Ray's New Intellectual Arithmetic · Lesson XXIII · Unit 3: What fractions are
23. What part of one number is another?
Goal: Your child says what fraction one number is of another, such as “5 is five-sevenths of 7”.
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-four problems: what part of an apple 1 cent buys at 2 cents, what part of a yard $2 buys at $3, and “What part of 7 is 5?” (modelled as 5 times one-seventh of 7, or five-sevenths).
The lesson, step by step
Warm up
Ask three or four problems from the last lesson again, out of order. Your child answers and says why.
Show the reasoning
Say1 is one-seventh of 7, so 5 is five-sevenths of 7.
In stories: at $3 a yard, $1 buys one-third of a yard, so $2 buys two-thirds of a yard.
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:
At $3 a yard, what part of a yard will $2 buy?
When clover seed is $8 a bushel, what part of a bushel can be bought for $5?
What part of 7 is 5?
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.
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) ½. 2) ⅔ yard. 9) ⅝ bushel. 10) 5/7.
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 ↗.