1. Unit 5. Day 16.

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

3. 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?

4. 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

5. 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

6. 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

7. 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
$ 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 ∙ =

8. 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

9. 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
$ 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 =

10. 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

11. 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

12. 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

13. 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)

14. 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

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

17. 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

18. Impossible with the 5th grade method
Example B1: They completed of the quilt in 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

19. 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

20. = = 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 ℎ𝑟 = 𝑥 𝑞𝑢𝑖𝑙𝑡 ℎ𝑟
= 𝑞𝑢𝑖𝑙𝑡 ℎ𝑟
1 28
1 2
÷ 21 4
3 8 𝑞𝑢𝑖𝑙𝑡 ℎ𝑟
𝑞𝑢𝑖𝑙𝑡 1 ℎ𝑟
1 2
÷ 21 4
3 8 ÷ 21 4
3 8 ∙ 4 21
1 14
12 168
1 14 = =

21. 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

22. 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 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 = =

23. 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

24. = 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 𝑥 =
3 16
21 4 𝑥 =
21 4
21 4
3 16 ÷ 21 4
3 16 ∙ 4 21
12 336
1 28 = = = = 𝑥

25. 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

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

27. 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