Ray's New Practical Arithmetic · Art. 74 · Unit 7: Reduction of Compound Numbers

40. Measure problems of every kind

Goal: Your child solves story problems that need reduction and the four operations with measures.

⏱ About 35 minutes · 6 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

Twenty-seven promiscuous (mixed) examples using all the tables: prices by the pint or peck, bags, kegs, land, water weight, heartbeats and travel. Answers are printed for nearly all.

The lesson, step by step

  1. Warm-up

    Mental: pints in a bushel? (64.) Ounces in 15 pounds? (240.)

  2. Reduce first

    Read:

    What cost 2 bu. of plums, at 5 ct. a pint?

    SayThe price is per pint, so change the bushels to pints first: 2 × 64 = 128 pints; 128 × 5 = 640 cents = $6.40.

  3. Dividing measures

    Read:

    How many spikes, weighing 4 oz. each, are in a parcel weighing 15 lb. 12 oz.?

    The book's remark: reduce both quantities to the same unit, then divide. 15 lb. 12 oz. = 252 oz.; 252 ÷ 4 = 63.

  4. Guided practice

    Together:

    At 15 ct. a peck, how many bushels of apples can be bought for $3?

    If a human heart beat 70 times a minute, how many times will it beat in a day?

  5. Independent practice

    Your child does about ten problems from 3 to 27.

  6. Check and wrap-up

    Answers are printed (problem 3 below has none). Your child takes their own pulse for a minute and works out a day's heartbeats.

Answers to the book's problems

Problem 3 (3 pk. 3 qt. of barley at 3 ct. a pint): 54 pints × 3 ct. = $1.62.

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

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