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

9. Review: adding and subtracting together

Goal: Your child solves two-step stories that add and then subtract.

⏱ 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

Fourteen mixed problems, with model solutions such as: James gave away 2 marbles and 3 marbles, which are 5 marbles; then he had left 13 marbles less 5 marbles, which are 8 marbles.

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

    SayFirst, how many did he give away? 2 and 3 are 5. Then, how many were left? 13 less 5 are 8.

    Teach your child to find the middle number first and say it aloud.

  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 merchant had 40 barrels of flour; he sold 9 to one man and 21 to another: how many had he left?

    A man paid 30 dollars for a horse, spent 9 keeping him and sold him for 29: how much did he lose?

    A man owes A 5 dollars, B 6 and C 10; he has 20 in cash and goods worth 10: what is he worth after paying?

  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) 8. 2) 10. 3) 11 cents. 4) $10. 5) $9. 6) $11. 7) cost 53 cents, change 7 cents. 8) 11. 10) 16. 11) 4 sheep. 12) $7. 13) 15 cents. 14) $9.

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 ↗.

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