' 

REF ID:A70431 e 

.Patented Oct 6, 1931 1,826,034 

J~ J - ry 

..,_ 

' .. l l -.J: 

T 

I 

UNITED ST A TES PATENT OFFICE I 

ROBERT MARSHALL WILLIAMSON, OF BURLEY, RINGWOOD, ENGLAND l I 

DEVICE FOR TEACHING; ARITHMETIC 

) 

Appllcation filed March 27, 1929, Serial No 350,373, and in Great :Bntam March 28, 1928 

The present rnvent10n h'ls for it::. obJect to 

p1ovide a snnple and imp1oved deHce or appliance fo1 use rn teadnng antluuetu,., accordmg t-0 the <lecimal sy::.tcm of not it1011 by 

5 the method m wluch groups of numbered and 

p1efernbly coloured 1.ablet::i are a11 mge<l m 

columns accordmg to then nume11cal denommat10ns or sigmficances an<l &nnple a11thmct1cal p1ocesses carried out b) vaiyrng Lhe num10 lier of tabletf:i contarned m one or more of 

the columns 

An appliance m accoidance with tlus rnvent10n broadly compn::.es a plurality of rectangular frames 01 receive1::i conespondmg 

l > to ilifte1ent or<le1s of digits 01 different J..lO\\'-

ers of ten, each fi allle 01 recen er eithe1 of 

itself, or when restmg on a smtable supportmg smface, fo1mmg a t1ough-like structure 

'ldapted to accommodate n umber-sigmiymg 

20 tablets to the number of nme or a multiple of 

nme, and the plmaht:> of buch t.:LLlets bemg 

adapteu when placed m siud receptacles m 

any desired numbe1 to be grouped therem 

m column u fasluon "lnle exhibitmg them25 d1c'ltions \\hich drstmgmsh their numerical 

values 

Any number of such t1ough-hke receivers 

may be piovided, but preferably not less than 

three, with each subdivisible mtq two. or 

30 more, or with three sets of two 01 more not 

subdivisible, although m the sl1llplest form 

of the appliance two or t\rn sets of two may 

suffice Lower powers of ten as well as l11ghe1 powers thereof may also be dealt with 

35 Accordrng to one an angement 01 method 

of carryrng out the mvent10n1 a number of 

separate iectangnlar frame structmes or 

frames 0£ um£o1m su:e is provided, compr1smg preferably two or more sets of flames 

40 of identical pattern, there bemg two 01 more 

sinnlar :frames m each of the said sets, such 

frames bemg adapted to be ]U)..taposed on 'lny 

_smtable supportmg surface to form a complete appliance m which columns of tablets 

45 0£ drfferent denommat10ns C'lll be set up 

If deSJ.red, a carrier board or eqmvalent 

me'lllS may be pro' ided to support a plurality 

of the trough-hke tablet holdmg frames and 

to keep them together m the <lesired relation90 slup In any case the smface on which the 

frames rest may coru;titute the trough bottom on wluch the tablet& rest 01 alternatively each frame may have rts o"n boUorn member 01 members for the s'lid taLletr:, to rest on 

Tablets of a chfterenl clenommation for each 155 

set of frames are also p1 ovided 

In a mochfied au angement a rectangula1 

bo.:L1d 01 U'lbe m'ly be proHded with one or 

more nLs or ndge-:; parallel to a pair of oppor:,1te sides, so that parallel recesses or trough- 60 

like r eceptacleb, he1 emafte1 called ti oughs, 

are formed on e'lch side of the rib, or between 

e'lch pair of consecutn e ridges, each hough 

bemg adapteu to receive nme, or a multiple of 

nme numbe1erl t tblets and m the latter case 65 

Lung sub <ln rsible by 'l r:,mgle trnnsve1se partition 01 by a senes of ti ans' e1se partitions 

mt.o a plur d1t} of sections of equal length, 

each cone&pondmg ,1pp1ox1mately to the 

total length occupied L,; mne Lableis placed 70 

togethe1 m columnar fashion 

In eithe1 a1 r angement the d1stmci sets of 

tablets allocate<l to ih_e r:,everal sets of frames 01 boughs may, mste.:Lu of or m addition to 

bearmg numbe1s of dr.ffuent orders or 115 

poweis 0£ ten, be distmctively marked or 

colom ed acco1 drng to the particular set of 

frames or boughs wluch they are mtended 

norm 111) to occupy Thus, for mstance, the 

colommg, "hether of the surface as a whole 80 

01 of the numLeung figures may be ahke m 

the case of all t..tbleb mtended to be placed 

m any one pa1 ticular set of fr a mes or troughs 

but may differ m respect of d1ffeient sets 0£ 

fr am es or troughs 85 

Each tablet fo1 mser tion m one set of 

frames or troughs may be numbered 1, m 

another 10, 'lnd for others l11ghe1 powers of 

10 01 lower powers, such as 1, 01 

At one side or both sides of each frame or oo 

of each of the t\\ o or more sections of each 

trough a scale m'ly be 'lrranged beaung the 

figmes 9, 8, 7 1, m descendmg order so 

as to rndicate the number of tablets present 

m the frame 01 hough sect10n when tablets 95 

ue phccd m column"> touchmg each othe1 

sta1 tmg from the end of the f1 ame or ti oughsect1on whe1e the numbe1 1 appears 

In the accompanymg dr'lwmgs wluch illustrate p1act1cal embodiments of the mvent10n, l.AJ 
e REF ID:A70431 e 

ar I'='"~ -. 

2 "' ' ..... ~ 1,826,034 

Fig 1 rs a per c:pectn e view of a smgle w1ll be obv10us however that lugher or iower 

frame element with hbk1.s therem powPrc; of ten may be md1cateu, usmg either 

Fig 2 rs a phn uew of an 'lppfrrnce com- the same set 0£ troughs or a d1:flerent set, the 

pnsmg three sets of two fr 'lmes, each set of htter bemg prefer'lble if a uiffeient distmc5 frumes liemg used with t lblets of d1fl'e1ent tn e colourmg is 'lllOc'lted to every d1ffe1ent 70 

~ !' 

• 

denommat].ons An opt10nal supportmg hay power of ten -

for the se,e11l1 trames IS mc1uded 111 tlus IJlhe iablets fil!llmg 111tb Slitd l"eC61VCIS 1Il t 

hgme F10" 3 is ~a sechott'll view taken dh cbiuntn ar'tdngem~nt to a tnn~11rltJ.fn •d'f. nme 

the lme nf-III of Fig 2 and mclu<lmg a !U'e col01ed coirespondm1:7ly to the recen ers 

10 section th1 ough a co' er 01 hd for the ha,y to which they are related. or mtendecl to be 75 

a£o1es'licl, such cove1 bemg also aaapted to p1aced 1ney m'ly'be d1stmctnely c.olomed 

sen e as a receptacle or "bnn1.' for -spare on foe1r re' orse, as \\ell as on their ob' e1 sc 

tablets when the apphance rs bemg used surfaces 'lnrl the colourmg, or numbeung, 

Refenmg fir:::it'to Fig 1, the teforeM~ ehllt'- if an~, may be th~ 'Sllthe on both surfaces 01 

1;; 'lcter a <le:::i1gn'lies a rectangular fIJ.me, con- may d1ffe1 'ls be1.N;een the ti\ o Thus, for so 

sr1 ucted from ahy st1Itable n1ater1•11 such, fdr ihshnce, a h'blt:'t wlnt!h tnfuctltes a h1ghe1 

iilShnce, 'l& IilC't ll, wood or c'l.rtlbdatcl and b p01' er of t~n bn dtle face ffitl.) be 'uBed 'for 

'l rnfrhlJe1 of li'ke d1g1t-md1c'lt:lng tdblef.s ind1cnt10n of 'l lo\\ el po''" e1 df ~n on the 1l}p-

,l,111ch .i.re clthpied to nt mto the a pct tute a 1 poslte face, if desired, l:tntl the two 1:haes may 2,0 b'f thL ti ough 'In the c 'l:::ie Illu:::iiIJ.ted, e•1ch actbrdmgly be of different colours il5 

hbl~i be us 'l nnmbe1 md1c'ltmg Its nutnet1- Th1, film is1on d:f 'l cat1'1e'.t ':frl1me or dis 

c'll 1:,1gmhc111ce 'lnd it is to be ass11tnC'd 'that pluy board, :::iUch as c to hol<l a ljlurnhr) uf 

a11 the ttbleb uc:ed 1Il one fr'lm~ (or set of flames Ih ptder,ibly pat'l:Ilel ielat1on:!h1p 1"3 

fr,ime", a& he1 em'lfiu refu1ed to) at tlhy opi1tln'll When .Pt av1<lel:l lt lli!IJ' hdltl ~he 

'~;, tune i\1il Jia,e t11e S'llne numerical sigmfi- f:r.imes bi &el:s bf Ii 1nres "fl the samellevtl or ttl 

C<i:Me If such J. fr une b1:, laid d11 a fiat sttr- on d1fle1ent le\ els, acco1dmg to the1flenon11n•1 

'face (fo1 msta11ce, 011 a t,1ble') a shallow t1dns trf the t lbleb'to be cotit..un~t:l'i11lthe 5e' - frough is formed, the t'lbleb resting on the cl tl troughs 

table 'lnd bemg held 111 colutnn·u f lSluon by 'I'he tle' ke of the present nn·~11t1011, us a-e ~~ fhe sud fr 'lmc a 1f desm~d, a bottom mem- scdbetl, r:mJudes l:Ile'1ns for 'tcudnng the •'J[ 

bL'1 a"' niay be attached to the fr 'line am such s1gnificrrhce df the figur'es 'tlnl:l chg1b rn com- 1~ rnnh 1.., 'to su12po1 t lhe t lblcis eY"en When lllbh use by 'ltl'ung1ng tablets 111 cdlumn.:tr 

'the SlI UCtme JS hfteLl f1om the table Or Other faJlUOil 'ag'amSt the ~ale ih 'tb;f ~Ch(ln df 

:Snp.._PoHmg surhce, but tins ts not necesS'lfy, trough 'It also permits of rrdi:Ht1ons, e1ib 

85 Aespec1alh if the fidme'ha:::i t b1ckmg us ttrn- t:r,1ctrnns 'l'.nd E-Imple p1ocesses of mult11JlWl itoo 

er all.) p1efu1 eel Mo1 ea' e:r the p·u ts a aha tfon 'l11tl dn is1on berng 'c lrt1ed out \Vith coi1-

a'2 -ml.) be JllJ.de mteg1 ally fl 0111 Ohe solid Ct:ete ObJeCts ( tluit IS to say, With the t H:llet~) 

'hlock of m 1teu 1l, m wluch c tSe d1 111ust be m ~tt~h 'l 'vttS as to com ey i111press1t:H1:::i'to1the. 

iqf'l1clcd ts Lle-.1gn 1hhg t re~~ss d.the't th m pnJ!il\ 1111nU through the visuul sense, 1tlrns 40 1n ove"'l1 tpei'tme 'Although otily a ol1'lllow teachh112: the ptm'c1ples of .11itllmetH, by ~on- '10'i tiou~11 is illu-.tdh.J it may 0Lv10usly Le <J..f c1ete me'lns 'llld mtroclucrng the pu1)1l Ly 

-an.) des11eL1 depth m ptoportitlh to it:::i width conc:r~te illustratwn 1to the nor'!b.'11 iceluuc 1

lmt p1 deidLl v ib <lepth h the s'lme -is the of '.r'ecor<lrng ~r1tl11netlc'll calcul'attons 111 fig- Hucl~ness of lhe tablets b As sht>wn in Utes ntctrtlfmg 1

to the Uec1mal sy'Ste11 or 

J45 UF1g 1 the -l'1 une is p10v1ckd 'llong ~ne edge not lhon '111 111 su~h 1pplt m~ec; ft, :t;, d1:,- 1110 

a8 with the figmL:::i !), 8, 'j 11, 'lirlilg'efi fn Sll tble tb ptOHde l St<:lr lg'e (01, "lS lt mUy 

Ue..,ce~1J1n~ orLler so ,1s to indicate the 1rnn1- c1:n'n E!nre1Hly be te:r111eH, -i' b,1nt'~) for talJWs 

}Jer of tablets g1ouped togethe1 at 'lny'tune, tempot'atlly ot1t of u~e, suJh a ~tore being 

m the sa1CI fI 'lme, the left h'lntl end of \vlnch e~ceedmgly usMul £o1 rnstunee •111 lfotnoil- -~o 1s of comse, 'lssumecl 1.o be the botrntn end d£ stl"atmg the rtl'ithmehtal 'J?'.l:o'Ce~es ih \vluch 115 

'the columns of hUlels ien'tablet:::i ii1 orn!tiough fat, e'tdbe Cx'.changed 

Fig 2showsacompleiete1cl11ngapphance fo1 one'tatliet m'fh1, next trnugh to Ure ldi 

built up by 'lr1''lngm~ on any' snit.i.ble surhC'e or vice ve'.t!;'l, fhose tbm11g "lsstHne<l to 'be di 

(it lll'lY be on l bO'll Cl 01 ti ay c) a plm 1hty df -equnl 'al'ue tinder the dech:nal srstelll of l\0-

' 55 trough-hke receIVers or frJ.111_es_a m sets of !._Jt10n In the deHte of th'e p1esent unen- '120 

'two or more, e'lch set phced m colutnna1 rtion iany c5tl'(-effientfonn df1tal.Het rec~pmek 1

f tsh10n 'Each c;et represent:::, 'l d1fl'e1ent or- (pn!fetably':futn1:shed \\lth1 t1oughs) rn<ty be 

aer 0£ cbgits or chire1ent PO\\ er of fon, t:ltilet':> 'lS'$t:>d'ated with the I Hev1C'e 'heremabove dechshnctn ely numbered, or d1stmctively col- scribed' but I prefer to nsel'for tins' purpose~ ~GO 0Uled1 Or 1

both, bemg plOHcled 1fot each set fl lt b't h6llow lid t'.)1 COH~l' d 'l1'rran~etl io pel'- f25 

6£ £rumes for use the1e1h m 'lny des1reU nnm 1fotm th{, du.il funettons df p'.Ioteebngrtlm rtp- Lu T1oughs icpresentmg lntnclreds, tern phun~e ·~heh nM in u~e al\d M prov1tl1ng ia 

'lnd unit::. are heu~ sho\\n remov'lhl:y 'lt1 H'lgetl 't.lblet "batik') when lhe 11r1thmefacal pwt".e:::i~'l!s 

side by srde and encl to end in the 1ecess nr•e1being de:mon~t1ated 1Ribs or pJrtl.t\~ns 

35 ~paces Of the recta'ngular bJ.se member c 'It are'insel'iethn tlus W'Ver to1fo1m•tbe <lesz1'ed '130 
) 

j 

r 

REF ID:A70431 

1,826,034 

lablet holding troughs f1om which tablets of 

any desired denommat10n may be d1awn as 

required and to will.ch such tablets may be 

returned when not ID use ID the display 

5 troughs a 

\Vliut I claim is - 1 An arithmetical teachmg device, comprismg a rechngular base member, a plurality 

of t10ugh-like recerve1s removably arranged 

10 side by s1Je 'lnd end to end thereon m iecess 

spaces, smJ receivers bemg identifiable each 

from the othe1s by different colormg and mchc1'l of different powe1s 01 multiples of 10 

'lnd each havmg the figures 9 to 1 applied 

15 m descendmg 01 der from top to bottom along 

one n1'l1gm, a plurality of sets 0£ separate 

digit bearmg t tblets, e'lch of said sets bea1-

mg numeucal denommabons d1:1Ie11ng from 

the others and fittmg m column ariangement. 

20 "\"\Iilun S'lid receivers to a maxmrnm of rune 

'lnd each of said sets bemg col01ed correspondmgly to the receiver to "'luch rt is related by the' alue of the <lrgits borne thereby 

2 An anthmetical teachmg device, com25 prismg 't flat base member m the form of 'l. 

p1ctme frame subdrv1ded by part1t1onmg 

m1.o 1ect'lngula1 spaces, 'l phuahty of flat 

flame hl~e receivers fitted 1emovably w1thm 

the subd1v1ded i:.paces of said member m a 

30 side by side relation, said receivers hem~ chstrngmshed e'lch fiom the othe1s by different 

colors and by applied md1cia of d1fterent 

powers or multiples 0£ 10 and each also havmg the figures 1 to 9 applied thereto ID as35 cendmg order fiom bottom to top along one 

edge or m'lrgm, a plurality of sets of sep-

'lI 'lte tableti:. Lea11ng mdicia of digit valuation with 'lll m e'lch set denommated alike 

and each set thereof bemg of a d1:ffe1ent 

10 nume11c'll valn'ltion coirespondmg to themchci 'l on the se\ e1 'll I ecei vers, said sets of 

t,tLlets fittmg m column a11angement w1thm 

thur designated receivers to a rn't:i..1mum of 

nme rn each and each set bemg colored cor45 respondmgly to its mtended receiver 

Signed at Burley, Rmgwood, Ihnts, England, this eleventh day of March, 1929 

ROBERT MARSHALL WILLIAMSON 

50 

55 

C.0 

3 
Oct 6, 1931 

c 

• 

R M WILLIAMSON 

DEVICE FOR TEACHING ARITHMETIC 

Filed March 27 1929 

Fig2 

d--.__ F1g3 

1,826,034 

c~~~c (! (/ /NVENTOR 

BY~~~ 

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/1TTORNeYJ"