1. Unit 3. Day 4.

2. Example A*: During their last workout, Izzy ran miles in 15 minutes, and her friend Julia ran miles in 25 minutes. Each girl thought she was the faster runner. Based on their last run, which girl is correct? ?
Izzy ?
Julia

3. Example A*: During their last workout, Izzy ran miles in 15 minutes, and her friend Julia ran miles in 25 minutes. Each girl thought she was the faster runner. Based on their last run, which girl is correct? Use any approach to find the solution
9 4
1 15
15 1
9 60
3 20
3 20 ÷ ∙ 15 = =
2 1 4
9 4
÷15
𝑚𝑖𝑛 𝑚𝑖
𝑚𝑖 𝑚𝑖𝑛
𝑚𝑖 1 𝑚𝑖𝑛
Izzy 15
÷15
15 4
1 25
25 1
15 100
3 20
3 20 ÷ ∙ 25 = =
3 3 4
15 4
÷25
𝑚𝑖 𝑚𝑖𝑛
𝑚𝑖𝑛 𝑚𝑖
𝑚𝑖 1 𝑚𝑖𝑛 25
Julia
÷25

4. Example A*: During their last workout, Izzy ran miles in 15 minutes, and her friend Julia ran miles in 25 minutes. Each girl thought she was the faster runner. Based on their last run, which girl is correct? Use any approach to find the solution
9 4
60 15
15 60
540 60 ÷ ∙ = = 9 9
2 1 4
9 4
÷ 15 60
𝑚𝑖 ℎ
𝑚𝑖 1 ℎ
Izzy
15 60
÷ 15 60
3 3 4
15 4
15 4
60 25
÷ 25 60
25 60 ÷ ∙ = = 9 9
𝑚𝑖 ℎ
𝑚𝑖 1 ℎ
25 60
÷ 25 60
Julia

5. Example A*: During their last workout, Izzy ran miles in 15 minutes, and her friend Julia ran miles in 25 minutes. Each girl thought she was the faster runner. Based on their last run, which girl is correct? Use any approach to find the solution
= 45 4
2 1 4
9 4
9 4
9 4
9 4
9 4
𝑀𝑖𝑙𝑒𝑠
𝑀𝑖𝑛𝑢𝑡𝑒 15 30 45 60 75
Izzy
= 45 4
3 3 4
15 4
15 4
15 4
9 4
9 4
𝑀𝑖𝑙𝑒𝑠
Julia
𝑀𝑖𝑛𝑢𝑡𝑒 25 50 75
100
125

6. is often used to compare!
Unit Rate
is often used to compare! 5 8
5 km
in 30 min
𝑘𝑚 ℎ
𝑘𝑚 ℎ
8 km
in 40 min
30 60
1 2
40 60
2 3
10 𝑘𝑚 1 ℎ
12 𝑘𝑚 1 ℎ

7. is often used to compare!
Unit Rate
is often used to compare!
5 lbs.
for $12
$ 𝑙𝑏 12
$ 𝑙𝑏 7
3 lbs.
for $7 5 3
$ 𝑙𝑏
$ 𝑙𝑏

8. Example B. : The Exchange sells a large and a small pack of pencils
Example B*: The Exchange sells a large and a small pack of pencils. A pack of 30 pencils sells for $7.80. A smaller pack of 12 costs $4.20. which pack provides the better deal?
$ 𝑝𝑒𝑛𝑐𝑖𝑙
4.20
÷12
$ 𝑝𝑒𝑛𝑐𝑖𝑙
𝑝𝑒𝑛𝑐𝑖𝑙 $
$ 𝑝𝑒𝑛𝑐𝑖𝑙
$ 𝑝𝑒𝑛𝑐𝑖𝑙
7.80
÷30 12
÷12 30
÷30
0.3 5 . 3 5
0.2 6 . 2 6 12
3 6 30 − −
6 0 6 −
6 0
1 8 −
1 8 0

9. is not always used for comparison!
Unit Rate
is not always used for comparison!
Example C*: A turtle walks of a mile in 50 minutes. What is the unit rate when the turtle’s speed is expressed in miles per hour?

10. Example C. : A turtle walks 7 8 of a mile in 50 minutes
Example C*: A turtle walks of a mile in 50 minutes. What is the unit rate when the turtle’s speed is expressed in miles per hour?
7 8
5 6
6 5
42 40
21 20
1 1 20
1 1 20 ÷ ∙ = = =
7 8
7 8
÷ 5 6
𝑚𝑖 ℎ
𝑚𝑖 ℎ
𝑚𝑖 1 ℎ = 50
5 6
50 60
÷ 5 6

11. 𝑐𝑢𝑝𝑠 𝑑𝑜𝑧𝑒𝑛 𝑐𝑢𝑝𝑠 1 𝑑𝑜𝑧𝑒𝑛 𝑑𝑜𝑧𝑒𝑛 𝑐𝑢𝑝𝑠 𝑑𝑜𝑧𝑒𝑛 1 𝑐𝑢𝑝
Example D: For Anthony’s birthday, his mother is making cupcakes for his 𝟏𝟐 friends at his daycare. The recipe calls for 𝟑 𝟏 𝟑 cups of flour. This recipe makes 𝟐 𝟏 𝟐 dozen cupcakes. Anthony’s mother has only 𝟏 cup of flour. Is there enough flour for each of his friends to get a cupcake?
10 3
5 2
2 5
20 15
4 3
1 1 3
1 1 3 ÷ ∙ = =
3 1 3
10 3
10 3
÷ 5 2
𝑐𝑢𝑝𝑠 𝑑𝑜𝑧𝑒𝑛
𝑐𝑢𝑝𝑠 1 𝑑𝑜𝑧𝑒𝑛
2 1 2
5 2
5 2
÷ 5 2
5 2
10 3
3 10
3 4
15 20
3 4 ÷ ∙ =
÷ 10 3
𝑑𝑜𝑧𝑒𝑛 𝑐𝑢𝑝𝑠
𝑑𝑜𝑧𝑒𝑛 1 𝑐𝑢𝑝
She does not have enough flour!
÷ 10 3