Ray's New Intellectual Arithmetic · Lesson XXIV · Unit 3: What fractions are
24. Finding the whole from a part
Goal: Your child finds the whole when a fraction of it is known.
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-five problems such as “If two-thirds of a lemon is worth 6 cents, what is a lemon worth?” The model: one-third is worth 3 cents, so the whole, three-thirds, is worth 9 cents.
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
SayTwo-thirds are worth 6 cents, so one-third is worth half of 6 cents, or 3 cents. The whole lemon is three-thirds, 3 times 3 cents, or 9 cents.
Divide to get one part, then multiply to get the whole.
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 two-thirds of a lemon is worth 6 cents, what is a lemon worth?
6 is two-sevenths of what number?
A fraction of 18 is a fraction of what number? (fractions given in the book)
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) 2 cents. 3) 9 cents. 8) 21. 17) 9 cents. 19) 25.
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 ↗.