Unit 5. Day 8.

Predicting with Proportions 5th grade simple method Remember this?

Example --: Mr. Jordan went to a doughnut shop and paid $3 for four doughnuts. At this price, how much would eight doughnuts cost? 3 4 ? 8 2 𝑥 6 $ 𝑑 = $ 𝑑 2 𝐷𝑜 𝐼 𝑘𝑛𝑜𝑤 𝑡ℎ𝑒 𝑢𝑛𝑖𝑡 𝑟𝑎𝑡𝑒?

Predicting with Proportions 5th grade simple method NO!!!!!!!!!!!!!!! Does this always work for us?

Example A1: Mr. Jordan went to a doughnut shop and paid $3 for four doughnuts. At this price, how much would six doughnuts cost? 3 4 ? 6 ? 𝑥 $ 𝑑 = $ 𝑑 ? ?

Predicting with Proportions 5th grade simple method Unit Rate 5th grade simple method Equation

Example A2: Mr. Jordan went to a doughnut shop and paid $3 for four doughnuts. At this price, how much would six doughnuts cost? 3 ? 4 6 𝑥 $ 𝑑 = $ 𝑑 = $ 6 𝑑 = $ 6 𝑑 6 $ 3 4 𝑑 ÷4 $ 1 𝑑 ÷4 6 $ 3 4 𝑑 ÷4 3 4 6 $ 1 𝑑 0.75 . 7 5 3 ÷4 6 0 . 7 5 4 3 . 6 3 4 6 1 − 4 1 2 18 4 9 2 2 8 × 4 1 2 ∙ = 4 . 2 4.50 5

Predicting with Proportions Unit Rate 5th grade simple method Equation

Example A3: Mr. Jordan went to a doughnut shop and paid $3 for four doughnuts. At this price, how much would six doughnuts cost? 0.75 $ 3 4 1 𝑑 $0.75 1 𝑑 3 4 𝐶 = ∙ 𝑑 𝐶 = ∙ 𝑑 3 4 6 1 4 1 2 4 1 2 18 4 9 2 ∙ 𝐶= 3 4 = 𝐶=0.75 𝑑 6 6 𝑑 0 . 7 5 𝐶 = 6 𝐶 = × 4 4.50 . 5

Predicting with Proportions 5th grade simple method Unit Rate Graph 5th grade simple method Equation

1, ? Proportional , , 4.5 4.5 3 4 3 4 0.75 3 4 6 ($4.50) 𝑛 ? 𝑥 𝑦 $ 𝐶 $ By the way … 3 4 3 4 0.75 𝑛 ? 1, ? Proportional We expect doughnuts to be: Example A4: Mr. Jordan went to a doughnut shop and paid $3 for four doughnuts. At this price, how much would six doughnuts cost? 3 4 6 ($4.50)

2 𝐶 $ 3 4 𝑑 $ 8 𝑑 6 2 8,6 6 $ 3 4 1 𝑑 8 $ 8 𝑑 6 8 𝑛 𝐶= 3 4 𝑑 8 8 𝐶 = 3 4 8 1 24 4 Example A5: How much do 8 doughnuts cost? ∙ = = 6 6

? 𝐶 $ 3 4 𝑑 $ 10 𝑑 ? 8,7𝑖𝑠ℎ ? 7𝑖𝑠ℎ 7 1 2 $ 3 4 1 𝑑 10 $ 10 𝑑 10 𝑛 𝐶= 3 4 𝑑 10 10 𝐶 = 3 4 10 1 30 4 Example A6: How much do 10 doughnuts cost? 7 1 2 15 2 ∙ = =

? 𝐶 $ 3 4 𝑑 $ 5 𝑑 ? ? 6𝑖𝑠ℎ,5 $ 3 4 1 𝑑 ? $ 5 𝑑 5 ? ? 𝑛 = 3 4 𝑑 5 𝐶 6𝑖𝑠ℎ 3 4 3 4 5 1 3 4 5 1 ∙ 4 3 Example A7: How many doughnuts can you get for $5? 20 3 6 2 3 = 𝑑 ÷ = = = 6.67

Predicting with Proportions 5th grade simple method Unit Rate Graph 5th grade simple method Equation

Example B1: Gabriela walked 5 miles in 2 hours Example B1: Gabriela walked 5 miles in 2 hours. At this rate, how many miles would she walk in 3 hours? 5 ? 𝑥 𝑚𝑖 ℎ𝑟 𝑚𝑖 ℎ𝑟 = 2 ? 3

Predicting with Proportions 5th grade simple method Unit Rate 5th grade simple method Equation

Example B2: Gabriela walked 5 miles in 2 hours Example B2: Gabriela walked 5 miles in 2 hours. At this rate, how many miles would she walk in 3 hours? 𝑥 𝑚𝑖 ℎ𝑟 = 𝑚𝑖 ℎ𝑟 5 = 𝑚𝑖 3 ℎ𝑟 = 𝑚𝑖 3 ℎ𝑟 2 3 3 5 𝑚𝑖 2 ℎ𝑟 ÷2 𝑚𝑖 1 ℎ𝑟 ÷2 3 5 2 5 𝑚𝑖 2 ℎ𝑟 ÷2 3 𝑚𝑖 1 ℎ𝑟 2 2.5 . 5 1 ÷2 2 . 5 3 2 5 . 3 5 2 3 1 − 7 1 2 4 × 7 1 2 15 2 ∙ = 7.5 7 . 1 5

Predicting with Proportions Unit Rate 5th grade simple method Equation

Example B3: Gabriela walked 5 miles in 2 hours Example B3: Gabriela walked 5 miles in 2 hours. At this rate, how many miles would she walk in 3 hours? 2.5 2.5 𝑚𝑖 1 ℎ𝑟 5 2 𝑚𝑖 1 ℎ𝑟 5 2 𝐷 = ∙ 𝑡 𝐷 = ∙ 𝑡 5 2 3 1 7 1 2 7 1 2 15 2 ∙ 𝐷= 5 2 = 𝐷=2.5 𝑡 3 𝑡 3 2 . 5 𝐷 = 3 𝐷 = × 7 7.5 . 5

Predicting with Proportions 5th grade simple method Unit Rate Graph 5th grade simple method Equation

𝑥 𝑡 𝑦 ? 𝐷 𝐷 , , 7.5 7.5 5 2 5 2 2.5 By the way … ? 𝑡 1, ? Proportional We expect doughnuts to be: Example B4: Gabriela walked 5 miles in 2 hours. At this rate, how many miles would she walk in 3 hours? 5 2 3 (7 1 2 )

? 𝐷 5 𝑚𝑖 2 ℎ𝑟 𝑚𝑖 7 ℎ𝑟 ? ? 7,? ? 17 1 2 35 2 5 2 𝑚𝑖 1 ℎ𝑟 7 𝑚𝑖 7 ℎ𝑟 7 𝑡 𝐷= 5 2 𝑡 7 𝐷 = 5 2 7 1 35 2 Example B5: How many miles would she walk in 7 hours? 17 1 2 17 1 2 ∙ = =

? 𝐷 5 𝑚𝑖 2 ℎ𝑟 7 𝑚𝑖 ℎ𝑟 ? ? 2.5 𝑖𝑠ℎ,7 7 5 2 𝑚𝑖 1 ℎ𝑟 ? 7 𝑚𝑖 ℎ𝑟 ? ? 𝑡 = 5 2 𝑡 7 𝐷 2.5 𝑖𝑠ℎ 5 2 5 2 7 1 5 2 7 1 ∙ 2 5 Example B6: How long would it take to walk 7 miles? 14 5 2 4 5 = 𝑡 ÷ = = = 2.8

Predicting with Proportions 5th grade simple method Unit Rate Graph 5th grade simple method Equation