Ray's New Intellectual Arithmetic · Lesson XXXIX · Unit 4: Working with fractions
39. Finding the whole, with fractions
Goal: Your child finds a whole when a fractional part is known, in harder stories.
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-eight problems: poles partly in earth, water and air, money left after a gift, cloth cost when part is lost, a horse priced in barrels of flour.
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
SayIf ⅖ of a pole is in the air and that part is 8 feet, then ⅕ is 4 feet, and the whole pole, 5 fifths, is 20 feet.
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:
A pole has a fraction in the earth, a fraction in the water and 8 feet in the air: how long is it?
After giving away part of his money a boy had 15 cents: how much had he?
A horse is worth some barrels of flour: find its price.
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.