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Drawing to Scale: I

Name of Corresponding Unit Plan: Archaeological Documentation

Grade Level: 5-12

Common Core Standards:
RS9-10. 3. Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.

M.6.RP 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Content Areas: Math, Science

Recommended Length/Duration: 45-60 minute period

Learning Goals: Students will learn to use scale to enlarge or reduce images.

Description/Sequence:

  1. Discuss how archeologists frequently need to produce images of very large areas or objects on maps or diagrams.  The maps and diagrams are much smaller than the actual objects, so a “scale” drawing must be made.  A scale drawing is “similar” to the original in that it has the same proportions between its parts.  It is not “congruent” because the image is smaller.
  2. Describe how scale drawings are expressed in ratios.  A drawing that is half the size of the actual object would have a ratio of 1:2 which means that one unit of measure on the drawing is equal to 2 units of measure on the actual object.  If an actual object is 30 cm long, its image would be 15 cm long using a 1:2 scale.  Using a 1:30 scale, it would be 1 cm long.  Discuss how ratios work like fractions.
    Large scale drawings (e.g. 1:2, 1:3, 1:50) are usually of small objects or areas. Small scales (e.g. 1:1000, 1:250,000) are usually for maps of large areas.  A typical globe of the Earth has a scale of 1:40,000,000.
  3. Have students look at the ship outline on their worksheet.  Point out that the grid provides reference points to help measure the outline’s shape.
  4. Have students use the grid and rulers to measure reference points to redraw the ship on the 1:2 scale grid below.
  5. Have students redraw the ship outline again in 1:4 scale.
  6. Informally ask students which parts of the drawing are more difficult to draw.  What changes as the drawing is reduced?

Assessments: Check worksheets for accuracy.

Materials/Resources: Worksheets, Rulers

Special Considerations: Scientific measurements are generally easier to take and calculate in metric than in English units.  Additional work may be needed if students are not familiar with metric measurements, or if the teacher chooses to use English units.

Extensions:
Interested students may want to make a scale drawings of more complicated objects.

Interested students may want to look at house plans, architectural drawings, product plans, and maps to see how they are drawn.