Ray's New Higher Arithmetic · Arts. 191–198 · Unit 11: Compound Denominate Numbers

49. Measures of length and surface

Goal: Your student uses the tables of long measure, chain measure, mariners' measure and square and surveyors' measure, including acres and sections.

⏱ About 40 minutes · 7 steps

Open it at the Internet Archive ↗

You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil

What's in the book

Extension defined; long or linear measure (inches to miles, with rods), chain measure (links and chains), mariners' measure (fathoms, cable-lengths), the old cloth measure, square measure, and surveyors' measure for land (acres, sections, townships).

The lesson, step by step

  1. Warm-up

    Ask: How many feet in a mile? (5280.) How many inches in a yard?

  2. Length

    Read:

    Extension is that property of matter by which it occupies space.

    Linear Measure is used in measuring distances, or length, in any direction.

    Table: 12 in. = 1 ft., 3 ft. = 1 yd., 5½ yd. = 1 rod, 320 rd. = 1 mile.

  3. Surveyors and sailors

    Read:

    Chain Measure is used by surveyors in measuring land, laying out roads, establishing boundaries, etc.

    (7.92 inches = 1 link, 100 links = 1 chain, 80 chains = 1 mile)

    Mariners' Measure is used in measuring the depth of the sea, and also distances on its surface.

    (6 feet = 1 fathom)

  4. Surface

    Read:

    Superficial Measure is used in estimating the numerical value of surfaces

    Table: 144 sq. in. = 1 sq. ft., 9 sq. ft. = 1 sq. yd., 30¼ sq. yd. = 1 sq. rd., 160 sq. rd. = 1 acre.

  5. Land

    Read:

    Surveyors' Measure is a kind of superficial measure, which is used chiefly in government surveys.

    640 acres = 1 square mile (a section); 36 square miles = 1 township. Much of the American Midwest was surveyed this way, which is why so many roads run in a grid a mile apart.

  6. Practice

    Your student finds: rods in a mile and a half; square feet in an acre (43560, as the table shows); acres in a quarter section.

  7. Wrap-up

    Ask: Why is a square rod 30¼ square yards? (5½ × 5½.)

Answers to the book's problems

Practice: 1½ miles = 480 rods; 1 acre = 43560 sq. ft.; a quarter section = 160 acres.

Worked out for this site from the scan. If a number in your copy differs, trust the book.

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