Ray's New Intellectual Arithmetic · Lesson XXII · Unit 3: What fractions are
22. A fraction of a number
Goal: Your child finds a fraction of a number by finding one part first, and goes from many to one to some.
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
About twenty-three problems. Model solutions: a third of 9 is 3, so two-thirds of 9 are 2 times 3, or 6; and if 3 oranges are worth 15 cents, 1 is worth a third of 15, or 5 cents, so 2 are worth 10 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
SayTo find two-thirds of 9, first find one-third: 9 divided into 3 equal parts is 3. Two-thirds are 2 times 3, which are 6.
Always find one part first.
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 yard of tape is worth 2 cents, what is half a yard worth?
What are two-thirds of 9?
If 5 barrels of flour sell for $30, what would 3 barrels sell for?
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) 1 cent. 3) $4. 8) 6. 17) 2 cents. 18) $3. 19) 10 cents. 20) $18. 21) 50 cents.
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 ↗.