Fingers and Hands
[We're counting thumbs as fingers!]
Ordering the pictures by the number of people we would have $30,
40, 50, 60, 70$ fingers.
Pupils may have counted/calculated these in many different
ways.
The first picture many have resulted in things like;
pupils saying "$5,10,15,20,25,30$",
counting hands $1,2,3,4,5,6$ and $6$ lots of $5$ make $30$,
counting pairs of hands as representing each person $1,2,3$ ten
$3$'s are $30$,
counting each finger
$1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30$.
saying there are $4,8,12,16,20,24$ fingers and $1,2,3,4,5,6$
thumbs, so $24+6=30$.
Some pupils will nearly alway count in twos so we'd have
$2,4,6,8,10,12,14,16,18,20,22,24,26,28,30$
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Moving onto those pupils who have a go at Alien Counting and then
returning to this challenge we could have things like this
occuring;
"To keep the same number of 'fingers' in each picture we could
have
$5$ Threebees or $3$ Chindis to make up picture $1$
$10$ Dobus, $10$ Quorts or $4$ Chidis to make up picture $2$
$5$ Chindis to make up picture $3$
$15$ Dobus, $10$ Threebees, $6$ Chindis or $5$ Sendas to make up
picture $4$
and just $7$ Chindis to make picture $5$."
"If we keep the number of human/aliens the same for each picture we
could have the following totals for pictures;
picture $1$ --- $12$, $18$, $24$, $30$, $36$
picture $2$ --- $16$, $24$, $32$, $40$, $48$
picture $3$ --- $20$, $30$, $40$, $50$, $60$
picture $4$ --- $24$, $36$, $48$, $60$, $72$
picture $5$ --- $28$, $42$, $56$, $70$, $84$"
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[Also - What numbers would the aliens say for all of the above,
since they do not count in tens.
So for example $28$ in human counting, it would be for;
Dubo $11100$ [one $2x2x2x2$, one $2x2x2$, one $2x2$, no $2$'s and
no units]
Threebee $1001$ [one $3x3x3$, no $3x3$, no $3$'s and one
unit]
Quort $130$ [one $4x4$, three $4$'s and no units]
Chindi $103$ [one $5x5$, no $5$'s and three units]
Senda $44$ [ four $6$'s and $4$ units]
What if different aliens were having to make up some of the
pictures? Using the same number of aliens as humans did in the
beginning.
For example we need $3$ different Aliens for the first picture.
]
"If those numbers were given in the ways that the aliens count we
would have;
Picture $1$ -- $1100, 200, 120, 110, 100$
Picture $2$ -- $10000, 220, 200, 130, 120$
Picture $3$ -- $10100, 1010, 220, 200, 140$
Picture $4$ -- $11000, 1100, 300, 220, 200$
Picture $5$ -- $11100, 1120, 320, 240, 220$
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For different Aliens making up
pictures $1, 2, 3$
We could have for picture $1$;
Dubo, Threebee, Quort
Dubo, Threebee, Chindi
Dubo, Threebee, Senda
Threebee, Quort, Chindi
Threebee, Quort, Senda
Quort, Chindi, Senda
We could have for picture $2$
Dubo, Threebee, Quort, Chindi
Dubo, Threebee, Quort, Senda
Dubo, Threebee, Chindi, Senda
Dubo, Quort, Chindi, Senda,
Threebee, Quort, Chidi, Senda
And for picture $3$
All $5$ of them.