Unit 5. Day 1.

Today’s Lesson Proportion Examples A, B, C, & D. What Unit 5 is all about (proportions) Review 5th grade Review Unit Rate options Proportion Examples A, B, C, & D. fraction decimal

(Unit rate & proportionality) $ 2 1 𝑝𝑒𝑛 $ 𝑥 7 𝑝𝑒𝑛 Unit 3 (Unit rate & proportionality) Unit 4 (Equations) $ 24 12 𝑝𝑒𝑛 $ 6 3 𝑝𝑒𝑛 = Proportion

400 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 25 𝑡𝑒𝑎𝑐ℎ𝑒𝑟 = 32 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 2 𝑡𝑒𝑎𝑐ℎ𝑒𝑟𝑠 Proportion 400 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 25 𝑡𝑒𝑎𝑐ℎ𝑒𝑟 = 32 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 2 𝑡𝑒𝑎𝑐ℎ𝑒𝑟𝑠 $ 2 3 𝑎𝑝𝑝𝑙𝑒𝑠 = $ 𝑥 8 𝑎𝑝𝑝𝑙𝑒𝑠 3 𝑜𝑖𝑙 4 𝑤𝑎𝑡𝑒𝑟 = 9 𝑜𝑖𝑙 12 𝑤𝑎𝑡𝑒𝑟 = 1 2 = 5 10 3 5 = 𝑥 17

Today’s Lesson Proportion Examples A, B, C, & D. What Unit 5 is all about (proportions) Review 5th grade Review Unit Rate options Proportion Examples A, B, C, & D. fraction decimal

Review 1: Replace each with a number so the fractions are equivalent 12 10 5 6 2 = 2

Review 2: Replace each with a number so the fractions are equivalent 21 7 8 3 = 24 3

Today’s Lesson Proportion Examples A, B, C, & D. What Unit 5 is all about (proportions) Review 5th grade Review Unit Rate options Proportion Examples A, B, C, & D. fraction decimal

. . Unit Rate Options 8 0.8 $ 4 5 𝑜𝑟𝑎𝑛𝑔𝑒𝑠 $ 1 𝑜𝑟𝑎𝑛𝑔𝑒 0.80 5 4 − 4 0 ÷5 $ 1 𝑜𝑟𝑎𝑛𝑔𝑒 0.80 5 4 . − 4 0 ÷5 4 5 $ 4 5 𝑜𝑟𝑎𝑛𝑔𝑒𝑠 ÷5 $ 1 𝑜𝑟𝑎𝑛𝑔𝑒 ÷5

. . Unit Rate Options 0.375 3 7 5 $ 3 8 𝑑𝑜𝑛𝑢𝑡𝑠 $ 1 𝑑𝑜𝑛𝑢𝑡 0.375 8 3 − ÷8 $ 1 𝑑𝑜𝑛𝑢𝑡 0.375 8 3 . − 2 4 ÷8 6 − 5 6 4 3 8 $ 3 8 𝑑𝑜𝑛𝑢𝑡𝑠 ÷8 $ 1 𝑑𝑜𝑛𝑢𝑡 ÷8

Today’s Lesson Proportion Examples A, B, C, & D. What Unit 5 is all about (proportions) Review 5th grade Review Unit Rate options Proportion Examples A, B, C, & D. fraction decimal

Example A: Mr. Jordan was able to travel 130 miles on 5 gallons of gas Example A: Mr. Jordan was able to travel 130 miles on 5 gallons of gas. If he fills his tank (16 gallons), how many miles can he drive? 130 5 ? 16 𝑥 𝑥 𝑚𝑖 𝑔𝑎𝑙 = 𝑚𝑖 𝑔𝑎𝑙 = 𝑚𝑖 𝑔𝑎𝑙 16 130 𝑚𝑖 5 𝑔𝑎𝑙 ÷5 𝑚𝑖 1 𝑔𝑎𝑙 16 416 ÷5 16 2 26 6 . 3 26 5 1 3 0 . 16 − × 1 0 1 3 1 5 6 − 30 + 2 6 ∎ 4 1 6

Watashi wa sūgaku o aishi ? 𝐼𝑜 𝑎𝑚𝑜 𝑙𝑎 𝑚𝑎𝑡𝑒𝑚𝑎𝑡𝑖𝑐𝑎 I love math 私は数学と私の妻を愛し Watashi wa sūgaku o aishi

Example A: Mr. Jordan was able to travel 130 miles on 5 gallons of gas Example A: Mr. Jordan was able to travel 130 miles on 5 gallons of gas. If he fills his tank (16 gallons), how many miles can he drive? 130 𝑚𝑖 5 𝑔𝑎𝑙 = 𝑥 𝑚𝑖 16 𝑔𝑎𝑙 26 𝑚𝑖 1 𝑔𝑎𝑙 416 𝑚𝑖 16 𝑔𝑎𝑙

Example B: The city is conducting a traffic count on the street to determine how many cars use the road in a year. 380 cars are counted in four days. How many cars use the road in one month (30 days)? 380 ? 4 30 𝑐𝑎𝑟𝑠 𝑑𝑎𝑦𝑠 = 𝑐𝑎𝑟𝑠 𝑑𝑎𝑦𝑠 = 𝑐𝑎𝑟𝑠 𝑑𝑎𝑦𝑠 𝑥 𝑥 30 380 𝑐𝑎𝑟𝑠 4 𝑑𝑎𝑦𝑠 ÷4 2850 𝑐𝑎𝑟𝑠 1 𝑑𝑎𝑦 30 ÷4 30 . 95 9 5 1 95 4 . 3 8 0 30 × − 3 6 2 − + 2 8 5 ∎ 2 0 2 8 5

Example C: Mr. Jordan bought four pizzas to feed 10 students Example C: Mr. Jordan bought four pizzas to feed 10 students. If this is the right amount of pizza, then how much pizza will he need to buy for a class of 24 students? 4 10 ? 24 𝑥 𝑝 𝑠 = 𝑝 𝑠 = 𝑝 𝑠 𝑥 24 9.6 4 𝑝 10 𝑠 ÷10 24 𝑝 1 𝑠 24 ÷10 0.4 . 4 1 2 4 10 4 . 0.4 × − 4 0 . 9 6

Example C: Mr. Jordan bought four pizzas to feed 10 students Example C: Mr. Jordan bought four pizzas to feed 10 students. If this is the right amount of pizza, then how much pizza will he need to buy for a class of 24 students? 4 10 ? 24 𝑝 𝑠 = 𝑝 𝑠 = 𝑝 𝑠 𝑥 𝑥 24 9 3 5 2 5 4 10 4 𝑝 10 𝑠 ÷10 24 𝑝 1 𝑠 24 ÷10 2 5 24 1 48 5 9 3 5 ∙ = =

Example D: Mr. Jordan grading tests Example D: Mr. Jordan grading tests. It took him eight minutes to grade seven quizzes. It is now 4:00 pm. His wife want him home by 5:00 pm. If it takes him 25 minutes to get home, how many more quizzes can he finish grading? 8 7 35 ? 𝑥 𝑞𝑢𝑖𝑧 𝑚𝑖𝑛 = 𝑞𝑢𝑖𝑧 𝑚𝑖𝑛 = 𝑞𝑢𝑖𝑧 𝑚𝑖𝑛 𝑥 35 30 5 8 7 8 7 𝑞𝑢𝑖𝑧 8 𝑚𝑖𝑛 ÷8 𝑞𝑢𝑖𝑧 1 𝑚𝑖𝑛 35 ÷8 35 30 5 8 7 8 ∙ 35 1 245 8 = =

Example D: Mr. Jordan grading tests Example D: Mr. Jordan grading tests. It took him eight minutes to grade seven quizzes. It is now 4:00 pm. His wife want him home by 5:00 pm. If it takes him 25 minutes to get home, how many more quizzes can he finish grading? 8 7 35 ? 0.875 . 8 7 5 𝑥 = 𝑞𝑢𝑖𝑧 𝑚𝑖𝑛 8 . 𝑞𝑢𝑖𝑧 𝑚𝑖𝑛 = 𝑞𝑢𝑖𝑧 𝑚𝑖𝑛 𝑥 7 − 6 4 35 6 − 56 4 30.625 7 𝑞𝑢𝑖𝑧 8 𝑚𝑖𝑛 ÷8 𝑞𝑢𝑖𝑧 1 𝑚𝑖𝑛 35 ÷8 35 3 2 2 1 0.875 35 × 4 3 1 1 7 5 + 2 6 2 5 ∎ 3 . 6 2 5