Ray's New Intellectual Arithmetic · Lesson LXIV · Unit 8: Percentage and interest
64. Per cent: what it means
Goal: Your child knows that per cent means hundredths and changes common per cents to 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
The start of percentage: per cent as so many in each hundred, with problems ending in changing per cents to fractions (37½% is ⅜; 66⅔% is ⅔).
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
SayPer cent means “for each hundred”. 25 per cent is 25 hundredths, which is one-fourth.
Use the table of parts of 100 from Lesson XLIV: you already know 12½ is ⅛ of 100, so 12½% is ⅛.
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:
What fraction is 25 per cent? 50 per cent? 75 per cent?
What fraction is 37½ per cent?
What fraction is 66⅔ per cent?
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
17–20) 3/8, 9/16, 2/3, 7/8.
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 ↗.