compare. 3) Introduction to proportions

Example E*:𝑊ℎ𝑜 𝑖𝑠 𝑓𝑎𝑠𝑡𝑒𝑟? Barry Larry 5 ℎ𝑜𝑢𝑟𝑠 𝑡𝑜 𝑔𝑜 48 𝑘𝑚 6 ℎ𝑜𝑢𝑟𝑠 𝑡𝑜 𝑔𝑜 52 𝑘𝑚 9.6 8. 6 𝑘𝑚 1 ℎ𝑟 48 𝑘𝑚 5 ℎ𝑟 ÷5 5 ℎ𝑟 48 𝑘𝑚 𝑘𝑚 1 ℎ𝑟 52 𝑘𝑚 6 ℎ𝑟 ÷6 𝑜𝑟 ÷5 ÷6 . 6 . 8 6 9 6 6 5 2 . 5 4 8 . − 4 8 − 4 5 4 3 Dependent − − 3 6 3 0 Independent 4

Example E*:𝑊ℎ𝑜 𝑖𝑠 𝑓𝑎𝑠𝑡𝑒𝑟? 5 ℎ𝑜𝑢𝑟𝑠 𝑡𝑜 𝑔𝑜 48 𝑘𝑚 6 ℎ𝑜𝑢𝑟𝑠 𝑡𝑜 𝑔𝑜 52 𝑘𝑚 8 4 6 52 6 9 3 5 48 5 ÷6 𝑘𝑚 1 ℎ𝑟 48 𝑘𝑚 5 ℎ𝑟 ÷5 5 ℎ𝑟 48 𝑘𝑚 𝑘𝑚 1 ℎ𝑟 52 𝑘𝑚 6 ℎ𝑟 𝑜𝑟 ÷6 ÷5 Dependent Independent

𝑎𝑐𝑟𝑒 1 ℎ𝑟 𝑎𝑐𝑟𝑒 1 ℎ𝑟 21 4 𝑎𝑐𝑟𝑒 7 2 ℎ𝑟 𝑎𝑐𝑟𝑒 ℎ𝑟 ℎ𝑟 𝑎𝑐𝑟𝑒 𝑜𝑟 = 𝑎𝑐𝑟𝑒 ℎ𝑟 = = Example F*: Richard Ritter, Ms. Ritter’s dad, hired two people to help him on the farm. Drew plowed 5.25 acres in 3 1 2 hours. Steven plowed 1 4 an acre in 8 minutes. Which is the better (more efficient) worker? 5 25 100 5 1 4 21 4 𝑎𝑐𝑟𝑒 7 2 ℎ𝑟 ÷ 7 2 5.25 𝑎𝑐𝑟𝑒 ℎ𝑟 ℎ𝑟 𝑎𝑐𝑟𝑒 𝑎𝑐𝑟𝑒 1 ℎ𝑟 𝑜𝑟 = 3 1 2 ÷ 7 2 1 4 ÷ 2 15 𝑎𝑐𝑟𝑒 ℎ𝑟 𝑎𝑐𝑟𝑒 1 ℎ𝑟 2 15 8 60 ÷ 2 15 1 4 ÷ 2 15 1 4 ∙ 15 2 2∙3∙7 3∙5 1 1 2 1 1 2 1 7 8 1 7 8 21 4 ÷ 7 2 21 4 ∙ 2 7 42 28 15 8 3 2 15 8 = = = = = = = = = = 2∙2∙2 2∙2∙7

Today’s Lesson 1) Review Unit Rate 2) Using Unit Rate to compare. 3) Introduction to proportions

7.RP.A.1.a Decide whether two quantities are in a proportional relationship

8 Is this proportional? 𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛 8 12 Is this fair? 𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛 9 24 9 12 24 3 8 2 3 0. 375 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛 0. 6 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛

4 Is this proportional? 𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛 4 8 Is this fair? 𝑏𝑟𝑒𝑎𝑑 𝑝𝑒𝑟𝑠𝑜𝑛 15 30 15 8 30 1 2 1 2 0. 5 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛 0.5 𝑏𝑟𝑒𝑎𝑑 1 𝑝𝑒𝑟𝑠𝑜𝑛

3 𝑐𝑎𝑛𝑐𝑒𝑟 100 𝑝𝑒𝑜𝑝𝑙𝑒 = 30,000 𝑐𝑎𝑛𝑐𝑒𝑟 1,000,000 𝑝𝑒𝑜𝑝𝑙𝑒 $1 2 ℎ𝑜𝑢𝑟𝑠 $4 8 ℎ𝑜𝑢𝑟𝑠 A proportion is an stating that two ratios (or rates) are equivalent. equation = 1 4 = 2 8 $3 2 𝑠𝑜𝑑𝑎𝑠 = $9 6 𝑠𝑜𝑑𝑎𝑠 60 𝑚𝑖𝑙𝑒𝑠 60 𝑚𝑖𝑛 = 1 𝑚𝑖𝑙𝑒 1 𝑚𝑖𝑛 3 𝑐𝑎𝑛𝑐𝑒𝑟 100 𝑝𝑒𝑜𝑝𝑙𝑒 = 30,000 𝑐𝑎𝑛𝑐𝑒𝑟 1,000,000 𝑝𝑒𝑜𝑝𝑙𝑒