 # Ratio Tables, Double Number Lines and Coordinate Plane

Video solutions to help Grade 6 students learn how to represent ratios in ratio tables, equations, and double number line diagrams and then represent those ratios in the coordinate plane.

### New York State Common Core Math Module 1, Grade 6, Lesson 14

Lesson 14 Student Outcomes

• Students associate with each ratio A:B the ordered pair (A, B) and plot it in the - coordinate plane.
• Students represent ratios in ratio tables, equations, and double number line diagrams and then represent those ratios in the coordinate plane.

Lesson 14 Summary

A ratio table, equation, or double number line diagram can be used to create ordered pairs. These ordered pairs can then be graphed on a coordinate plane as a representation of the ratio.

Lesson 14 Classwork

Representing Ratios
Kelli is traveling by train with her soccer team from Yonkers, NY to Morgantown, WV for a tournament. The distance between Yonkers and Morgantown is 400 miles. The total trip will take 8 hours. The train schedule is provided below:

Exercise 1
Create a table to show the time it will take Kelli and her team to travel from Yonkers to each town listed in the schedule assuming that the ratio of the amount of time traveled to the distance traveled is the same for each city. Then, extend the table to include the cumulative time it will take to reach each destination on the ride home.

Exercise 2
Create a double number line diagram to show the time it will take Kelli and her team to travel from Yonkers to each town listed in the schedule. Then, extend the double number line diagram to include the cumulative time it will take to reach each destination on the ride home. Represent the ratio of the distance traveled on the round trip to the amount of time taken with an equation.
Using the information from the double number line diagram, how many miles would be traveled in one hour?
How do you know?

Example 1
Dinner service starts once the train is 250 miles away from Yonkers. What is the minimum time the team will have to wait before they can have their meal?

Lesson 14 Problem Set

1. Complete the table of values to find the following: Find the number of cups of sugar needed if for each pie Karrie makes, she has to use 3 cups of sugar.
Use a graph to represent the relationship:
Create a double number line diagram to show the relationship:

2. Write a story context that would be represented by the ratio 1:4.
Complete a table of values for this equation and graph. Write two equations for the table.

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