Introduction: What is the hook, the attention grabber, the interesting beginning?
Begin lesson with an introduction to Mount Rushmore and discuss how the sculptor, Gutzon Borglum, decided to carve the heads of the four Presidents. Simply put, he had to carve “shapes” into the rock. Show two pictures of Mount Rushmore: before and after carving. Help the students recognize that there are now new shapes in the Mountain that weren’t there before. How was math involved in designing and sculpting Mount Rushmore? Look at complex objects in the classroom. Students should be able to identify that these complex shapes could be broken down into smaller, simpler, geometric shapes.
After completing the introduction, begin with a brief history background about Mount Rushmore (where is Mount Rushmore, when was it carved, who carved it and why, where did the name come from? etc.). Begin looking closer at the sculpture by using the provided Measurable 3D PDF file or the 3D Viewer on the CyArk website. In both the 3D PDF and online 3D Viewer, the teacher can cut sections through the model to better illustrate the presence of geometric shapes.
To explain how the faces and all the shapes within them came to be, show the introduction video, which shows how the sculpture was created.
Introduce students to the pointing system used by sculptor Gutzon Borglum to figure out the geometry of the heads and facial features. Use the provided Dec. 1933 article from Modern Mechanix as an aid.
-Hands-on activity 1: Activity demonstrating the concept of the plumb-bob. Once the students watch the introduction video which shows the system used by the carvers of Mount Rushmore, help students construct their own plumb-bob pointing system using a protractor, ruler, string, and a small object for weight. Help the students construct two plumb-bobs so the class may split into two teams. The first team will draw a simple geometric shape on the front face of their cardboard box then use the plumb-bob pointing system to measure the vertices of their geometric shape and instruct the second team on how to replicate the drawing by giving them the angle and distance measurements of the vertices. The second team will take the measurement instructions and use their plumb-bob pointing system to reconstruct the drawing on the front face of their cardboard box.
-Hands-on activity 2: Activity using gridded image of Mount Rushmore to count how many grid squares or fractions of a grid square a nose takes up or, for higher class levels, divide the squares of the grid into smaller geometric shapes to calculate more accurate areas (use geometric area formulas along with the scale of the grid to determine the size of the shapes).
-Hands-on activity 3: Activity to recognize line of symmetry within the faces of Mount Rushmore. Use gridded elevations of each President’s face to draw an approximate line of symmetry. Then measure the distance of symmetric features from the center line and compare. Explain how faces are never perfectly symmetric.
Summary and conclusion of lesson: What helps set a course of action or leaves them thinking? Summarize concepts covered through activities.
Theme statement: (The “big picture”, the final result, the “so what?!)
Gutzon Borglum was able to use math from his studio to design the sculpture on the Mountain. Math can help us figure out larger objects on a small piece of paper.
Talk about ideal symmetry and ideal shapes and how we use these ideals to estimate geometry in the real world which is usually never perfectly symmetric. While symmetry and shapes are “ideal” they don’t always make for interesting art.