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Topic: Numeracy problem based on history of U.S. flag
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Charles Roll

Posts: 18
From: Amador County, California
Registered: 6/8/09
Numeracy problem based on history of U.S. flag
Posted: Jul 23, 2009 5:04 PM
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NOTE: The problem is available in PDF format WITH the blue fields of the flags shown in jgeg files gotten from the Wikipedia article on the U.S. flag. Wiki also provided the informational basis for the history presented in the problem.


I will be happy to email the PDF as an attachment upon request.


I am posting another email here to discuss organization of GED curriculum. My thinking is that the separation of math and social studies may not be the best way to teach GED, even though the GED test is divided into math, science, social studies, etc..

HERE'S THE PROBLEM, constructed for GED students who have completed or could skip the basic arithmetic operations with integers and are getting into percents in the 'fractions, decimals and percents' area:


From July 4, 1912, until July 4, 1959, there was the 48-star flag: 6 rows of 8 stars each in the blue field at the upper left corner of the flag.

[In the PDF, there's a jpeg image here, with a caption under it, as follows:]
Blue field of the old 48-star flag (1912-1959)

Then, when Alaska became a state, in 1959, the country needed a 49-star flag, even though that flag was to last only for a year, until the admission of Hawaii into the union in 1960. The blue field for the stars had been wider across than it was high since 1795, so even though 7 rows of 7 stars makes 49, the rows of stars were staggered to make the pattern longer -- which was the proposal of Robert G. Heft, a high school student whose mother was a seamstress. Heft made his proposal and constructed his flag -- his mother insisting that he do the sewing himself -- as part of a school project. Although his teacher gave him only a B- (i.e., B minus) for the project, his grade was upped to an A after his design was chosen and adopted by presidential proclamation after Alaska and before Hawaii was admitted into the union in 1959.

[In the PDF, there's a jpeg image here, with a caption under it, as follows:]
Blue field of the 49-star flag (1959-1960)

In the 1950s, more than 1,000 designs were spontaneously submitted to President Dwight D. (?Ike?) Eisenhower for a 50-star flag, anticipating the admission of both Alaska and Hawaii as the 50th state. At least three, and probably more, of these designs were identical to the present design of the 50-star flag, which alternates between five rows of 6 stars and four rows of 5 stars.

[In the PDF, there's a jpeg image here, with a caption under it, as follows:]
Blue field of the 50-star flag (1960 to the present)


What is the total number of rows in the 50-star flag? What percent of all the rows of stars contain 6 stars? What percent contain 5 stars?

What percent of the total number of stars are in rows of 6 stars? What percent are in rows of 5 stars?

Going back to the original 13-star flag, the blue field was square in shape. On June 14, 1777, the Marine Committee of the Second Continental Congress passed the Flag Resolution which stated: "Resolved, That the flag of the United States be thirteen stripes, alternate red and white; that the union be thirteen stars, white in a blue field, representing a new Constellation." The Flag Resolution did not specify any particular arrangement, number of points, nor orientation for the stars. The flag known as the "Betsy Ross flag" shows 13 outwardly-oriented five-pointed stars arranged in a circle.. Although it?s controversial among historians whether Betsy Ross originated the design, it is among the oldest of any U.S. flags. Popular designs at the time were varied and most were individually crafted by seamstresses. Whether she originated the flag named for her, or not, Betsy Ross is probably the most famous seamstress in the history of the United States of America.

[In the PDF, there's a jpeg image here, with a caption under it, as follows:]
13-star "Betsy Ross" flag

In 1795, the number of stars and stripes was increased from 13 to 15 (to include Vermont and Kentucky as states). That flag -- sometimes known as the "The Star-Spangled Banner" flag because it was the flag that inspired Francis Scott Key -- originated the oblong rectangular blue field that continues to this day.

What about flags of the future? The Progressive Party of Puerto Rico has proposed a flag to include Puerto Rico as the 51st state, and that proposal may be inspired by the idea of going back to the original circular pattern of the Betsy Ross flag.

[In the PDF, there's a jpeg image here, with a caption under it, as follows:]
The proposed circular-pattern 51-star flag


On the GED there is always one right answer for each question, but in real life there are often more ways than one to look at a problem, a pattern or a situation.

How many rows of stars in the proposed 51-star flag? How many columns? Can you think of a better way to look at this problem? (A better way to organize the way you look at how the stars are arranged.)


If the picture were visible here, you'd likely figure that the circular pattern is best thought of as composed of a central star surrounded by four concentric circles of stars: 5, 10, 15 and 20, making a total of 51 with the center star.

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