Ray's New Practical Arithmetic · Arts. 246–247 · Unit 25: Mensuration
115. Lines, angles, figures; area of a parallelogram
Goal: Your child names the kinds of angles, triangles, quadrilaterals and circle parts, and finds the area of any parallelogram.
You'll need
- Paper and pencil, or a slate or small whiteboard
- A sheet of paper and scissors
- A ruler
What's in the book
Pages 316–318 give the definitions of Measurement of Surfaces (Art. 246), with small figures. Page 318 gives the parallelogram rule (Art. 247), and page 319 has problems 1–11 with printed answers.
The lesson, step by step
Warm-up
Walk around the room and find a right angle, an acute angle, a rectangle and a circle.
The words
Read a few aloud and match them to the book's figures:
When two straight lines are perpendicular to each other, they form a right angle.
An acute angle is less than a right angle.
When two straight lines are everywhere equally distant they are parallel.
A parallelogram is a quadrilateral with its opposite sides equal and parallel.
The radius of a circle is a straight line drawn from the center to the circumference; it is half the diameter.
Note Ray's old names: a "trapezium" has no parallel sides and a "trapezoid" has two.
The rule
Multiply the base by the altitude.
The book explains: a slanted parallelogram has the same area as a rectangle with the same base and height. Show it by cutting a triangle off one end of a paper parallelogram and moving it to the other end.
Guided practice
Do these together:
How many square feet in a floor 17 ft. long and 15 ft. wide?
How many acres in a square field, each side of which is 65 rd.?
(160 square rods = 1 acre.)
Independent practice and check
Your child works problems 2 and 4–13 on pages 319–320. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.
Mental-math wrap-up
Aloud: area of 6 by 8; base 10, altitude 4; a square of side 9.