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

2. Adding drills and counting on

Goal: Your child adds chains of small numbers aloud, counts on by 2s and 3s, and finds pairs that make 10 and 12.

⏱ 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

Quick drills (“One and one are two”; “Two and four are six; six and one are seven”), counting by 2s and 3s, then word problems. One model solution adds dozens of eggs: 8 dozen and 4 dozen are 12 dozen; 12 dozen and 3 dozen are 15 dozen.

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

    Show how to add a chain one step at a time.

    SayTwo and four are six; six and one are seven.

    Your child says every middle total aloud. Then show that dozens add like anything else: 8 dozen and 4 dozen are 12 dozen.

  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:

    I have 8 dozen eggs in one basket, 4 dozen in another and 3 dozen in another: how many in all?

    Oliver has 4 cents in one hand, 3 in the other and 4 in his pocket: how many cents has he?

    A girl bought tape for 3 cents and pins for 5 cents and got 2 cents change: how much had she at first?

  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

13) 11. 14) 11. 15) 15 dozen. 16) 10 cents. 17) 10. 19) 10 cents. 20) $11. 21) 11 cents. 22) 16 yd. 23) 18 cents. 25) 21.

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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