Ray's New Intellectual Arithmetic · Lesson LIII · Unit 6: Money, weights and measures
53. Problems with mixed units
Goal: Your child solves costs and rates with quantities in mixed units, like 5 bushels 3 pecks.
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-one problems: corn by the bushel, fences by the rod, a steamer's distance from its time and speed.
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
Say5 bushels 3 pecks at 60 cents a bushel: 3 pecks are ¾ of a bushel, so the cost is 5¾ times 60 cents, which is $3.45.
Change to one unit first.
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:
What is the cost of 5 bu. 3 pk. of corn at 60 cents a bushel?
What will a fence 5 rd. 2 yd. 2 ft. 3 in. long cost at $12 a rod?
A steamer averages 9 miles an hour for 9 hr. 26 min. 40 sec.: how far does it go?
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) $3.45. 2) $1.85. 3) 77½ cents. 4) $66. 5) 85 mi. 6) 2 gal 3 qt 1 pt. 11) 95 cents. 12) 23 yd 1 ft. 14) 25 mi an hour. 15) 3 revolutions. 16) 13 weeks. 17) 5 lb 14 oz. 18) $18. 19) 60 cents a bushel. 20) $22.50; 15 cents a bushel.
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 ↗.