Ray's New Intellectual Arithmetic · Lesson XXVI · Unit 3: What fractions are
26. Mixed numbers into improper fractions
Goal: Your child changes a mixed number such as 3½ into halves, thirds or other parts.
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
Twelve problems of the form “How many halves in 3½? 4½?”. The model: in 1 there are 2 halves, so in 3 there are 6 halves, and with the other half, 7 halves.
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
SayIn 1 there are 2 halves, so in 3 there are 3 times 2, or 6 halves. And one more half makes 7 halves. So 3½ is 7/2.
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:
How many halves in 3½? 4½? 5½? 6½?
How many fourths in 3¾? 4¾? 5¾?
How many eighths in 2⅜?
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
2) 7, 9, 11, 13. 4) 15, 19, 23.
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 ↗.