Unit 5. Day 16.

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

Student council sells 3 bags of chips for $2 Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9?

Student council sells 3 bags of chips for $2 Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? 5th grade simple method

Impossible with the 5th grade method Example A1: Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? $ 𝑏𝑎𝑔 = $ 𝑏𝑎𝑔 2 9 ? 𝑥 3 ? Impossible with the 5th grade method

Example A: Student council sells 3 bags of chips for $2 Example A: Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? 5th grade simple method Unit Rate FAIL 5th grade method

Example A2: Student council sells 3 bags of chips for $2 Example A2: Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? 2 3 ÷3 $ 1 𝑏 $ 2 3 𝑏 ÷3 2 3 2 ? $ 𝑏 = $ 𝑏 9 3 2 ÷2 𝑏 $ 1 1 3 𝑥 ? 3 𝑏 $ 2 ÷2 3 2 𝑏 $ = 𝑏 $ 9 3 9 𝑥 1 2 9 3 2 9 1 13 1 2 27 2 13 1 2 ∙ =

Example A: Student council sells 3 bags of chips for $2 Example A: Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? 5th grade simple method Unit Rate FAIL 5th grade method Equation

𝑑 = ∙ 𝑏 𝑏 = ∙ 𝑑 𝑏=1.5𝑑 𝑑=0. 6 𝑏 𝑑=0.67𝑏 𝑏= 3 2 𝑑 9 = 2 3 𝑏 9 𝑑 13 1 2 Example A3: Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? 3 2 2 3 3 2 2 3 ÷2 3 𝑏 $2 𝑏 $1 ÷3 $2 3 𝑏 $ 1 𝑏 ÷2 ÷3 𝑑 = ∙ 𝑏 𝑏 = ∙ 𝑑 𝑏=1.5𝑑 𝑑=0. 6 𝑏 𝑑=0.67𝑏 𝑏= 3 2 9 1 𝑑 9 = 2 3 𝑏 9 𝑑 13 1 2 27 2 2 3 2 3 9 1 ÷ 2 3 9 1 ∙ 3 2 27 2 13 1 2 𝑏 = 𝑏 =

Example A: Student council sells 3 bags of chips for $2 Example A: Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? 5th grade simple method Unit Rate Cross Multiplication FAIL 5th grade method Equation

2𝑥 2 𝑥 = 3 9 = 27 2 2 𝑥 = 13.5 13.5 $9 𝑤𝑖𝑙𝑙 𝑏𝑢𝑦 13.5 𝑏𝑎𝑔𝑠 𝑜𝑓 𝑐ℎ𝑖𝑝𝑠 3 2 Example A4: Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? 3 2 ? 9 $ 𝑏𝑎𝑔 = $ 𝑏𝑎𝑔 𝑥 2 𝑥 = 3 9 2𝑥 = 27 2 2 1 3 5 . 2 2 7 7 . 𝑥 = 13.5 13.5 − 2 − 6 $9 𝑤𝑖𝑙𝑙 𝑏𝑢𝑦 13.5 𝑏𝑎𝑔𝑠 𝑜𝑓 𝑐ℎ𝑖𝑝𝑠 1

Example A: Student council sells 3 bags of chips for $2 Example A: Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? Graph 5th grade simple method Unit Rate Cross Multiplication FAIL 5th grade method Equation

𝑏 𝑦 ? 𝑥 $ 𝑑 $ 𝑑 Proportional , , By the way … 1, ? 2 3 2 3 0. 6 𝑏 ? 13.5 13.5 Example A5: Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? 3 2 9 (13.5)

FAIL FAIL-ish Estimate Example A: Student council sells 3 bags of chips for $2. At this price, how many bags can we buy for $9? Cross Multiplication FAIL-ish Estimate Graph 5th grade simple method Unit Rate FAIL 5th grade method Equation

Example B: Mr. Jordan and his wife are making a quilt Example B: Mr. Jordan and his wife are making a quilt. They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes?

Example B: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 5th grade simple method

Impossible with the 5th grade method Example B1: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 3 8 ? 𝑥 𝑞𝑢𝑖𝑙𝑡 ℎ𝑟 = 𝑞𝑢𝑖𝑙𝑡 ℎ𝑟 5 1 4 21 4 1 2 ? Impossible with the 5th grade method

FAIL Example B: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 5th grade simple method Unit Rate FAIL 5th grade method

= = Example B2: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 3 8 𝑞𝑢𝑖𝑙𝑡 21 4 ℎ𝑟 = 𝑥 𝑞𝑢𝑖𝑙𝑡 1 2 ℎ𝑟 = 𝑞𝑢𝑖𝑙𝑡 1 2 ℎ𝑟 1 28 1 2 ÷ 21 4 3 8 𝑞𝑢𝑖𝑙𝑡 21 4 ℎ𝑟 𝑞𝑢𝑖𝑙𝑡 1 ℎ𝑟 1 2 ÷ 21 4 3 8 ÷ 21 4 3 8 ∙ 4 21 1 14 12 168 1 14 = =

FAIL Example B: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 5th grade simple method Unit Rate FAIL 5th grade method Equation

Example B3: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 1 14 3 8 𝑞𝑢𝑖𝑙𝑡 21 4 ℎ𝑟 ÷ 21 4 𝑞𝑢𝑖𝑙𝑡 1 ℎ𝑟 ÷ 21 4 𝑞 = ∙ 𝑡 𝑞 = 1 14 1 2 𝑡 1 28 𝑞 = 3 8 ÷ 21 4 3 8 ∙ 4 21 1 14 12 168 1 14 = =

FAIL Example B: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 5th grade simple method Unit Rate FAIL 5th grade method Equation Cross Multiplication

= 𝑥 Example B4: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 3 8 𝑥 𝑞𝑢𝑖𝑙𝑡 ℎ𝑟 = 𝑞𝑢𝑖𝑙𝑡 ℎ𝑟 5 1 4 21 4 1 2 21 4 𝑥 3 8 1 2 = 3 16 21 4 𝑥 = 21 4 21 4 3 16 ÷ 21 4 3 16 ∙ 4 21 12 336 1 28 = = = = 𝑥

FAIL Example B: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 5th grade simple method Unit Rate FAIL Graph 5th grade method Equation Cross Multiplication

Proportional , , 1 14 𝑞 𝑥 𝑡 𝑦 ? 𝑞 By the way … ? 𝑡 21 4 Example B5: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 3 8 1 14 1 2

FAIL FAIL Example B: They completed 3 8 of the quilt in 5 1 4 hr. At this rate, how much of the quilt can they complete in 30 minutes? 5th grade simple method Unit Rate FAIL FAIL Graph 5th grade method Equation Cross Multiplication