Ray's New Practical Arithmetic · Arts. 61–63 · Unit 7: Reduction of Compound Numbers

33. Dry measure and the rules for reduction

Goal: Your child knows pints, quarts, pecks and bushels and changes a measure to a smaller or larger unit by multiplying or dividing.

⏱ About 35 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

The table of dry measure, the legal weight of a bushel of different goods, oral questions for the teacher to ask, then worked examples and the two rules for reduction with problems.

The lesson, step by step

  1. Warm-up

    Mental: How many cups in a pint? Pints in a quart? (2 and 2.) How many quarts in 3 gallons? (12.)

  2. The table

    Read:

    Dry Measure is used in measuring grain, vegetables, fruit, coal, etc.

    The table: 2 pints make 1 quart, 8 quarts make 1 peck, 4 pecks make 1 bushel.

    Note for you: pecks and bushels are still used for apples at farm stands; the rest is history.

  3. Ask the questions

    The page "To Teachers" gives oral questions. Ask a few:

    How many pints in 2 quarts? In 4? In 6? In 8? In 10?

    How many pecks in 9 bu.? In 11? In 13? In 15? In 17? In 19?

  4. Down: multiply

    Work together:

    Reduce 7 bu. 3 pk. 6 qt. 1 pt. to pints.

    7 bu. × 4 = 28 pk., + 3 = 31 pk. 31 × 8 = 248 qt., + 6 = 254 qt. 254 × 2 = 508 pt., + 1 = 509 pt.

    Read the rule:

    Multiply the highest denomination given, by that number of the next lower which makes a unit of the higher.

    Add to the product the number, if any, of the lower denomination.

  5. Up: divide

    Now go back: 509 pt. ÷ 2 = 254 qt., 1 pt. left. 254 ÷ 8 = 31 pk., 6 qt. left. 31 ÷ 4 = 7 bu., 3 pk. left. So 7 bu. 3 pk. 6 qt. 1 pt.

    The last quotient, with the several remainders, if any, annexed, will be the answer.

    SayGoing down and going up prove each other.

  6. Independent practice

    Your child does problems 5 to 11, such as:

    Reduce 4 bu. 2 pk. 1 qt. to pints.

    Answers are printed; prove one by reducing back.

  7. Wrap-up

    Mental: pecks in 3 bushels? (12.) Quarts in a peck and a half? (12.)

Answers to the book's problems

Teacher's questions: 1. 4, 8, 12, 16, 20 pints. 2. 24, 40, 56, 72 quarts. 3. 36, 44, 52, 60, 68, 76 pecks. 4. 320, 384, 448, 576, 800, 1792 quarts. 5. 2, 3, 4, 5, 6, 8 pecks. 6. 1, 2, 3 bushels. 7. 64, 128, 320 pints.

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

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