Scale drawings

In this lesson for grade seven, students will use maps to measure the distances between cities in North Carolina. Students will write equations using the maps' scales to calculate the actual distances in miles.

A lesson plan for grade 7 Mathematics

By Peggy Dickey and Barbara Turner · Adapted by Sharon Abell

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CareerStart lessons: Grade seven

This collection of lessons aligns the seventh grade curriculum in math, science, English language arts, and social studies with potential career opportunities.

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Related topics

• Learn more about careers, maps, mathematics, and scale drawings.

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Learning outcomes

Students will gain an understanding of how to use maps and scale drawings.

Teacher preparation

Time required for lesson

Approximately 60 minutes. Homework time may be needed to complete activity sheet.

Materials needed

• Rulers
• Scissors
• String
• Pencil
• Overhead projector, chalkboard, or whiteboard
• Printed road maps of North Carolina with scale labeled — one for each pair of students
• Map distances worksheet
• Transparency copy of map distances worksheet
• Map distances worksheet answer key
• Calculators (optional)
• Computer with projector and internet access to access information about Surveyors, Cartographers, Photogrammetrists, and Surveying and Mapping Technicians from the Bureau of Labor Statistics’ Occupational Outlook Handbook
• Optional: If you don’t have access to computers, you may print the information and hand out paper copies to students.

Activities

1. Hand out the map distances worksheets. Discuss why maps are helpful and how/why we use scale drawings. Have the studets brainstorm a list of jobs that might use this skill. (Answers may include mapmakers, surveyors, architects, comic strip artists, firemen, police officers, and textbook publishers.) Access the information from the Occupational Outlook Handbook about Surveyors, Cartographers, Photogrammetrists, and Surveying and Mapping Technicians and discuss the careers with the class. (15 minutes)
2. Divide the students into pairs. Have each pair of students to measure and cut a piece of string 10 inches or 10 cm long. (The unit of measurement will depend on the scale of the maps you’re using.)
3. Complete the first distance on the worksheet, Asheville to Winston-Salem, as an example. (10 minutes)
   1. Instruct the students to use the string to measure the distance of the road from Asheville to Winston-Salem using the scale given on the map.
   2. Write a proportion. This will vary by the scale of the map. An example for a map with a scale of .25 inches = 30 miles:
      .25 in/1.38 in = 30 mi/x
   3. Ask the students how to solve a proportion. (Cross-multipy and divide.)
   4. Demonstrate how to solve the equation. Using the example given:
      .25x = 30 x 1.375
      .25x = 41.25
      x = 41.25 / .25
      x = 165 mi.
   5. Instruct students to round answers with decimals or fractions to the nearest whole number.
4. Have the students work with their partners to complete their worksheets. Encourage students to take turns checking each other’s work for accuracy in math and labeling. (25 min.)