Ray's New Intellectual Arithmetic · Lesson XV · Unit 2: Multiplying and dividing

15. Review: adding, subtracting and multiplying

Goal: Your child solves mixed stories that need two or three operations.

⏱ About 20 minutes · 5 steps

Open it at the Internet Archive ↗

You'll need

  • The book page (press “📖 Book page”, or use a printed copy)
  • Paper for jotting, though the work is meant to be done in the head

What's in the book

Thirty-eight mixed problems, such as two travellers going different speeds, and “What is 3 times the difference between 15 and the sum of 5 and 2?”

The lesson, step by step

  1. Warm up

    Ask three or four problems from the last lesson again, out of order. Your child answers and says why.

  2. Show the reasoning

    SayTwo men travel the same way, one 5 miles an hour, the other 7. Each hour they get 2 miles further apart, so in 10 hours they are 10 times 2 miles, or 20 miles, apart.

    Ask first: what changes each hour? Then multiply.

  3. Work the problems aloud

    Read each problem on the page aloud. Your child answers, then explains in a full sentence, the way the book's model solutions do. The problems go like this:

    Two men travel the same way, one 5 miles an hour, the other 7: how far apart in 10 hours?

    What is 3 times the difference between 15 and the sum of 5 and 2?

    A miller buys 10 bushels of wheat at $1, makes 2 barrels of flour and sells them at $7 a barrel: how much more did he get than he paid?

  4. Ask “Why?”

    After each answer ask “Why?” or “How do you know?” Ray's wants the reasoning said aloud, not just the number. If your child stalls, go back to the model and say the first half of the explanation together.

  5. Wrap up

    Pick the two problems that were hardest today. Tomorrow, start with those as the warm-up.

Afterwards

Do the rest of the lesson's problems over the next day or two, a few at a time. Move on when your child can explain them without help.

Answers to the book's problems

1) 15 cents. 2) 20 mi. 3) 144 mi. 4) spent $12, left $3. 5) 39 cents. 6) 4. 7) 56 shillings. 8) $38. 9) $56. 10) 36 dimes. 11) 120 horses. 12) 24. 13) 60. 14) 40. 15) 20 cents. 16) $1. 18) $8. 19) $10. 20) 21 mi. 21) 48 mi.

Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in Ray's own Key ↗.

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