The only remaining branch of numerical knowledge, which
consists in an
ability to comprehend the powers of numbers, without either visible
objects or signs--is imparted as follows:
_Addition_.
One of the children is placed before the gallery, and repeats aloud,
in a kind of chaunt, the whole of the school repeating after him; One
and one are two; two and one are three; three and one are four, &c.
up
to twelve.
Two and two are four; four and two are six; six and two are eight,
&c.
to twenty-four.
Three and three are six; six and three are nine; nine and three are
twelve, &c. to thirty-six.
_Subtraction_.
One from twelve leaves eleven; one from eleven leaves ten, &c.
Two from twenty-four leave twenty-two; two from twenty-two leave
twenty, &c.
_Multiplication_.
Twice one are two; twice two are four, &c. &c. Three times
three are
nine, three times four are twelve, &c. &c.
Twelve times two are twenty-four; eleven times two are twenty-two,
&c.
&c.
Twelve times three are thirty-six; eleven times three are
thirty-three, &c. &c. until the whole of the multiplication
table is
gone through.
_Division_.
There are twelve twos in twenty-four.--There are
eleven twos in twenty-two, &c. &c.
There are twelve threes in thirty-six, &c.
There are twelve fours in forty-eight, &c. &c.
_Fractions_.
Two are the half (1/2) of four.
" " " third (1/3) of six.
" " " fourth (1/2) of eight.
" " " fifth (1/5) of ten.
" " " sixth (1/6) of twelve.
" " " seventh (1/7) of fourteen.
" " " twelfth (1/12) of twenty-four; two are the
eleventh (1/11) of twenty-two, &c. &c.
Three are the half (1/2) of six.
" " " third (1/3) of nine.
" " " fourth (1/4) of twelve.
Three are the twelfth (1/12) of thirty-six; three are
the eleventh (1/11) of thirty-three, &c. &c.
Four are the half (1/2) of eight, &c.
In twenty-three are four times five, and three-fifths
(3/5) of five; in thirty-five are four times eight, and three-eighths
(3/8) of eight.
In twenty-two are seven times three, and one-third
(1/3) of three.
In thirty-four are four times eight, and one-fourth
(1/4) of eight.
The tables subjoined are repeated by the same method, each section
being a distinct lesson. To give an idea to the reader, the boy in the
rostrum says ten shillings the half (1/2) of a pound; six shillings
and eightpence one-third (1/3) of a pound, &c.
Sixpence the half (1/2) of a shilling, &c. Always remembering,
that
whatever the boy says in the rostrum, the other children must repeat
after him, but not till the monitor has ended his sentence; and before
the monitor delivers the second sentence, he waits till the children
have concluded the first, they waiting for him, and he for them; this
prevents confusion, and is the means of enabling persons to understand
perfectly what is going on in the school.
In a book lately published, which is a compilation by two London
masters, it is stated, in the preface, that they were at a loss
for proper lessons: had they used those in existence I cannot help
thinking they were enough for the capacity of children under six years
of age.
254 ARITHMETICAL TABLES.
Numeration, Addition, Subtraction, Multiplication, Division, and Pence
Tables.
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| ADDITION AND SUBTRACTION TABLE |
| 1 & | 2 & | 3 & | 4 & | 5 & | 6 & |
| 1 are 2 | 1 are 3 | 1 are 4 | 1 are 5 | 1 are 6 | 1 are 7 |
| 2 -- 3 | 2 -- 4 | 2 -- 5 | 2 -- 6 | 2 -- 7 | 2 -- 8 |
| 3 -- 4 | 3 -- 5 | 3 -- 6 | 3 -- 7 | 3 -- 8 | 3 -- 9 |
| 4 -- 5 | 4 -- 6 | 4 -- 7 | 4 -- 8 | 4 -- 9 | 4 -- 10 |
| 5 -- 6 | 5 -- 7 | 5 -- 8 | 5 -- 9 | 5 -- 10 | 5 -- 11 |
| 6 -- 7 | 6 -- 8 | 6 -- 9 | 6 -- 10 | 6 -- 11 | 6 -- 12 |
| 7 -- 8 | 7 -- 9 | 7 -- l0 | 7 -- 11 | 7 -- 12 | 7 -- 13 |
| 8 -- 9 | 8 -- 10 | 8 -- 11 | 8 -- 12 | 8 -- 13 | 8 -- 14 |
| 9 -- 10 | 9 -- 11 | 9 -- 12 | 9 -- 13 | 9 -- 14 | 9 -- 15 |
| 10 -- 11 | 10 -- 12 | 10 -- 13 | 10 -- 14 | 10 -- 15 | 10 -- 16 |
| 11 -- l2 | 11 -- 13 | 11 -- 14 | 11 -- 15 | 11 -- 16 | 11 -- 17 |
| l2 -- 13 | 12 -- 14 | 12 -- 14 | 12 -- 16 | 12 -- 17 | l2 -- 18 |
-------------------------------------------------------------------
| 7 & | 8 & | 9 & | 10 & | 11 & | 12 & |
| 1 are 8 | 1 are 9 | 1 are 10 | 1 are 11 | 1 are 12 | 1 are 13 |
| 2 -- 9 | 2 -- 10 | 2 -- 11 | 2 -- 12 | 2 -- 13 | 2 -- 14 |
| 3 -- 10 | 3 -- 11 | 3 -- 12 | 3 -- 13 | 3 -- 14 | 3 -- 15 |
| 4 -- 11 | 4 -- 12 | 4 -- 13 | 4 -- 14 | 4 -- 15 | 4 -- 16 |
| 5 -- 12 | 5 -- 13 | 5 -- 14 | 5 -- 15 | 5 -- 16 | 5 -- 17 |
| 6 -- 13 | 6 -- 14 | 6 -- 15 | 6 -- 16 | 6 -- 17 | 6 -- 18 |
| 7 -- 14 | 7 -- 15 | 7 -- 16 | 7 -- 17 | 7 -- 18 | 7 -- 19 |
| 8 -- 15 | 8 -- 16 | 8 -- 17 | 8 -- 18 | 8 -- 19 | 8 -- 20 |
| 9 -- 16 | 9 -- 17 | 9 -- 18 | 9 -- 19 | 9 -- 20 | 9 -- 21 |
| 10 -- 17 | 10 -- 18 | 10 -- 19 | 10 -- 20 | 10 -- 21 | 10 -- 22 |
| 11 -- l8 | 11 -- 19 | 11 -- 20 | 11 -- 21 | 11 -- 22 | 11 -- 23 |
| 12 -- 19 | 12 -- 20 | 11 -- 21 | l2 -- 22 | 12 -- 23 | 12 -- 24 |
===================================================================
| MULTIPLICATION AND DIVISION TABLE. || NUMERATION TABLE. |
|------------------------------------||---------------------------|
|2--2 are 4|4--5 are 20| 6--12 are 72|| 1 Units. |
| 3 -- 6| 6 -- 24| 7-- 7 -- 49|| 21 Tens. |
| 4 -- 8| 7 -- 28| 8 -- 56|| 321 Hundreds |
| 5 -- 10| 8 -- 32| 9 -- 63|| 4,321 Thousands. |
| 6 -- 12| 9 -- 36| 10 -- 70|| 54,321 X of Thousands.|
| 7 -- 14| 10 -- 40| 11 -- 77|| 654,321 C of Thousands.|
| 8 -- 16| 11 -- 44| 12 -- 84|| 7,654,321 Millions. |
| 9 -- 18| 12 -- 48| 8-- 8 -- 64|| 87,654,321 X of Millions. |
| 10 -- 20|5--5 -- 25| 9 -- 72||987,654,321 C of Millions. |
| 11 -- 22| 6 -- 30| 10 -- 80||===========================|
| 12 -- 24| 7 -- 35| 11 -- 88|| |
|3--3 -- 9| 8 -- 40| 12 -- 96|| PENCE TABLE |
| 4 -- 12| 9 -- 45| 9-- 9 -- 81|| |
| 5 -- 15| 10 -- 50| 10 -- 90||---------------------------|
| 6 -- 18| 11 -- 55| 11 -- 99|| _d_. _s. d._|_d._ _s. d._|
| 7 -- 21| 12 -- 60| 12 -- 108|| 20 is 1 8 | 90 is 7 6 |
| 8 -- 24|6--6 -- 36|10--10 -- 100|| 30 -- 2 6 |100 -- 8 4 |
| 9 -- 27| 7 -- 42| 11 -- 110|| 40 -- 3 4 |110 -- 9 2 |
| 10 -- 30| 8 -- 48| 12 -- 120|| 50 -- 4 2 |120 --10 0 |
| 11 -- 33| 9 -- 54|11--11 -- 121|| 60 -- 5 0 |130 --10 10 |
| 12 -- 36| 10 -- 60| 12 -- 132|| 70 -- 5 10 |140 --11 8 |
|4--4 -- 16| 11 -- 66|12--12 -- 144|| 80 -- 6 8 |144 --12 0 |
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|
