Ray's New Intellectual Arithmetic · Lesson XXXVI · Unit 4: Working with fractions
36. Paying with something else (barter)
Goal: Your child solves trading problems with fractions and does “how many times” drills.
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
Twenty-three problems. Models: 5 boxes of raisins at $4 come to $24, which pays for 4 barrels of flour at $6; and cloth worth $14 pays for 2 hundredweight of cheese at $7.
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
SayFirst find what the first goods are worth: 5 boxes at $4 are $24. Then see how many of the second thing that buys: $6 is contained in $24 four times. So 4 barrels.
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 barrels of flour at $6 will pay for 5 boxes of raisins at $4?
Cloth worth $14 pays for cheese at $7 a hundredweight: how much cheese?
How many times is ⅔ contained in 4?
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) 4 barrels. 16) 2 hundredweight.
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 ↗.