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

11. Mixed adding and subtracting stories

Goal: Your child solves longer stories that mix adding and subtracting, including gain and loss.

⏱ 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-one word problems, with a model for one that takes a difference from a sum: 19 and 10 are 29; 17 less 10 is 7; 29 less 7 is 22.

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

    SayFrom the sum of 19 and 10, take the difference between 17 and 10. The sum is 29; the difference is 7; 29 less 7 is 22.

    Find each part first, then combine them.

  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:

    From the sum of 19 and 10, take the difference between 17 and 10: what is left?

    A jeweler bought a watch for $40, a chain for $15 and a key for $3, and sold them all for $63: what did he gain?

    Two numbers differ by 17; the greater is 85: 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) 9 cents. 2) 8 gallons. 3) 11. 4) 22. 5) $15. 6) $17. 7) 2 less. 8) $15. 9) 16. 10) $5. 11) 10 sheep. 12) $3. 14) 5. 15) 38. 16) $20. 17) $80. 18) 68. 19) $40. 20) 8 gallons. 21) 8 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