Ray's New Intellectual Arithmetic · Lesson LXI · Unit 7: Reasoning puzzles, ratio and proportion
61. Ratio with three or more parts
Goal: Your child divides a quantity into three or more parts in a given ratio.
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
Eighteen problems, such as dividing 60 in the ratio 3, 4 and 5, and horses, cows and sheep on a farm.
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
Say3 and 4 and 5 are 12 parts. 60 divided into 12 parts is 5 each. So the parts are 15, 20 and 25.
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:
Divide 60 into three parts in the ratio of 3, 4 and 5.
A farm has 60 horses, cows and sheep: 3 cows to each horse and 2 sheep to each cow: how many of each?
Divide 35 cherries so Agnes has twice as many as Emma and Sarah twice as many as Agnes.
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) 10 and 12. 9) 15, 20, 25. 10) 7, 14, 21, 28. 12) 9, 12, 15 peaches. 15) A 20 cents, B 15, C 10. 16) 6 horses, 18 cows, 36 sheep. 17) 7, 14, 21. 18) Emma 5, Agnes 10, Sarah 20.
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 ↗.