1. Unit 5. Day 7.

2. 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.

3. 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

4. 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

5. 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

6. 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

7. 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

9. 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

10. 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

11. Getting Comfortable with Tables
independent 𝑥
dependent 𝑦 𝑥 𝑦

13. 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

14. Barbara’s Produce Stand
Example A: Al’s Produce Stand sells 6 ears of corn for $ Barbara’s Produce Stand sells 13 ears of corn for $ 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

15. 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
$ 𝑒𝑎𝑟
$ 𝑒𝑎𝑟
$ 𝑒𝑎𝑟 ÷6
0.25
÷13
$ 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 2 − −
1 2
2 6 3 5 − − 30 52

16. 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