APRIL 20.] THE NEW ZEALAND GAZETTE. 1069

arithmetic is, probably, that it enables the pupil to have before his eyes
the several logical steps by which a given result is obtained. It is no
doubt true that many minds cannot deal with large numbers without
some visual aid, but it is equally true that greater attention given to oral
work would produce a much greater amount of skill in dealing mentally
with comparatively large numbers than is usually found in our schools.

STANDARD II.

The numbers up to 1,000.
The composition of every number up to 1,000 should be known: e.g.
100 would be known as 10 tens, 200 as 2 hundreds or 20 tens, &c.;
340 as 3 hundreds and 4 tens, or as 34 tens, or as 10 times 34, &c.;
672 as 6 hundreds, 7 tens, and 2 ones or units, or as 67 tens and 2 units.
The composition of these numbers should be taught from the concrete,
by the use of cubes, bundles of sticks, bags of shot, &c., or by means of
diagrams. The four simple rules, multipliers and divisors being confined
to the numbers 1 to 12 and 20. The pupils should understand the meaning
of ½, ⅓ … ¹⁄₁₂, ¹⁄₂₀, applied to easy concrete examples. Reduction of pence
to shillings and pence, or of shillings and pence to pence; also of shillings
to pounds and shillings, or of pounds and shillings to shillings; but not
reduction of pounds shillings and pence to pence, or vice versâ. Com-
pound rules (money), multipliers and divisors not to exceed 12, and sums
of money in the questions and answers not to exceed £20.

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 thou-
sands, &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. It is recommended that the principle of complementary addition
should be extended to long division
Work of Standard II. applied to higher numbers.
In teaching simple multiplication by higher multipliers than 12, the
first exercise should involve multiplication by 20, 30 … 90, and the differ-
ence explained (in a concrete manner at first) between the results thus
obtained and those obtained by multiplying by 2, 3 … 9. Even after this
point is understood, frequent reference to concrete illustrations will be
desirable until the pupil begins habitually to visualise the process and
the result. For this reason also the numbers should be as small as can
be employed to illustrate the process. Then teach 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, 260 ÷ 13, 2,600 ÷ 13; and so on.
Simple multiplication by factors should precede compound multiplica-
tion by factors.

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 (excluding poles or
perches), square measure (excluding square poles or perches and roods),
capacity (pint, quart, gallon, peck, bushel, quarter), time, angular measure.
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 class-room and to square yards in the play-
ground. (See also clause 56.) 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 three times the result.
Mental arithmetic and problems to be adapted to this stage of
progress.

STANDARD V.

Simple proportion; it is recommended that this should be taught
from first principles as set forth in 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