Ray's New Intellectual Arithmetic · Lesson XXVIII · Unit 3: What fractions are
28. Changing a fraction to a new denominator
Goal: Your child changes fractions to equal fractions with more parts, such as halves to fourths or sixths.
You'll need
- Paper strips for folding
- 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-three problems changing halves, thirds and others to fourths, sixths, eighths and up. The model: in 1 there are 4 fourths, so in ½ there are 2 fourths.
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 4 fourths, so in one-half there are half of 4, or 2 fourths. One-half is two-fourths.
Show it by folding a paper strip.
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:
Change ½ to fourths, sixths, eighths.
Change ⅔ to sixths, ninths, twelfths.
Change ¾ to eighths and twelfths.
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.