Unit 5. Day 7.

Please get out paper for today’s lesson Name Date Period -------------------------------------------------------- Topic: Creating Proportional Equations CCSS.MATH.CONTENT.7.RP.A.2.C Represent proportional relationships by equations. CCSS.MATH.CONTENT.7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems.

Today’s Lesson 2) Connecting tables to unit rate. 1) Creating and using (proportional) equations 2) Connecting tables to unit rate. 3) Example to practice

Independent vs. Dependent Equation Pattern (i) 3 cups of flour will make 24 cookies. 𝑐𝑜𝑜𝑘𝑖𝑒𝑠 𝑓𝑙𝑜𝑢𝑟 𝑓𝑙𝑜𝑢𝑟 𝑐𝑜𝑜𝑘𝑖𝑒𝑠 8 24 𝑐𝑜𝑜𝑘𝑖𝑒𝑠 3 𝑓𝑙𝑜𝑢𝑟 𝑐 1 𝑓 dep. 𝑐 𝑐 = 8 ∙ 𝑓 indep. f 𝑦=𝑟∙𝑥 Independent vs. Dependent independent dependent Unit rate

𝑐=8𝑓 𝑐=8𝑓 𝑐=8𝑓 𝑐=8 =8𝑓 7 100 3 cups of flour will make 24 cookies. 8 𝑐𝑜𝑜𝑘𝑖𝑒 1 𝑓𝑙𝑜𝑢𝑟 𝑐=8𝑓 𝑐=8𝑓 𝑐=8𝑓 How many cookies can be made using 7 cups of flour? How much flour is required to make 100 cookies? 7 100 𝑐=8 =8𝑓

Independent vs. Dependent Equation Pattern* (ii) A car travels 65 miles using 2 gallons of gas. 𝑔𝑎𝑙 𝑚𝑖 𝑚𝑖 𝑔𝑎𝑙 65 𝑚𝑖 2 𝑔𝑎𝑙 𝑚𝑖 1 𝑔𝑎𝑙 32.5 dep. D 𝐷 = 32.5 𝑔 indep. g 𝑦=𝑟∙𝑥 Independent vs. Dependent independent dependent Unit rate

A car travels 65 miles using 2 gallons of gas. 32.5 𝑚𝑖 1 𝑔𝑎𝑙 𝐷=32.5𝑔 𝐷=32.5𝑔 𝐷=32.5𝑔 At this rate, how far can one travel with 12 gallons? At this rate, how much gas is needed to drive would it take to travel 2775 miles? 12 2775 =32.5𝑔 𝐷=32.5

Today’s Lesson 2) Connecting tables to unit rate. 1) Creating and using (proportional) equations 2) Connecting tables to unit rate. 3) Example to practice

Getting Comfortable with Tables 3 cups of flour will make 24 cookies. 𝑐=8𝑓 𝑦=8𝑥 input dependent output independent flour flour cookies cookies 𝑥 𝑦 dep. 𝑦 3 24 6 48 9 72 indep. x 5 ? ? 100

Getting Comfortable with Tables independent 𝑥 dependent 𝑦 𝑥 𝑦

Today’s Lesson 2) Connecting tables to unit rate. 1) Creating and using (proportional) equations 2) Connecting tables to unit rate. 3) Example to practice

Barbara’s Produce Stand Example A: Al’s Produce Stand sells 6 ears of corn for $1.50. Barbara’s Produce Stand sells 13 ears of corn for $3.12. Write two equations, one for each produce stand, that model the relationship between the number of ears of corn sold and the cost. Then, use each equation to help complete the tables below. Al’s Produce Stand Barbara’s Produce Stand Ears 6 14 21   13 Cost $1.50 $50.00 $3.12 $49.92 $ 𝑒𝑎𝑟 1.50 $ 𝑒𝑎𝑟 3.12 6 13

Barbara’s Produce Stand Al’s Produce Stand Barbara’s Produce Stand Ears 6 14 21   13 Cost $1.50 $50.00 $3.12 $49.92 𝑥 𝑦 $ 1.50 6 𝑒𝑎𝑟 $ 1 𝑒𝑎𝑟 $ 3.12 13 𝑒𝑎𝑟 ÷6 0.25 ÷13 $ 1 𝑒𝑎𝑟 0.24 ÷6 ÷13 C ost = 0.25 ∙ 𝑒 𝑎𝑟𝑠 C ost = 0.24 ∙ 𝑒 𝑎𝑟𝑠 𝑦 = 0.25𝑥 𝑦=0.24𝑥 . 2 5 . 2 4 6 13 1 . 5 0 3 . 1 2 2 − − 1 2 2 6 3 5 − − 30 52

Barbara’s Produce Stand Al’s Produce Stand Barbara’s Produce Stand Ears 6 14 21   13 Cost $1.50 $50.00 $3.12 $49.92 𝑥 14 21 14 21 𝑦 50 49.92 𝐶=0.25𝑒 𝐶=0.24𝑒 𝑦=0.25𝑥 𝑦=0.24𝑥 𝐶 =0.25 𝑒 𝐶 =0.24 𝑒 0.25 0.25 0.24 0.24 𝐶= 3.50 5.25 𝐶= 3.36 5.04 200=𝑒 200 208=𝑒 208