2.7 Scale drawings
Students will gain an understanding of how to use maps and scale drawings.
Time required for lesson
Approximately 60 minutes. Homework time may be needed to complete activity sheet.
- 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 Surveying and Mapping Technicians and Cartographers and Photogrammetrists 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.
- Hand out the map distances worksheets. Discuss why maps are helpful and how/why we use scale drawings. Have the students 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 Surveying and Mapping Technicians and Cartographers and Photogrammetrists from the Bureau of Labor Statistics’ Occupational Outlook Handbookand discuss the careers with the class. (15 minutes)
- 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.)
- Complete the first distance on the worksheet, Asheville to Winston-Salem, as an example. (10 minutes)
- 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.
- 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
- Ask the students how to solve a proportion. (Cross-multipy and divide.)
- 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.
- Instruct students to round answers with decimals or fractions to the nearest whole number.
- 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.)
North Carolina curriculum alignment
- Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
- Objective 1.01: Develop and use ratios, proportions, and percents to solve problems.
- Goal 2: Measurement - The learner will understand and use measurement involving two- and three-dimensional figures.
- Objective 2.01: Draw objects to scale and use scale drawings to solve problems.
- Common Core State Standards
- Mathematics (2010)
- 7.G.1Solve 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.
- Ratios & Proportional Relationships
- 7.RPR.2Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph...
- Mathematics (2010)