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

18. Sharing, rates and the cost of one

Goal: Your child divides to find a share, a rate or the cost of one thing.

⏱ 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

Drills (“Two is contained in 12 how many times?”), then nineteen word problems. One model: a third of 12 is 4. Another: $5 is contained in $40 eight times, so 8 weeks.

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

    SayIf 12 peaches are shared equally among 3 children, each has one-third of 12 peaches, which is 4 peaches.

    Then the step backwards: if 6 men earn $84 in 7 days, the 6 men earn $12 a day, so each earns $2 a day.

  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:

    If 12 peaches are divided equally among 3 children, how many will each have?

    If 1 pipe empties a cistern in 63 hours, in how many hours will 9 such pipes empty it?

    Six men earn $84 in 7 days: how much does each earn a day?

  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

7) 4. 8) 6. 9) 10 cents. 10) 7 cents. 11) 8 weeks. 14) 6 days. 15) 8 days. 16) 7 hr. 18) $6. 19) 8 cents. 20) $9. 21) 12 trees. 22) $12 a week, $2 a day. 23) $2. 24) $12 per man, $4 a day. 25) 5 miles a day more.

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