1. Unit 5. Day 8.

2. Predicting with Proportions
5th grade simple method
Remember this?

3. 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?

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

5. 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 ? ?

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

7. 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
= $ 𝑑
= $ 𝑑 6
$ 3 4 𝑑 ÷4
$ 𝑑 ÷4 6
$ 3 4 𝑑 ÷4
3 4 6
$ 𝑑
0.75 . 7 5 3 ÷4 6 4 3 . 6
3 4
6 1 −
4 1 2
18 4
9 2
2 8 ×
4 1 2 ∙ = 4 . 2
4.50 5

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

9. 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
$ 𝑑
$ 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 𝐶 = 6 𝐶 = × 4
4.50 . 5

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

11. 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)

12. 2 𝐶
$ 3 4 𝑑
$ 𝑑 6 2
8,6 6
$ 𝑑 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

13. ? 𝐶
$ 3 4 𝑑
$ 𝑑 ?
8,7𝑖𝑠ℎ ?
7𝑖𝑠ℎ
7 1 2
$ 𝑑 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 ∙ = =

14. ? 𝐶
$ 3 4 𝑑
$ 𝑑 ? ?
6𝑖𝑠ℎ,5
$ 𝑑 ?
$ 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

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

17. 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

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

19. 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 ℎ𝑟
= 𝑚𝑖 ℎ𝑟 2 3 3
5 𝑚𝑖 2 ℎ𝑟 ÷2
𝑚𝑖 ℎ𝑟 ÷2 3
5 2
5 𝑚𝑖 2 ℎ𝑟 ÷2 3
𝑚𝑖 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

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

21. 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

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

23. 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 )

24. ? 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 ∙ = =

25. ? 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

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