Ray's New Intellectual Arithmetic · Lesson LI · Unit 6: Money, weights and measures
51. Long measure
Goal: Your child knows the table by heart and changes quantities to larger and smaller units.
You'll need
- The book page
- Real measures or coins if you have them
What's in the book
The table: 12 inches make 1 foot; 3 feet, 1 yard; 5½ yards, 1 rod; 40 rods, 1 furlong; 8 furlongs, 1 mile. Then problems that change to smaller units (multiply) and to larger units (divide).
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
SayA mile is 8 furlongs of 40 rods, so 320 rods. 16 rods are 16/320, or one-twentieth, of a mile.
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 yards are in 2 rods? In 4 rods?
Six hundred and forty rods are how many miles?
Sixteen rods are what part of a mile?
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.
Tip
Rods and furlongs are old, but furlongs are still used in horse racing.
Answers to the book's problems
1) 24 in. 2) 6, 9, 12, 15, 21, 27 ft. 3) 11, 22, 27½, 38½, 55 yd. 4) 120, 160, 200, 240, 280, 360 rd. 5) 72 fur. 6) 3 ft; 4 ft. 7) 5 yd; 7 yd. 8) 4 rd; 6 rd. 9) 2 mi. 15) 1/20. 16) 3/40. 17) 6/11.
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 ↗.