2510
THE NEW ZEALAND GAZETTE
[No. 82

pence to pence, or vice versa. A beginning will be made with the compound rules by teaching addition and subtraction of money in easy sums, excluding farthings, together with very easy oral examples involving multiplication and division of money. The multiplication and division tables as far as 12 times 12 to be known, money tables, and also, in long measure, yards, feet, and inches, which should be taught from actual measurements made by the children.

Standard III.

The numbers up to 1,000,000. The composition of these numbers should be known in a general way, e.g., 10,000 would be known as 10 thousands, or as 100 hundreds, or as 1,000 tens; 20,000 as 20 thousands, &c., and so on up to 1,000,000, which would be known as 1,000 thousands. Simple and compound rules (money), multipliers and divisors not to exceed 99; multipliers, if over 12, to be reducible to factors not over 12; sums of money in the questions and answers not to exceed £1,000. Work of Standard II applied to higher numbers. In teaching simple multiplication by multipliers higher than 12, the first exercises should involve multiplication by 20, 30, …90, and the difference should be explained (in a concrete manner at first) between the results thus obtained and those obtained by multiplying by 2, 3, …9. Next should be taught multiplication by numbers 13…99, e.g., by 86, i.e., 80 times + 6 times.

The first exercises in long division should be as simple as possible, e.g., 26 ÷ 13, 2,600 ÷ 13, and so on.

Simple multiplication by factors should precede compound multiplication by factors. Revision of tables of former standards; and, in long measure, the chain and mile; also, in measures of weight, the ounce, pound, quarter, hundredweight, and ton.

Standard IV.

Long multiplication of money; reduction of money and of the weights and measures named below; simple practice, and the making out of easy bills of accounts and receipts such as occur in ordinary retail transactions. Tables of money, avoirdupois weight, long measure (inches, feet, yards, chains, miles), square measure (inches, feet, yards, chains, acres), capacity (pint, quart, gallon, peck, bushel, quarter), time, angular measure (degree only). Mensuration—to find the area of a square and of a rectangle with given sides expressed in one denomination only (as in inches, feet, or yards, but not in feet and inches, &c.): this should be demonstrated by making each child draw and cut out a square and a rectangle with a given integral number of inches in each side, and then fold or rule the paper so as to show the number of square inches. The principle may be extended to square feet on the floor of the classroom, and to square yards in the playground. The meaning of proper fractions, with denominator not greater than 20, is to be known and applied to concrete examples in a simple manner, e.g., ⅗ of £4 10s., ⅕ to be found first, and ⅗ to be shown to be 3 times the result.

Mental arithmetic and problems to be adapted to this stage of progress.

Standard V.

Simple proportion by the unitary method, the steps of which may be curtailed when the children become accustomed to the thought involved in the process. Practice and harder bills of accounts; the easier cases of vulgar fractions (excluding complex fractions). The meaning of ·1, ·2, &c., is to be known as ¹⁄₁₀, ²⁄₁₀, &c.; that of ·01, ·02, &c., as ¹⁄₁₀₀, ²⁄₁₀₀, &c.; of ·11, ·12…, ·49…, ·95…, ·99, to be known as ¹¹⁄₁₀₀ and ¹¹⁄₁₀₀, or ¹¹⁄₁₀₀, &c.; that of ·001, ·002, &c., as ¹⁄₁₀₀₀, ²⁄₁₀₀₀, &c., and applied to concrete examples in a simple manner, e.g., the value of ·1, ·15, ·2, 25…, ·999 of a pound sterling or of a ton should be understood. The pupils should be able to express money and common weights and measures in decimal form to three or four places of decimals, and to work very easy sums thereby, multipliers and divisors in all cases being integers. Mensuration of walls and floors and other simple rectangular areas as far as possible from actual measurement. The relative values of the cubic foot and cubic inch, and of the cubic yard and cubic foot: these should be actually demonstrated by models made of cardboard or paper. Relative values of kilometer, meter, decimeter, centimeter, and the equivalent in yards and inches; relative value of kilogram