Math Investigations

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Chapter 5

Part 1: For the problem in the Teacher's Edition, page 108

Provide students with the Problem Worksheet (PDF file).

To find the average speed of the Concorde students need to divide 17,400 miles by 12. To find how many miles Amelia Earhart could have traveled in 12 hours, students need to find her average speed per hour by dividing 2,205 by 15. Then take the answer, 147, and multiply it by 12 to find how many miles Amelia Earhart could have traveled in 12 hours.

Answers:
The average speed of the Concorde was about 1,450 miles per hour (mi/h).
Amelia Earhart could have traveled about 1,764 miles in 12 hours.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 5 on division with greater numbers.

Introducing the Investigation

Introduce the investigation by reading aloud the assignment at the top of the first page of the Description of Investigation and Student Report (PDF file), by having one of your students read aloud the assignment, or by having the students read the assignment individually.

Ask, How would you find the average speed in miles per hour (mi/h) of one of these flights? (divide the distance by the amount of time)

Ask, Which average speed is not in terms of mi/h?(the Wright Brothers' average speed)

Doing the Investigation

Have students share both their solution and how they found it.

Answers for the Data Sheet

Date Name Flight Distance Length of Time Average Speed
December 17, 1903 Wright Brothers First flight 120 feet 12 seconds about
7 mi/h
May 17, 1913 Domingo Rosillo First flight from Florida to Cuba 90 miles about 3 hours about
30 mi/h
May 20, 1927 Charles Lindbergh New York to Paris 3,610 miles about 34 hours about
106 mi/h
May 20, 1932 Amelia Earhart First solo flight across the Atlantic by a woman 2,026 miles about 15 hours about
135 mi/h

Student Report

The student report gives students an opportunity to show the results of the work they have done calculating the average speed of some famous flights.

Extending the Investigation

You might want to have the students use a calculator to calculate the average speed of the Wright Brothers flight in miles per hour. This would make it easier to compare their speed with the other speeds.

Answer:
To convert to find the average speed in hours rather than seconds, you would have to determine the number of seconds in an hour. There are 60 seconds in one minute and 60 minutes in an hour, so there are 60 × 60 or 3,600 seconds in an hour. 10 ft/s is multiplied by 3,600s\3,600s (which is equal to 1) in order to find the number of feet per hour (ft/h). This would be 36,000 ft\3,600s or 36,000 ft/h. To find the number of miles per hour (mi/h), divide 36,000 by the number of feet in a mile, 5,280. This is about 7 mi/h.


Houghton Mifflin Math Grade 5