Ray's New Higher Arithmetic · Art. 231, Examples 1–49 · Unit 13: Proportion

61. Simple proportion: practice

Goal: Your student sets up and solves many kinds of simple proportion, including inverse ones and thermometer and machine problems.

⏱ About 45 minutes · 6 steps

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You'll need

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

What's in the book

Forty-nine examples for practice with printed answers (some marked to be done mentally): pulse rates, rents, gains in trade, coffee, Fahrenheit, Centigrade and Réaumur thermometers, levers and powers, and inverse variation.

The lesson, step by step

  1. Warm-up

    Mental (starred problem style): If 4 yards cost $6, what do 10 yards cost?

  2. Guided practice

    Together:

    If a pulse beats 28 times in 16 sec., how many times does it beat in a minute?

    If a farm of 160 A. rents for $450, how much should be charged for one of 840 A?

    (105 times; $2362.50.)

  3. Independent practice

    Your student works Examples 1 to 28, writing the statement for each before multiplying. Try:

    If I gain $160.29 in 2 yr. 3 mon., what would I gain in 5 yr. 6 mon., at that rate?

    ($391.82.)

  4. Thermometers and machines

    On another day, Examples 29 to 49. The book notes that on Fahrenheit

    the freezing point of water is marked 32°, and the boiling point 212°

    and explains inverse variation:

    Inverse variation exists between two numbers when one increases as the other decreases.

  5. Check

    All answers are printed. Check one by multiplying means and extremes.

  6. Wrap-up

    Ask: Is the time to dig a ditch direct or inverse to the number of workers? (Inverse.)

Afterwards

Two or three sittings: 1–13, 14–28, 29–49.

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