Improvements in and relating to Frames for Setting Addition Sums.
Year: 1891

page_text: COMPLETE SPECIFICATION.
Improvements in and relating to Frames for Setting Addition Sums.
I, LEWIS CHALICE of 89 Cambridge Street, Plymouth in the County of Devon
Certificated Master 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 :-
My invention relates to means whereby teachers in schools may be able to set a
great variety of addition sums and readily find the answer to each sum set by
means of a book of answers compiled in a manner to reduce as far as possible the
number of answers entered the teacher finding a direct answer to many of the
combinations of lines forming the sums and in other cases being required only to
make short calculations such as adding together two or more answers obtained
from the answers book or multiplying one or more such answers by a single
figure.
I make a frame as shown in the accompanying drawings in which
Figure 1 is a front elevation of a double frame exhibiting two five line addition
sums set for calculation by pupils.
Figure 2 is a sectional elevation upon the line A B in Figure 1 and
Figure 3 is an isometric view of a part of one side of a double frame or of a
part of a single frame the double frame being the equivalent of two frames.
oppositely made as regards the position of the door or cover and the openings to
the receptacles, and placed side by side.
Each side of the frame is provided with openings C in which to slide slips of
card, wood or other material upon each of which one line of an addition sum is
written printed or painted in a position to be exhibited at an opening in the front
of the frame corresponding with the said side opening.
Immediately in the rear of the side openings C1 form receptacles D each of
such receptacles being employed for keeping in store a group of the figured slips
each of such groups being lettered in a manner to identify them as belonging to
the particular receptacle in which they are to be stored. In the frame shown by
the accompanying drawing there are twenty openings for each side at which lines
of figures to form one or more sums at each side may be exhibited.
Thus sums may be set at each side of the frame varying in length from two to
twenty lines and twenty receptacles D are provided at each side of the frame each
one to contain one of twenty duplicate groups of figured slips.
The twenty receptacles at each side of the frame may conveniently be identified
by the letters of the alphabet A to T the groups of figured slips being corre-
spondingly lettered at one or both ends upon both sides with letters of the
alphabet A to T indicating the receptacle in which they are to be stored so that
these figured slips may be kept in distinguishable groups. These initial letters at
both sides of one or both ends of the slips are written printed or painted in such a
position as to be concealed when the figures thereon are duly exhibited in the
frame to form part of an addition sum and serving only for arrangement as to the
combination in which they may form parts of a sum and as an index to find
the answer in an answers book in which the answers to various combinations of
these lines of sums are recorded or may be found by working some simple addition
or multiplication sum.
Each group of figured slips consists of five which as to four are lettered on one
side at one or both ends simply with the initial letter by which the group is
identified, and on the other side with the same initial letter with the numeral I
affixed thereto upon two of them and the same initial letter with the numeral 2
affixed thereto. upon the other two of them. The fifth slip in the set is lettered at

page_text: one or both ends upon one side with the same initial letter with the numeral 3
affixed thereto and upon the other side at one or both ends with the same initial
letter with the numeral 4 affixed thereto.
Thus a group of figured slips to be kept in the receptacle A will be figured at
both sides and lettered at one or both ends, of, one side as follows A A A A A³
being when reversed A¹ A1 A2 A2 A. The group of figured slips to be kept in
the receptacle B being lettered on one side B B BBB will, when reversed,
be B B B B B³ and the same system of numbering and lettering the figured
slips is pursued throughout the whole set of groups from A to T.
The figures upon the several slips of each group are arranged so that the
amounts represented are co-related thus the sum of the four lines of figures on
the four slips at the sides marked A. is equal to the sum of the figures on the two
slips at the sides marked A' or the two slips at the sides marked A and is also
equal to the figures on the one slip at the side marked A³; the figures on the
opposite side of this slip marked A are double the amount of those on the side A
and hence are equal to the sum of the figures on the four slips A' A¹ A² A² or
twice the sum of the figures on the four slips A A A A.
This co-relation between the amounts of the figures marked on the several slips
and on the two sides of the said slips facilitates the record of answers indexed in
an answers book which contains under the letter A the sum of four slips
marked A; under B the sum of four slips marked B and so on according to the
number of groups employed. In the case of a frame for twenty groups as herein-
before described the index letters proceed to the twentieth letter of the alphabet
giving the sums of each of the four slips of groups A to T exhibited at the sides
marked A to T only. If the slips be reversed they must be employed in a
restricted order, thus if one slip A' be selected so must the other, slip A' be
employed because the sum of these two being equal to the sum of the four slips at
the side marked A the initial A in the answers book indicates the sum of the two
slips A. So if the slip A be selected, the other slip A² must be employed also
because if either of these slips were alone selected the advantage of the co-relation
between their sums and that of their other sides would be lost. The second part
of the answers book gives the sums of the combined groups A B to A T; the third
part, the sums of the combined groups BC to BT; the fourth part, the sums of
the combined groups CD to CT and so on, the eighteenth part being RS to RT
and the nineteenth part ST. The twentieth part gives the sums.of combinations
of three groups A B C to ABT then ACD to ACT; ADE to ADT;
AEF to AET. By this means a great number of answers are recorded under a
simple index and many others may be found by adding together two or more
answers or by multiplying an answer by a single figure. Thus if a sum be set
consisting of the four slips of each group A D L P the answer may be obtained by
adding together the answers found under the index AD and L P or A L and D P
or ADL and P or ALP and D.
When the slips are reversed exhibiting the sides marked by the initial letters
with the addition of a numeral it is necessary in some cases to exercise judgment in
obtaining the answer bearing in mind the effect of the co-relation of the amount
on each slip with the answers given in the book of answers under the initial or
combination of initials by which the slips employed are distinguished. For
example I give the following sums consisting of 67 and 8 lines made up from two
groups and indicate the mode of obtaining the answers by addition or multiplica-
tion of answers recorded in the answers book.
6 line sum
7 line sum
8 line sum
-
A A A A+B¹ B¹
A'A + A A² + B¹ B' + B³
AAAA+ A+B B + B³
Answer = A B record.
= 2 x A B record.
=2, x A.B,record.

page_text: answer A record multiplied by two and B₁ B¹, B' B³, B*; answer B record
multiplied by four.
I have shown in the drawings the frame made with the openings to the store
receptacles and the side openings uncovered but a cover or door may be provided
hinged at the front of the frame at the top and bottom the position for the upper
hinge being indicated at E in Figure 3. In this case the figured slips being of the
required length to reach to the outer extremity of the side openings C the closing
of the door justifies the alignement of the units in the pounds shillings and pence
columns.
Having now particularly described and ascertained the nature of my said
invention and in what manner the same is to be performed I declare that what
I claim is :-.
1. A frame for storing classified groups of figured slips to form part in a
variety of combinations for setting addition sums by exhibiting certain ones of the
slips at suitable openings in the frame substantially as described.
2. Figured slips figured in a manner to produce a series of co-relative answers
when employed in various combinations to form addition sums substantially as
described.
Dated this 30th day of November 1891.
AYRTON & THOMAS,
Agents for the Applicant.