Ray's New Intellectual Arithmetic · Lesson XLV · Unit 5: Review

45. Review: mixed problems

Goal: Your child solves a mixed set of whole-number problems on money, rates and work.

⏱ 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

Twenty-eight problems with no model solutions: money, unit rate (“the rule of three” done by reasoning), and horses with oats and hay.

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

    There are no new methods here. Ask your child to say which method each problem needs before solving it: add, subtract, multiply, divide, or “go through one”.

  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:

    Five men bought a horse for $42; the first gave $13, the second $7, the third $5, the fourth $9: how much did the fifth give?

    A father husks 7 rows of corn while Joseph husks 3: how many will Joseph husk while his father husks 42?

    How many horses can eat in 9 days the hay that 12 horses eat in 6 days?

  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) 34 cents. 2) $43. 3) 8 cents. 4) $8. 5) $64. 6) 35 cents. 7) $19. 8) $26. 9) 9 cents. 10) $24. 11) $13. 12) $78. 13) $42; $30. 14) $16; $36. 15) $49. 16) $56. 17) 12 cents. 18) 9 apples. 19) 54 cents. 20) $49. 21) 48, 64, 80 cents. 22) 21 mi. 23) 18 rows. 24) $63. 25) 20 bu. 26) 7 weeks. 27) 10 apples. 28) 8 horses.

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 ↗.

@teddyrookbook GitHub