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

46. Review: the big mixed set

Goal: Your child works through a long review of everything so far, including chases, cisterns and work together.

⏱ About 25 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

About ninety-three problems over six pages: fractions, buying and selling, work, overtaking (a hound and a hare), and cisterns with two pipes.

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

    Pick one classic to model.

    SayA hare is 90 yards ahead. The hound runs 10 feet a second, the hare 7, so the hound gains 3 feet a second. 90 yards are 270 feet, and 3 is contained in 270 ninety times. So 90 seconds.

  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:

    A hare is 90 yards ahead of a hound; the hound runs 10 feet a second, the hare 7: when will the hound catch it?

    A cistern holds 24 gallons; one pipe fills 8 gallons an hour, another empties 5: how long to fill it?

    A can do a piece of work in 2 days, B in 4 and C in 6: how long together?

  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.

Tip

This lesson is a few weeks of work. Do ten problems at a time.

Answers to the book's problems

1) $20; $36. 3) 8 oranges. 4) 16 times. 31) $3.75. 33) $1.50 a day. 35) 20 lemons. 56) $12; $4 a day. 62) 32 yd. 63) 12 days. 64) $48. 65) 14 days. 66) 20 days. 80) 8 days. 81) 90 seconds; the hound runs 900 ft, the hare 630 ft. 82) 20 rods. 84) 8 hr. 85) 12 hr. 90) 1 1/11 days.

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