Ray's New Intellectual Arithmetic · Lesson XXXVII · Unit 4: Working with fractions
37. A fraction of a fraction
Goal: Your child finds a fraction of a fraction, such as ⅔ of ¾.
You'll need
- Squared paper and colored pencils
- 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-seven problems: halving part of an orange, “what single fraction equals ⅔ of ¾”, and shares of a ship or bank stock. The model takes a unit fraction of the fraction first, then multiplies.
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
SayOne-third of three-fourths is one-fourth, so two-thirds of three-fourths are 2 times one-fourth, or two-fourths, which is one-half.
Draw it: shade ¾ of a bar, then shade ⅔ of the shaded part.
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:
Daniel divides part of a melon equally between his brother and sister: what part of the whole does each get?
What single fraction equals ⅔ of ¾?
A person owning part of a ship sold part of his share: what part of the ship did he sell?
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.