Ray's New Practical Arithmetic · Arts. 155–156 · Unit 13: The Metric System

73. The metric system: names and measures of length

Goal: Your child knows the metric prefixes and changes between meters, centimeters, kilometers and the rest by moving the decimal point.

⏱ About 35 minutes · 7 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 189–190 define the metric system (Art. 155): the meter, ar, liter and gram, and the Latin and Greek prefixes. Page 190 starts Measures of Length (Art. 156), and page 191 gives the table, worked examples and problems 1–4, with problems 5–10 on page 192.

The lesson, step by step

  1. Warm-up

    Find a meter stick or a metric ruler and a yardstick. Compare them. Ray gives a memory aid: the meter is nearly 3 ft. 3⅜ in., "the rule of the three threes".

  2. The idea

    The Metric System is so called from the meter, the unit upon which the system is based.

    All the units of the other measures are derived in a simple manner from the meter.

    Then the prefixes. The smaller ones are milli (.001), centi (.01) and deci (.1). The larger ones are deka (10), hekto (100), kilo (1000) and myria (10000).

    a millimeter is one thousandth of a meter; a centigram is one hundredth of a gram; and a deciliter is one tenth of a liter.

  3. A note on the old book

    Ray spells some names in the old way: "hektometer", "ar", and later "ster" and "tonneau". The "myria-" units are not used today. Ray gives the U.S. legal value:

    The Meter is the unit of length; it is legal in the United States at 39.37 inches.

  4. Work the book's examples

    Reduce 5.638 m. to centimeters.

    One meter is 100 cm, so move the point two places right: 563.8 cm.

    Reduce 3642.9 m. to kilometers.

    Divide by 1000, so move the point three places left: 3.6429 Km.

  5. Guided practice

    Do Ex. 3 and Ex. 4 on page 191 together: 4.27 Dm. to centimeters (×1000) and 5.6 dm. to hektometers (÷1000).

  6. Independent practice and check

    Your child works problems 5–10 on page 192. 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.

  7. Mental-math wrap-up

    Aloud: 3 m = ? cm; 250 cm = ? m; 2 km = ? m; 75 mm = ? m.

Tip

Ray writes Dm. for dekameter and dm. for decimeter, so the capital letter matters. Point this out before the problems.

@teddyrookbook GitHub