Ray's New Practical Arithmetic · Arts. 260–263 · Unit 25: Mensuration

120. Mensuration at work: tradesmen, lumber, masonry and bins

Goal: Your child applies area and volume to plastering, painting, flooring, board feet, brick and stone walls, and bushels and gallons.

⏱ About 40 minutes · 6 steps

Open it at the Internet Archive ↗

You'll need

  • Paper and pencil, or a slate or small whiteboard

What's in the book

Pages 328–329 list how tradesmen measured their work (Art. 260), with problems. Page 329 has Board Measure (Art. 261) and Masons' and Bricklayers' Work (Art. 262). Page 330 has the masonry problems and Measurement by Bushels or Gallons (Art. 263). Answers are printed.

The lesson, step by step

  1. Warm-up

    Ask: If a painter charges by the square yard, how would he measure a wall?

  2. Old trade measures

    Plastering, house-painting, paving, paper-hanging, etc., are measured by the square foot or square yard.

    Flooring and roofing were measured by the "square" of 100 sq. ft.

    A foot, board measure, is 1 foot long, 1 foot wide, and 1 inch thick.

    Stone masonry is usually measured by the perch, which is 24¾ or 24.75 cu. ft.

  3. Board feet

    1. Find the surface of the board in square feet. 2. Multiply the surface by the thickness in inches.

    How many feet in a two-inch plank 12 ft. 6 in. long and 2 ft. 3 in. wide?

    12.5 × 2.25 = 28.125 sq. ft.; × 2 = 56¼ ft. Lumberyards still sell hardwood by the board foot today.

  4. Bushels and gallons

    Find the volume in cubic inches, and divide by 2150.4.

    to get bushels, and

    Find the volume in cubic inches, and divide by 231.

    to get gallons.

  5. Guided practice

    Do these together:

    A floor is 36 ft. 3 in. long, 16 ft. 6 in. wide: what will it cost to lay it, at $3 a square?

    How many bushels in a bin 15 ft. long, 5 ft. wide, and 4 ft. deep?

  6. Independent practice and check

    Your child picks one problem from each kind on pages 328–330: painting or papering, board feet, bricks, and gallons. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.

Tip

This is a good lesson to take outside: measure a real board, a wall or a garden bed and price it at the book's rates.

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