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Activity Eight: Horatio’s Ratios


Subject
Mathematics

Grades
6-8

Objective
Students will apply the concept of averages, ratios and rates to calculate aspects of Horatio’s road trip



Background
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.



Activity I
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 travel-related 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.



Activity II
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



Related PBS Lessons
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/sb-auto.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



Standards
Correlation to NCTM Curriculum Standards and Expectations for Grades 6-8:

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.



    About the Author
    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.