Ray's New Practical Arithmetic · Arts. 67–69 · Unit 7: Reduction of Compound Numbers
36. Square measure and the area of a rectangle
Goal: Your child finds the area of a rectangle by multiplying length by breadth, finds a missing side by dividing, and reduces square measures.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Square measure: square inches, feet and yards, rods, acres and square miles, with reduction problems; then the rule for the area of a rectangle and its reverse, with carpet, floor and field problems.
The lesson, step by step
Warm-up
Mental: 4 × 3? 16 × 12? 5 × 4? Then ask: How many squares on a checkerboard 8 by 8?
Square units
Read:
Square Measure is used in measuring any thing which has both length and breadth
Draw a square foot on paper (12 inches each way) and rule it into inches. Count a row (12) and the rows (12): 144 square inches.
The rule
Read:
A Rectangle is a figure having four sides and four right angles.
Multiply the length by the breadth; the product will be the area.
Work:
In a floor 16 feet long and 12 feet wide, how many square feet?
(192 square feet.)
Backward
Read:
If the area of a rectangle be divided by either side, the quotient will be the other side.
Work:
A floor containing 132 square feet, is 11 feet wide: what is its length?
(12 ft.)
Guided practice
Together:
How many square yards of carpeting will cover a room 5 yards long and 4 yards wide?
Then measure a real room or table and find its area.
Independent practice
Your child does reduction problems 1 to 10 and area problems 3 to 8, then the four "missing side" problems.
Check and wrap-up
Most answers are printed. Note for you: an acre is 160 square rods (about the size of a football field without the end zones).
Answers to the book's problems
Reduction problem 6: 960 sq. rd. = 6 A. Area problem 6 (field 35 rods by 32 rods): 1120 sq. rd. = 7 A.
Worked out for this site from the scan. If a number in your copy differs, trust the book.