Ray's New Intellectual Arithmetic · Lesson VIII · Unit 1: Adding and subtracting in your head

8. Subtraction stories: how much more, how much gained

Goal: Your child solves “how much more”, gain and loss, and missing-number problems by subtraction.

⏱ 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-five problems on difference, gain and loss, with two model solutions, then abstract ones such as “The greater of two numbers is 12, and their difference is 5: what is the less?”

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

    SayA man bought a horse for 19 dollars and sold it for 27. He gained 8 dollars, because 27 dollars less 19 dollars are 8 dollars.

    Gain is always the selling price less the cost.

  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 boy paid 9 cents for a slate worth 7 cents: how much more did he pay than it was worth?

    A man bought a horse for 19 dollars and sold it for 27: how much did he gain?

    The greater of two numbers is 12, and their difference is 5: what is the less?

  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) 2 cents. 2) $4. 3) 5 cents. 4) 9 cents. 5) 6 cents. 6) 4. 7) 6 miles. 9) 5. 10) $8. 11) $8. 14) 4 cents. 15) 20. 16) 50 barrels. 18) 24 years. 19) 35 cents. 20) 18. 21) 28. 22) 10. 23) 20. 24) 7. 25) 13.

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