What is the length of George Washington’s Nose?

Michael Custard

Introduction

In the Black Hills of South Dakota, stands Mount Rushmore National Park. It was originally intended to bring tourism to the state, but it turned out to be much more. Then State historian, Doane Robinson, thought someone could carve figures of the American west into the mountain side. Robinson contacted master sculptor Gutzon Borglum. Borglum changed the original idea into something that would convey the meaning of America. The project began on October 4, 1927 and finally ended in 1941. Today, Mount Rushmore stands as a symbol of America and this great nation.

Who are the faces of Mount Rushmore? George Washington, being our first president, represents the birth of our country. Thomas Jefferson symbolizes the expansion of our nation; he is credited with the Louisiana Purchase in 1803. Abraham Lincoln embodies the preservation of the nation in confronting the challenges of the Civil War. Last but not least, Theodore Roosevelt represents the development of our country. He promoted the construction of the Panama Canal.

TaskWhat is the length of George Washington’s nose on Mount Rushmore?

Students will work in small groups to figure out the length of President George Washington’s nose on Mount Rushmore in South Dakota. Students will set up and solve a proportion using proportionalities found on the human face. Students must explore and report the proportionality of the human body. They will create a spreadsheet to record the results after measuring their own bodily proportions. Students will write a paragraph on how they created and solved the proportion. Finally, students will write a two paragraph summary on what they learned about Mount Rushmore National Park.

M7.A.2.2 Solve problems using ratios, proportions, percents and/or ratesM7.A.2.2.2 Solve for a variable in a given proportion

Process: Step 1

Body Proportions:

The human body is truly a masterpiece of art. There are many natural proportions that occur throughout the body. Lets see how you match up. Each person in the group must print out and complete the worksheet provided below. You will have to help each other with the measurements.

Body Proportion worksheet

Process: Step 2Measure in inches from the bottom of your nose to the spot between your eyes. Then measure the length of your face from the bottom of your chin to the top of your head. Record these measurements.

1. bottom of nose to eyes: ___________ in.2. bottom of chin to top of head: ___________ in.

In your group of four to five students, using excel, write down the data each person gathered for their nose height and face height in inches in a spreadsheet like the example given below. Then use a formula to find the average nose height and face height for your group.

Spreadsheet

Process: Step 3

Now, use your data from the spreadsheet and the fact that George Washington’s face is 60 feet tall to find the length of his nose using a proportion. You must write and solve the proportion showing all work. Then explain in one paragraph how to set it up and complete the work in your proportion.

How big?

Process: Step 4• Finally, you will write two paragraphs explaining

what you learned about Mount Rushmore. You may use these links below to aid in your research.

• http://www.nps.gov/moru/index.htm• http://en.wikipedia.org/wiki/Mount_Rushmore• http://www.buzzle.com/articles/facts-about-mou

nt-rushmore.html• http://www.mtrushmore.net/• http://www.destinationthere.com/5_Facts_abou

t_Mount_Rushmore

Resources• Step 1: Body Proportion worksheet• Step 2: Spreadsheet• Step 4: Internet sources • http://www.nps.gov/moru/index.htm• http://en.wikipedia.org/wiki/Mount_Rushmore• http://www.buzzle.com/articles/facts-about-

mount-rushmore.html• http://www.mtrushmore.net/• http://www.destinationthere.com/

5_Facts_about_Mount_Rushmore

EvaluationGrading Rubric for Mount Rushmore:

4 3 2 1

Spreadsheet The spreadsheet was set up correctly. All the results were recorded. The average formula was used.

The spreadsheet had one or two errors in the set up. All but one result was recorded. The average formula was used.

The spreadsheet had three errors in the set up. Two results were missing. The average formula was not used.

The spreadsheet had four or more errors in the set up. Three or more results were missing. The average formula was not used.

Proportion The proportion was set up correctly. The proportion was solved, with work shown, correctly. A complete explanation was given.

The proportion was set up correctly. The proportion was solved, but the work was not shown. A complete explanation was given.

The proportion was set up correctly. The proportion was solved, with work shown, correctly. A complete explanation was missing.

The proportion was not set up correctly. The proportion was not solved, with work shown, correctly. No explanation was given.

Mount Rushmore paragraphs

Two complete paragraphs with at least 4 sentences in each paragraph was written.

One complete paragraph with at least 4 sentences was written.

One to three sentences were written.

Group work Student worked well with others without any complaints or incidences.

Student worked with others with only one complaint or incidence.

Student worked with others with two complaints or incidences.

Student worked with others with three or more complaints or incidences.

Conclusion• Now you know more about proportions and Mount Rushmore. As you

found out in this Webquest, proportions can be used in everyday life to help solve problems. In your research, you measured each other’s faces. Why might this be a problem and lead to inaccurate data?

• I hope I have sparked some interest in our national parks. Now it is your turn, research other national parks that you would like to visit one day.

• George Washington’s nose is 20 feet long from the bottom of his nose to the spot between his eyes. Please explain why your answer may not be

exactly 20 feet long. Were you close to the exact answer?

How big? 20 ft.

Additional Webquest ComponentExploring Mount Rushmore Through Proportions7th Grade MathPA Standards: M7.A.2.2 Solve problems using ratios, proportions, percents and/or rates M7.A.2.2.2 Solve for a variable in a given proportion SWBAT write and solve a proportion in order to figure out the length of George Washington’s nose on

Mount Rushmore.SWBAT research and write two paragraphs explaining what they learned about Mount Rushmore

Materials: Computers, printer, tape measures or rulers

Procedures:Students will open the webpage that contains the Webquest on a computerStudents will read through the Introduction and Task pagesStudents will follow the four steps in the Process section of the WebquestStudents will hand in the body proportion w/s, spreadsheet with the facial measurements, the proportion and paragraph on notebook paper and the two paragraph summary about Mount Rushmore on notebook paperStudents will read the Conclusion page

Assessment: Students will be assessed using the rubric provided in the Webquest

CreditsImages provided by:Google imageshttp://www.nps.gov/moru/index.htm

Author Biography:Michael Custard 6 & 7 Grade Math Teacher Clear Run Intermediate School, Pocono Mountain School DistrictI have been teaching math for 9 years. I am married to Michelle Peechatka and I have a one year old son, Brody. I also have a Golden Retriever named Timber and two cats named Scout and Tahoe.

PermissionsWe all benefit by being generous with our work. Permission is granted for others to use and modify this WebQuest for educational, non-commercial purposes as long as the original authorship is credited. The modified WebQuest may be shared only under the same conditions. See the Creative Commons Attribution • Non-Commercial• Share-Alike license for details.