Ray's New Intellectual Arithmetic · Lesson XL · Unit 4: Working with fractions
40. A fraction of a number is how many times another?
Goal: Your child compares a fraction of one number with another number.
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
Thirty-two problems. Model: three-fourths of 24 is 18, and 18 is 2 times 9.
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
SayThree-fourths of 24 is 18. 9 is contained in 18 twice. So three-fourths of 24 is 2 times 9.
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:
Three-fourths of 24 is how many times 9?
Two-thirds of 21 is how many times 7?
Grain divided among people: how much does each get?
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
14) 2.
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 ↗.