Grade 6 Module 1 Lesson 14

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 1

Hours Miles

Exercise 1

Hours Miles2 100

Exercise 1

Hours Miles2 1004 200

Exercise 1

Hours Miles2 1004 2006 300

Exercise 1

Hours Miles2 1004 2006 3008 400

10 50012 60014 70016 800

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.

Exercise 2

Hours

___________________________________

___________________________________

Miles

Exercise 2

Hours 0 2 4 6 8 10 12 14 16 ___________________________________

___________________________________ 0 100 200 300 400 500 600 700 800

Miles

Exercise 2

Using the information from the double number line diagram, how many miles would be traveled in one hour?

Exercise 2

Using the information from the double number line diagram, how many miles would be traveled in one hour?

50 miles in one hour

How do you know?

Exercise 2

Using the information from the double number line diagram, how many miles would be traveled in one hour?50 miles in one hourHow do you know?

If the train is moving at a constant speed, half of 2 is 1, and half of 100 is 50.

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?

Example 1

2 100 (2,100)468

10121416

Hours Miles Ordered Pair

Example 1

2 100 (2,100)4 200 (4,200)6 300 (6,300)8 400 (8,400)

10 500 (10,500)12 600 (12,600)14 700 (14,700)16 800 (16,800)

Hours Miles Ordered Pair

Time and Distance of Travel

0 2 4 6 8 10 120

100

200

300

400

500

600

Miles

Miles

Hours

Miles

Discussion

How do we label this axis?

Discussion

How do we label the horizontal axis?HoursWhich quantity will we measure using the vertical axis, time or distance?

Discussion

How do we label the horizontal axis?HoursWhich quantity will we measure using the vertical axis, time or distance?Distance

Discussion

How do we label the horizontal axis?HoursWhich quantity will we measure using the vertical axis, time or distance?DistanceHow should we label the vertical axis?

Discussion

How do we label the horizontal axis?HoursWhich quantity will we measure using the vertical axis, time or distance?DistanceHow should we label the vertical axis?Miles

Discussion

Locate the ordered pair (4,200) on the coordinate plane.What does this point represent in the context of distance and time?

Discussion

Locate the ordered pair (4,200) on the coordinate plane.What does this point represent in the context of distance and time?The train traveled 200 miles in 4 hours.

Discussion

Locate the ordered pair (10,500) on the coordinate plane.How far did the train travel in 10 hours?

Discussion

Locate the ordered pair (10,500) on the coordinate plane.How far did the train travel in 10 hours?The train traveled 500 miles in 10 hours.

Discussion

Locate the ordered pair (14,700) on the coordinate plane.How many hours does it take the train to travel 700 miles?

Discussion

Locate the ordered pair (14,700) on the coordinate plane.How many hours does it take the train to travel 700 miles?The train has traveled 700 miles in 14 hours.

Discussion

What do you notice about the arrangement of the points on the coordinate plane?

Discussion

What do you notice about the arrangement of the points on the coordinate plane?They appear to be in a line.What do you think having an ordered paid of (0,0) mean since we drew the line to the origin?

Discussion

What do you notice about the arrangement of the points on the coordinate plane?They appear to be in a line.What do you think having an ordered paid of (0,0) mean since we drew the line to the origin?Zero hours after the trip began the train has traveled zero miles.

Discussion

Using this graph, we can determine how many hours the team will have to wait before being served dinner.What information do we know?

Discussion

Using this graph, we can determine how many hours the team will have to wait before being served dinner.What information do we know?Dinner is served at mile 250.

Discussion

Where can we find 250 miles on our graphs?

Closing

Why would you choose to use a graph to represent a ratio?

Closing

Why would you choose to use a graph to represent a ratio?Reading a graph can be more efficient than creating a table to determine missing values.

Lesson 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 Summary

Example: Equation: Y = 3x

Ordered Pairs (x,y) (0,0) (1,3) (2,6) (3,9)

X Y0 01 32 63 9

Lesson Summary

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50123456789

10

Y-Value 1

Y-Value 1