Jan. 10.] THE NEW ZEALAND GAZETTE. 21

3. Compound Rules.—The four rules applied to calculations involving sums of money not exceeding £100 (farthings excluded in all examples and halfpence excluded when the sum of money contains pounds). Multipliers and divisors not to exceed 12. Reduction of pounds to shillings and pence, and vice versa. Extension of practical exercises in handling money as in shopping transactions, no sum greater than £1 being used. Short methods of calculation applied to simple household accounts—e.g., easy examples of the dozen and the score rules, easy aliquot parts, half-crowns table.

4. Fractions.—Halves, thirds, quarters, eighths, tenths, twelfths, and twentieths to be known concretely, and applied to examples involving not more than one denomination, as well as to single objects—e.g., ⅜ of £16, but not ⅜ of £17 or ⅜ of £16 10s.. Very easy practical exercises in addition and subtraction: e.g., ½ + ¼, 1 — ¾, ⅞ — ½.

5. Measures.—
   (a) Length: Relative values of mile and chain; chain and yard.
   (b) Weight: Relative values of ton and hundredweight; pound and ounce.
   (c) Time: Relative values of year and calendar months; week and day; day and hour; hour and minute.
   (d) Capacity: Relative values of gallon, quart, pint.

All the above to be learnt as far as possible from actual measurement. Not more than two denominations to be used in any example. Easy exercises in judging distance, weight, and capacity.

6. Mensuration.—Construction of squares and rectangles from definite measurements. Graphical method of measuring areas of these; only whole numbers to be used.

7. Problems.—To be confined to two processes in simple rules, and one process in compound rules, weights, and measures.

STANDARD IV.

Exercises to secure the maximum degree of mechanical accuracy should still be given, but it should be possible in this class to give greater attention to practical and applied arithmetic. At least one-third of the time should be devoted to practical and mental arithmetic. Pupils should be taught to set out their written work neatly and methodically. They should also be able to make an oral statement of processes employed in mental and written arithmetic.

1. Numeration and notation to 1,000,000.

2. Simple rules.—
   (a) Continued revision of all tables and practice in exercises designed to secure mechanical accuracy in straightforward calculations.
   (b) Addition: Limited to three columns of eight figures, four columns of six figures, and five columns of five figures.
   (c) Subtraction: Numbers not to exceed 1,000,000.
   (d) Multiplication: Multipliers not to exceed three figures and product not to exceed 1,000,000.
   (e) Division: Divisors not to exceed three figures, except in the case of the three numbers 1760, 2240, 4840: Dividend not to exceed 1,000,000.

3. Compound Rules.—The four rules to be extended, the largest sum in any example not to exceed £1,000 (farthings excluded in all examples, halfpence excluded when the sum of money contains pounds). Long multiplication and division by numbers not greater than 99. Only examples likely to be found in common use to be given. Easy household accounts; short methods to be used where applicable. Simple practice to be taught only as a quick substitute for multiplication: involved and unpractical examples to be excluded.

4. Fractions.—Meaning of proper fractions with denominators—
   (a) 2, 4, 8, 16.
   (b) 3, 6, 12.
   (c) 5, 10, 20.

The relationships in the several groups (e.g., ²⁄₄ = ⁸⁄₁₆) to be learned by practical work. Addition and subtraction are to be confined to two fractions in any one of the groups (a), (b), (c) above: e.g., ¾ + ⅝ or ⅖ + ³⁄₁₀, not ⅝ + ³⁄₁₀. Multiplication of a whole number by a proper fraction, and vice versa. Division to be excluded.

5. Decimals.—The decimals 0·1 to 0·9 to be taught practically by the measurement and the setting-out of lines in inches and tenths, and to be known as equivalents of vulgar fractions with denominator 10. Practice