
Introduction
Activity One:
Ballad of Horatio
Activity Two:
Dear Swipes
Activity Three:
Diary of a Driver
Activity Four:
Family Road Trips
Activity Five:
The Horseless Carriage
Activity Six:
If Horatio Drove Today
Activity Seven:
New Frontiers
Activity Eight:
Horatio’s Ratios


Mathematics
68
Students will apply the concept of averages, ratios and rates to calculate aspects of Horatio’s road trip
The following definitions are critical to this learning activity. When explaining the concept, be sure to provide relevant examples for each term.
Average  The number obtained by dividing the sum of a set of numbers by the number of addends.
Rate  A ratio that compares two quantities having different units of measure. For example, a speed such as 66 miles per hour compares distance with time.
Ratio  A comparison of two quantities with like units. Ratios can be expressed with fractions, decimals, percents, or words; or they can be written with a colon between the two numbers being compared. For example, if a team wins 3 games out of 5 games played, the ratio of wins to total games is 3/5, 0.6, 60%, 3 to 5, or 3:5.
Ask students to reflect a long trip they have taken. Where did they go? How did they go? How long did it take to get there? How far was the destination from their home? How much money do they think they spent on food, souvenirs, lodging, and other travelrelated things? If they drove, how many miles did they travel? How much money did they spend on gas? Select and chart several students’ data and facilitate the class’ calculation of averages, i.e. — miles traveled per day, gallon of gas per day, monies spent each day on food, etc. Have the class compare and contrast the data to make determinations about the trips in terms of expense, distance, etc.
Introduce the concepts of rate and ratios, providing generic examples. For example: total gas= $8,000; total time=63 days; total distance=4,600 miles. Students can calculate dollars per, mile, or gallon of gas, or days per mile or gallon, or miles per day. Invite students to use data from the their stories to calculate rates and ratios.
Point out to students that Horatio’s extended road trip presents myriad data to calculate in terms of averages, rates, and ratios. Students, for example, can calculate how fast Horatio traveled between Kansas and Ohio, how much gasoline he used when traveling in the mountains of Oregon and in the deserts of Nevada, where he got more miles to the gallon of gas, or how many dollars he spent for each mile traveled.
Divide students into small groups, distributing a graphic organizer that enables them to gather data from the film and this Web site —distances covered, time traveled between destinations, gas costs, etc. Use Mapquest (www.mapquest.com) or How Far Is It? (www.indo.com/distance/) to determine the distances Horatio and his crew covered. (The class can choose to track the entire trip, or select specific parts of the journey.) A brief list of items might be provided to jump start student data collection. For data per category collected, instruct students to calculate averages, rates, and ratios, and discuss as a class how these calculations might look in the present.
Horatio’s Stops

May 23, 1903 
San Francisco to Tracy, California 
May 24 
To Sacramento, California 
May 25 
To Oroville, California 
May 26 
To Anderson, California 
May 27 
To Montgomery, California 
May 28 
To Bieber, California 
May 29 
To Alturas, California 
June 2 
To Lakeview, Oregon 
June 6 
To SL Ranch, Oregon 
June 7 
To Silver Creek, Oregon 
June 8 
To Buchanan's Ranch, Oregon 
June 9 
To Vale, Oregon 
June 10 
To Ontario, Oregon 
June 11 
To Caldwell, Idaho 
June 12 
To Orchard, Idaho 
June 15 
To Pocatello, Idaho 
June 16 
To Soda Springs, Idaho 
June 17 
To Montpelier, Idaho 
June 18 
To Diamondville, Wyoming 
June 21 
To Rock Springs, Wyoming 
June 23 
To Rawlins, Wyoming 
June 30 
To Laramie, Wyoming 
July 1 
To Cheyenne, Wyoming 
July 2 
To Archer, Wyoming 
July 12 
To Omaha, Nebraska 
July 17 
To Chicago 
July 18 
To South Bend, Indiana 
July 19 
To Toledo, Ohio 
July 20 
To Cleveland 
July 21 
To Buffalo, New York 
July 23 
To Syracuse, New York 
July 24 
To Little Falls, New York 
July 26, 1903 
Arrive New York City 

www.pbs.org/harriman/education/lessonplans/
transportation.html
Harriman Expedition  How Has Transportation Changed
www.pbs.org/goldrush/activities.html
Gold Rush  Teacher's Guide
www.pbs.org/opb/greatlodges/teachers/teachers.htm
Great Lodges  You Be The Tour Guide
www.pbs.org/kqed/springboard/sbauto.pdf
Springboard  The Changing Face of the Automobile
www.pbs.org/fmc/lessons/lesson1.htm
First Measured Century  The Demise of the Great American Frontier
www.pbs.org/fmc/lessons/lesson2.htm
First Measured Century  Writing a Play about Immigrant Life in America around 1910
Resource Type: Lesson Plan
www.pbs.org/lewisandclark/class/l03.html
Lewis And Clark  Lesson 3: Mapping and Cartography
Correlation to NCTM Curriculum Standards and Expectations for Grades 68:
Number and Operations
Understand and use ratios and proportions to represent quantitative relationships.
Algebra
Represent, analyze, and generalize a variety of patterns with tables, graphs, words,
and, when possible, symbolic rules
Model and solve contextualized problems using various representations,
such as graphs, tables, and equations.
Measurement
Solve simple problems involving rates and derived measurements for such attributes as velocity.
Data Analysis and Probability
Formulate questions
Communication
Communicate mathematical thinking coherently and clearly to peers, teachers, and others.
Analyze and evaluate the mathematical thinking and strategies of others.
Connections
Recognize and apply mathematics in contexts outside of mathematics.
Author Steve Crandall has taught secondary mathematics and science since 1979. An amateur entomologist and astronomer, he has presented lessons at state/national conferences for math, science, and middle school.

