Ray's New Intellectual Arithmetic · Lesson XXXIII · Unit 4: Working with fractions

33. Multiplying a fraction by a whole number

Goal: Your child multiplies a fraction by a whole number and changes the answer to a mixed number.

⏱ 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

Eighteen problems on oats for horses, pineapple and chestnuts, then “What are 6 times ¾?” and so on. The model: 3 times ½ an orange is 3/2, or 1½ oranges.

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

    Say3 times one-half is three-halves, which is 1½.

    Only the numerator is multiplied: 4 times 2/3 is 8/3, or 2⅔.

  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:

    If a horse eats ½ a peck of oats a day, how much in 3 days?

    What are 6 times ¾?

    What are 7 times 2/5?

  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) 1½ oranges.

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