# From Rates to Ratios

Video Solutions to help Grade 6 students learn how to solve problems by analyzing different unit rates.

## New York State Common Core Math Module 1, Grade 6, Lesson 17

Lesson 17 Outcome

• Given a rate, students find ratios associated with the rate, including a ratio where the second term is one and a ratio where both terms are whole numbers.
• Students recognize that all ratios associated to a given rate are equivalent because they have the same value.

Lesson 17 Summary

• A rate of 2/3 gal/min corresponds to the unit rate of 2/3 and also corresponds to the ratio 2:3.
• All ratios associated to a given rate are equivalent because they have the same value.

NYS Math Module 1 Grade 6 Lesson 19 Classwork

Analyze tables, graphs, and equations in order to compare rates.

Examples 1–2: Creating Tables from Equations

1. The ratio of cups of blue paint to cups of red paint is 1:2, which means for every cup of blue paint, there are two cups of red paint. In this case, the equation would be red = 2 x blue or r = 2b, where b represents the amount of blue paint and r represents the amount of red paint. Make a table of values.

2. Ms. Siple is a librarian who really enjoys reading. She can read 3/4 of a book in one day. This relationship can be represented by the equation days = 3/4 books, which can be written as d = 3/4 b, where b is the number of books and d is the number of days.

#### Exercises

1. Bryan and ShaNiece are both training for a bike race and want to compare who rides his or her bike at a faster rate. Both bikers use apps on their phones to record the time and distance of their bike rides. Bryan’s app keeps track of his route on a table, and ShaNiece’s app presents the information on a graph. The information is shown below.
a. At what rate does each biker travel? Explain how you arrived at your answer.
b. ShaNiece wants to win the bike race. Make a new graph to show the speed ShaNiece would have to ride her bike in order to beat Bryan.

2. Braylen and Tyce both work at a movie store and are paid by the hour. The manager told the boys they both earn the same amount of money per hour, but Braylen and Tyce did not agree. They each kept track of how much money they earned in order to determine if the manager was correct. Their data is shown below.
Braylen: m = 10.50h where h is the number of hours worked and m is the amount of money Braylen was paid
Tyce: ____
a. How much did each person earn in one hour?
b. Was the manager correct? Why or why not?

3. Claire and Kate are entering a cup stacking contest. Both girls have the same strategy: stack the cups at a constant rate so that they do not slow down at the end of the race. While practicing, they keep track of their progress, which is shown below.
a. At what rate does each girl stack her cups during the practice sessions?
b. Kate notices that she is not stacking her cups fast enough. What would Kate’s equation look like if she wanted to stack cups faster than Claire?