Ray's New Higher Arithmetic · Misc. Exercises 79–106 · Unit 29: Miscellaneous Exercises

127. Miscellaneous exercises, part 3

Goal: Your student finishes the book with harder mixed problems on profit and loss, measurement and geometry.

⏱ About 45 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

Problems 79 to 106: profit and loss, clocks, a body of militia, a tapering board, circles cut from a plate, balls in a box. Answers are printed. This is the end of the book.

The lesson, step by step

  1. Warm-up

    Ask your student to name five methods from this book they now know well.

  2. Work one together

    I sold an article at 20% gain; had it cost me $300 more, I would have lost 20%: find the cost.

    If the cost is C, the price is 1.2C, and also .8 × (C + $300). So .4C = $240, and C = $600.

  3. Guided practice

    I have an inch board 5 ft. long, 17 in. wide at one end, and 7 in. at the other: how far from the larger end must it be cut straight across, so that the solidities of the two parts shall be equal?

    Sketch the board first. Each part is a trapezoid.

  4. A puzzle

    How many inch balls can be put in a box which measures, inside, 10 in. square, and is 5 in. deep?

    Ask for a guess first. The printed answer, 568, is more than a simple 10 × 10 × 5 = 500. How could more balls fit? Think of how oranges are stacked at a grocery, each row and layer sitting in the hollows of the one below.

  5. Independent practice

    Your student picks problems that look interesting and works them, checking the printed answers.

  6. Wrap-up

    Celebrate finishing Ray's Higher Arithmetic. Ask your student which chapter was most useful and which was most surprising.

Afterwards

Several short sittings, or keep a few of these for review later.

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