Hand-tool lesson · Measure and mark

Sector

Use matching scales and a divider to transfer a fraction of a length.

Watch · practice · showInstructor-supervised
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In this lesson

Know the tool

Maplewoodshop photograph of a sector opened beside a divider.

Your goal: Use a demonstrated linear sector scale to find one third of a 6-inch reference length.

A sector opens like a hinged pair of arms. Matching linear scales on the arms create proportional gaps. Those scale numbers describe ratios; they are not automatically inch readings.

Have the instructor identify matching linear scales, their common hinge origin, and corresponding marks on both arms.

Watch and prepare

At your station

  • A sector, divider, ruler, pencil, approved backing, and a checked 6-inch reference line.
  • Use a sector whose matching linear scales include 6 and 2; have the instructor map an equivalent ratio if the supplied numbering differs.

Demonstration and setup

  • First complete the divider practice. Watch the instructor find corresponding marks on the same linear scale on each arm.
  • The demonstration must show how the opening stays fixed while the divider moves between the two pairs of marks.
  • Handle divider points on approved backing. Stop if you cannot identify the correct scale or keep the hinge setting steady.

Practice

Start after the demonstration and the instructor's setup check. Stop and ask for help if the work moves or the tool does not behave as demonstrated.

  1. Transfer the whole length.

    Set the divider tips to the two ends of the 6-inch reference line. Keep that opening while moving to the sector.

  2. Set the sector opening.

    Open the sector until the gap between its matching 6 marks equals the divider opening. Have the instructor check the marks and hold the sector steady.

  3. Read the fraction.

    Without changing the sector angle, reset the divider to the gap between the matching 2 marks. That gap is 2/6, or one third, of the original span.

  4. Transfer and check.

    Step the new opening three times along the reference line. Check the transferred spacing with a ruler; it should be about 2 inches.

Show your skill

Show the instructor these observable results before using the skill in a project:

  • You use corresponding marks from one matching linear scale.
  • The sector angle stays unchanged while the divider setting changes.
  • Three transferred intervals reach the original endpoint within the instructor's marking tolerance.

Check your understanding

Why does the gap at 2 give one third of the gap at 6?

Reveal the explanation

On matching linear scales at a fixed opening, corresponding gaps are proportional to their distances from the hinge: 2/6 = 1/3. One third of 6 inches is 2 inches.

Answer aloud or on paper, then compare with the explanation.

Use the skill

Use the skill again at the next instructor-approved practice station.

Maplewoodshop materials adapted with permission. Images © Maplewoodshop. Practice tasks and learning checks by STEM Guides. Maplewoodshop.