Ray's New Intellectual Arithmetic · Lesson XXV · Unit 3: What fractions are
25. Dividing with a fraction in the answer
Goal: Your child shares things that do not divide evenly and gives the answer as a mixed number.
You'll need
- Some crackers or paper strips to share
- 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-nine problems such as sharing 3 apples between 2 boys (each gets 3/2, or 1½), and “At 4 cents a yard, how much braid for 13 cents?”
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
SayEach boy gets half of 3 apples, which is three-halves, or 1½ apples.
Share real things: 3 crackers between 2 people, 4 between 3.
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:
A grocer gave 4 oranges to 3 boys to share equally: what was each one's share?
Harriet spent 13 cents for braid at 4 cents a yard: how many yards did she buy?
When milk is 5 cents a pint, how many pints can you get for 17 cents?
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
1) 1½. 2) 1⅓ oranges. 3) 2½ cents. 4) $1⅔. 5) 1¼ cents. 13) 2½ apples. 14) 2⅓ yd. 15) 3¼ yd. 16) 3⅖ pt. 17) 3⅚ bbl. 18) 3 4/7 yd. 19) 6½.
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 ↗.