Ray's New Higher Arithmetic · Arts. 219–220, Examples 1–56 · Unit 11: Compound Denominate Numbers
54. Reduction practice
Goal: Your student reduces compound numbers both ways quickly and solves practical problems with old and metric measures.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Fifty-six examples for practice with printed answers: reductions in money, length, area, volume, weight and time, and practical problems (a cubic yard of lead, silver spoons, corn in a wagon bed, steps from Kansas City to St. Louis, shingles for a barn roof).
The lesson, step by step
Warm-up
Mental: inches in 2 yards; ounces in 3 pounds; minutes in 2½ hours.
Guided practice
Together:
Reduce 16.02 chains to miles.
Reduce $117.14 to mills.
(16.02 ÷ 80 = .20025 mi.; 117140 mills.)
More together
Do one metric and one land problem:
Reduce 169 ars to square meters.
Reduce 47.3084 sq. mi. to sq. rd.
(16900 m²; 4844380.16 sq. rd.)
Independent practice
Your student works Examples 1 to 27 today. Keep the tables open; that is not cheating, it is how clerks worked.
Practical problems
On another day, Examples 28 to 56. One begins:
A cubic yard of lead weighs 19,128 lb.
Check
All answers are printed. Some decimals are long; accept answers that agree to the places printed.
Wrap-up
Your student picks one practical problem and explains the steps aloud.
Afterwards
Two or three sittings: 1–27, 28–45, 46–56.