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

1. Adding small numbers, and saying why

Goal: Your child adds small numbers in story problems and explains each answer: “Because 3 and 2 are 5.”

⏱ 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-six short addition stories about apples, cents and marbles. The first answers are modelled as “Ans. 2. Why? Because 1 and 1 are 2.” The lesson ends with the definitions of addition, sum, + (plus) and = (equals).

The lesson, step by step

  1. Warm up

    Ask a few facts to 10 aloud: 4 and 3, 5 and 5, 6 and 2.

  2. Show the reasoning

    Read the first problem aloud and answer it the book's way.

    SayJames had 1 apple and his brother gave him 1 more. He had 2 apples. Why? Because 1 and 1 are 2.

    This question-answer-reason pattern is the heart of the whole book. Practise it on the first three problems together.

  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:

    James had 1 apple, and his brother gave him 1 more: how many did he then have?

    Ida had 4 cents; her mother gave her 3 cents, then 1 cent more: how many had she?

    A lady paid 1 dollar for gloves, 3 for a shawl and 3 for a dress: how much did she spend?

  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

If your child has finished Ray's New Primary Arithmetic, the book says you may start at Lesson IV. Lessons I to III are still a gentle way to learn the “Why? Because…” habit.

Answers to the book's problems

1) 2. 2) 3. 3) 4. 4) 5. 5) 4. 6) 5. 7) 6. 8) 6. 9) 6. 10) 7. 12) 8. 13) 8. 14) 9. 15) 8. 16) 10. 17) 10. 18) $9. 19) 10. 20) $7. 21) 11. 22) 10 lb. 23) 10. 24) 7. 25) 10. 26) 8.

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