Ray's New Intellectual Arithmetic · Lesson XXXVIII · Unit 4: Working with fractions
38. Prices and amounts with fractions
Goal: Your child solves cost and quantity problems where both the price and the amount are fractions.
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
Fifteen or more problems on cider, oil and wine, a fraction times a fraction, and work done in fewer hours a day.
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 ¾ of a yard costs 6 cents, ¼ costs 2 cents, a yard costs 8 cents, and ½ a yard costs 4 cents.
Go to the unit fraction, then to the whole, then to what is asked.
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 ¾ of a yard costs 6 cents, what will ½ a yard cost?
What is ⅔ of ⅚?
If a man works part of a day, how long will a job take?
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.