Mathematics | Instruction

It’s in the Details: Math and Scale

Instruction

Students will learn the concept of scale and why it is important for architects.

Using a scale drawing of the Wainwright Building, students will take measurements and make calculations, culminating in the creation of their own detail drawing of the building.

Activity 1: The Wainwright Building

Two views of the Wainwright Building

  1. Facilitate a student discussion about scale, so students are able to:
    • Understand that a scale drawing has dimensions at a specific ratio with respect to an actual (existing or planned) object.
    • Understand that mathematical calculations are used to determine the dimensions of a drawing based on an actual object or vice versa.
    • Understand that more detail can be shown on larger scale drawings, as these are “close-ups” of a part of the building.
  2. Introduce the assignment to students. Explain they will be redrawing a part of the façade of the Wainwright Building to scale.
  3. Watch the Wainwright Building segment from the PBS special, 10 Buildings that Changed America, on DVD or at wttw.com/10buildings. Prompt students to take notes during the segment.
  4. Facilitate discussion about the Wainwright Building segment. Questions to prompt discussion may include:
    • What are some significant things about the Wainwright Building?
    • Based on the discussion of scale, what details on the Wainwright Building might be left off a drawing of the entire building?
    • Discuss the level of detail that can be seen from a distance (i.e., imagine looking up at the top of the Wainwright Building from the sidewalk). Consider how this compares to what is shown on drawings of different scales (i.e., a drawing of the entire building and a detail showing the entrance).

Activity 2: The Scale Façade

  1. Explain the assignment: Students will solve measurement and scale problems based on a façade drawing of the Wainwright Building on the worksheet titled “Mathematics Worksheet.”
    • A façade is the “face” or one side, often the front, of a building.
    • A pilaster is a rectangular protrusion from a wall that resembles a column.
  2. Guide the class through the first few questions on page one of the worksheet titled “Mathematics Worksheet.” demonstrating how to measure the pilaster and convert to 1/32-inch scale. It is approximately 2.5 inches tall (on paper), yielding an actual height of approximately 80 feet (2.5 inches x 32 feet/inch = 80 feet).
  3. Individually, have students complete the window calculations. If students finish quickly, have them do more measurements and calculations based on the façade – providing slower students with more time to complete the window calculations. This provides students with practice converting scale drawing dimensions into actual measurements.
  4. Guide the class through calculating scale dimensions from actual measurements on page two of the worksheet titled “Mathematics Worksheet.”
  5. Individually, have students complete the calculations and explanations.
  6. Explain how knowing the scale of one drawing and the scale of another drawing establishes a multiplier for determining how to transform the length or area of an object in one scale to another scale. In this case, from 1/32-inch scale to 1/8-inch scale, a multiplier of 4 converts the length of an object; because area is length times width, a multiplier of 16 (4 times 4) converts the area of an object. For example, an eight-foot-tall window would be represented by a rectangle 1/4-inch-tall in 1/32-inch scale; using the multiplier, this would be 1/4 inch x 4 = 1 inch in 1/8-inch scale. Multipliers vary based on which scales are being used.

Activity 3: Detail Drawing

  1. Explain that students will be creating detail drawings that show more information about the building than can be seen when the drawing is a small scale (such as 1/32-inch scale). The drawings will be created on the graph paper area of the worksheet titled “Mathematics Worksheet.” (page 3)
  2. Review the steps of the drawing assignment and check for understanding.
  3. Individually, have students complete the worksheet.

Assessment

Assignments are designed to address the standards and learning goals of the lesson. Each assignment is mapped to the appropriate standards and learning goals.

  1. Assess the students’ “WORKSHEET #1” for accuracy.
    • 7.G.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
  1. Assess the students’ process of problem-solving to identify how students solved calculation problems or where they made mistakes.
    • 7.G.6: Solve real-world and mathematical problems involving area, surface area, and volume.
    • Modeling with Geometry G-MG: Apply geometric concepts in modeling situations.