Improved Apparatus for use in Teaching Arithmetic.
Year: 1891

page_text: Date of Application, 20th Mar., 1891
Complete Specification Left, 19th Dec., 1891-Accepted, 19th Mar., 1892
PROVISIONAL SPECIFICATION.
Improved Apparatus for use in Teaching Arithmetic.
I CHARLES HENRY BRAY Middle Class School Coventry Trained Certificated
Teacher, Professor of Chemistry do hereby declare the nature of this invention to
be as follows:-
The "New Code" (1890-1), Instructions to Inspectors, par. 25, requires that
pupils be tested in rapid addition of columns both of figures and of pounds shillings
and pence.
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22
"
tots
"
"
con-
This throws upon the teacher the necessity for an enormous variety of "tots
ranging from "tots containing few rows of figures or amounts, to
taining many such rows. To set these "tots in the usual way (i.e. by writing
them upon the blackboard with chalk), takes up an enormous amount of time, and
as this is mere mechanical work, one object of my invention is to save this time.
Again, tots" having been set in this (the usual) way there is the further loss
of teachers time in getting at the answers to them; either by reckoning up the
suns, or by comparing different pupils' "totals" till some are found to agree (very
often a long task, and sometimes an impossible or fruitless task on account of
copying), or by referring to a separate book of answers, which, from its complexity
arising from the great number & variety of "tots" required causes often not less
waste of time than either of the preceding methods, and sometimes more than both,
"whose auswers
taking into account the extra time required in copying the "tots
are obtainable from an answer book. A second object of my invention is to obviate
this waste of time.
:
"
Further it is very evident that the pupils though starting together to learn
rapid addition will progress at very different rates: so that the more apt pupils
will very soon get far ahead of the others, and will require more difficult "tots
whilst the slower learners will require to be kept still at the casier kind with which
all had to commence. This renders it necessary for the teacher to place before
his class two " tots
at a time, differing in degrees of difficulty: hence the demand
upon his time for mere mechanical work is doubled & when his class requires,
(as it soon will) to be worked in three groups, that demand becomes a three-fold
one and so on for each additional group, till the teacher finds himself giving, of
necessity, the whole or nearly the whole of his time and attention to mere
mechanical work. A third object of my invention is to minimize, & at minimun
cost, the loss of time arising from the necessary grouping of the pupils.
=
Having displayed the main objects I had in view, I now proceed to show how I
attain those objects, among others, by my said invention.
I have printed on either or both sides of strips of cardboard, cartridge or other
suitable paper or material, the different numbers and amounts to be used in the
various "tots." These strips string lace or lash together into lengths," and
in such a manner that the long edges move freely upon each other as though
loosely hinged together: taking different numbers of strips" to form different
lengths according to the degrees of difficulty in the "tots required by the
different groups of learners.
"
When required for use the ends of these lengths severally, are temporarily joined
(tied) together either way; any two "strips" of a "length" are placed back to back,
and the whole of that length"hung upon the blackboard by a stout pin or pen
thrust through the middle contiguous lacing holes of these two strips-and the
class or group has a .. tot ready set up. The teacher glances below the cord or
lacing at the right hand end of the bottom "strip" (or any convenient place upon

page_text: the "strips
used in setting up the "tot," determined upon) and there is the
answer, but concealed from the pupils.
To set another "tot" for another group he hangs up another of the series of
"lengths" in the same manner, and finds the answer to it ready for him as before,
but out of the ken of the scholars.
"tot
"
"
To change any
for any group for another of corresponding difficulty,
any two other "strips "of the " length being used for that group are placed
back to back; the length hung up again as above, and the teacher finds the answer
to hand again, and as before.
Should more "tots." be required than those produced by the "lengths" having
their ends severally temporarily fastened (tied) together as above, the ends of
any "length" may be unloosed, and then tied the reverse way: (and so on till all
the lengths have been reversed), and a fresh set of "tots," with accompanying
answers available for the teacher only, is ready for use.
I have spoken only of "tots:" but of course I wish it to be understood that 1
may use my invention for instantaneous sum setting and changing, with accom-
panying answers as above, whenever and wherever applicable.
April 5th 1891.
CHARLES HENRY BRAY.
COMPLETE SPECIFICATION.
Improved Apparatus for use in Teaching Arithmetic.
I CHARLES HENRY BRAY Middle Class School, Coventry, Trained Certificated
Teacher do hereby declare the nature of this invention and in what manner the
same is to be performed, to be particularly described and ascertained in and by
the following statement :-
I print or otherwise fashion upon each or either side of convenient cards Fig. I
(such as the "three-hundred " Jacquard card) strips of cardboard, cartridge, or
other suitable paper or material, the different numbers and amounts to be used in
the various "tots." These strips I string lace or lash together into lengths
Fig. I-II, and in such a manner that the long edges of adjacent cards are
kept parallel with, and very near to each other by the lacing cord or tape passing
between them; whilst the cards themselves are free to move backwards and for-
wards as though loosely hinged together, as they in reality are by the lacing
cords Figs. Il to VI. The method of lacing commonly adopted for cards to be
used upon the Jacquard machines answers very well Fig. IV, but I may use any
modification of this method, as I do when using only one hole at each end Fig. III
(or elsewhere Fig. V) of the cards (two being usual) or when 1 dispense altogether
with lacing holes in any part of the cards-the middle generally Fig. III, but not
invariably Fig. XII-and use the interstices between the adjacent cards instead―
this latter method having the advantage of admitting between each card and the
lacing cord an additional card Fig. VII & Fig. XI a, bearing the title" & so
forth of the apparatus, and the symbols £ s. d. &c., &c., Fig. VII when compound
numbers are used. The end cards are then laced together the ends of the lacing
cords tied securely Figs. IV V VI (being the cards in Figs. III & III thus made
into cycles) and, when required for the purpose of tying and untying as explained
below, are left sufficiently long for that purpose. This gives a cycle of numbers
or amounts ready for fot" setting, Fig Xu, or X b. the tots being all of one
length, and suitable for one stage of a pupil's progress. Greater and lesser cycle-
for setting longer or shorter "tots are formed by lacing together a greater
Fig. Xor lesser Fig. X, number of cards.
77
"
To set a " tot one of these cycles has merely to be hung up in front of a class
or group and the method of hanging is immaterial, preference being given to the
following (1) Two consecutive cards are placed back to back and a stout pin
or such like Fig IV a. is thrust into the blackboard through the top middle lacing

page_text: holes of these two cards Fig. IV b. (2) A ring is inserted during the lacing
between the top of each card and the middle lacing cord. (3) A third method
is similar to the second: a separate hook Fig. VI a. being used to act at the
points in the cords suitable for the rings Fig. VI b. (4) A fourth method is the
usual one of hanging the cycle upon a wire like a sheet upon a line, and suspending
the whole by a cord attached to each end of the wire the ends being turned up
Fig. Va, and then crooked for the purpose of securing the cord Fig. V. A
tot having been set, the teacher glances below or near the cord or lacing at the
end of the bottom card Fig. X a, or any other convenient selected place upon the
cards, and there is the answer concealed from the pupil, or too small to be legible
by him.
To change any tot for another of the same length, according as a teacher has
adopted one or other of the typical methods of hanging, he-either (1) places
any other pair of consecutive cards of the cycle back to back, and uses the pin
or such like as before, (2) or, he hangs up the cycle by any other of the rings, or,
(3) he hangs up the cycle by the hook thrust beneath another part of the middle
lacing cord, as though it were one of the rings, or, (4) he raises the top front card
but one till its upper edge is just above the wire, and the cycle drops into the
required position. Should more tots he required than those produced by the cycles
tied as above, the ends of the cords may be untied as previously indicated, and
fresh cycles made up by tying the cards the reverse way when as many more
tots will be at hand, with accompanying answers available for the teacher only,
as have already been used.
I have spoken only of "tots for convenience; but of course I wish it to be
understood that I may use my invention for instantaneous sum setting and
changing, with accompanying answers wherever the invention fulfils its purpose,
wherever and whenever applicable.
For instance, and as better ascertaining the nature of my invention:
:-
1. A teacher desires to use my invention for the purpose of setting and changing,
instantaneously, subtraction sums. I select two cycles, Fig. XI 6 & c one con-
taining greater, the other lesser numbers or amounts. I couple the two by any
ordinary contrivance Figs. XI d, X d, XII d that allows each cycle to work
independently of the other as it would work alone, placing the cycle of minuends
Fig. Xabove the cycle of subtrahends Fig. XI c, with a slight even interval
between them Fig. XI, e and a large number of subtraction sums is at hand, a
minuend and a subtrahend respectively appearing immediately above and below
the interval, however each or either of the cycles may be turned about. When
the answers are required, preference is given to one of the following methods :-
(1) The answers are printed separately, preferably on the back of the adjustable
"titlecard. Each card in the cycle bears an index letter, (or No.). The
answers are so arranged that the index letter (or No.) on the card of the upper
cycle falling in a determined upon position (say top or bottom) taken in conjunction
with that upon the card of the lower cycle falling also in a position fore-determined
upon, shall be the index to the answer, or, (2), for the cycle of numbers (or
amounts) multiples only of some number (or amount) are used Fig. XI. A
number indicating its magnitude accompanies each multiple Fig. XI/g, h. The
difference between the index Nos. on the two cards used for the sum gives the No.
of the answer Fig. XI (10-19). This latter method has the additional
advantage of providing one piece of apparatus for both subtraction, and addition
sums of any length; since whatever part of the cycles may be cut off as may
readily and clearly be done by affixing the "title card at will Fig. XI, the
No. of the answer of the sum of the multiples on that part will always be the
sum of the index Nos. on the same part. Fig. XI (10 + 5 + 6 + 7 = 28; or,
2+3+1+10 + + 6 + 7 = = 34).
(2) Should such a number of tots be required as to ensure no tot being gone
over twice, or should a large number of unusually long tots for exceedingly rapid
work by unusually advanced pupils be required, two cycles would again be coupled

page_text: ether so that each could be worked as if hung alone Fig. Xa & b: any No. of
ots" of any conceivable length would be provided, each cycle giving the total
the part of the tot set by itself Fig. X c, Fig. Xe (as it would when used
ne), and the total of the whole extended tot would be obtainable merely by
ling together the totals of the two parts Fig. Xe &e (c++) given as they
uld be by the cycles used alone.
(3) Trained teachers early recognise the necessity of dividing a class into what
technically called A's & B's, to prevent copying. The invention is applicable
three forms—
(a) The cards are made long enough each to carry two Fig. XI (or more
if required) numbers or amounts, so that each cycle sets two (or more if
required) tots at a time (b & c). The cycles are made to set one sum only
at a time Fig X a, or b; when :-
(b) Two can be hung up side by side, separately, or,
(c) Two are coupled by either hanging side by side upon the wire supported
as shown above, or by one being coupled to the other and hanging below
it, the latter form being more eyeable when A's & B's are working sums of
unequal lengths Fig. Xa & . The form of coupling is immaterial. I
make a serviceable one as follows:-Take a piece of iron wire somewhat
longer than twice the length of the cards, and grip it in a vice horizontally.
Turn about half an inch of the right hand end sharply round upon the
next half inch bending it forwards & keeping it horizontal. This forms a
About
crook into which eventually the other end of the wire easily fits.
one inch from the bend of the crook make a right angle by turning the
crooked end downwards; & at a slightly greater distance from this right
angle than the width of the cards form another right angle by turning the
other end of the wire into the vertical position. At somewhat less than
an inch from this second right angle form a third by sharply bending the
free part of wire upwards, thereby bringing the end of it up to the crook.
The coupling is ready for use Fig. VIII (front view), Fig. IX (end view).
Having now particularly described & ascertained the nature of my said inven-
n, and in what manner the same is to be performed, I declare that what I
im is:-
In apparatus for use in teaching arithmetic the construction of cycles of numbers
so forth, with or without accompanying answers or index letters or Nos. in
ace of them, or an adjustable card bearing "title," directions, &c. &c., separately
conjoined, substantially as herein before described.
Dated this 18th day of December 1891.