Ray's New Intellectual Arithmetic · Lesson XX · Unit 3: What fractions are
20. Halves, thirds and other parts of a whole
Goal: Your child knows that a unit can be cut into equal parts and finds how many halves, thirds or ninths are in several units.
You'll need
- An apple and a knife, or paper circles and scissors
- 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
Definitions with pictures in words: one-half, two-halves or the whole; thirds; fourths; up to ninths. Then problems such as how many halves in 2 to 10 apples. The model: 1 apple has 2 halves, so 2 apples have 4.
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
Cut an apple (or a paper circle) into halves, then another into thirds.
SayOne apple has 2 halves, so 3 apples have 3 times 2 halves, or 6 halves.
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 2 apples? In 5? In 10?
How many thirds in 3 units? How many fifths? Sevenths? Ninths?
In 11 apples, how many sixths, halves, fifths, ninths?
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
9) 9, 15, 21, 27. 10) 20, 40, 15. 11) 66, 22, 55, 99.
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 ↗.