Water machine puzzle & representative solutions
Puzzle
Solve the following problem and remember your thought processes.
Bobbiy wanted to make a water machine. The diagram below shows how s/he took a container, put four holes in the side, a funnel on top, and connected a pipe to the funnel. Bobbiy wants to connect plastic tubes from the pipe to the holes so when water is poured into the funnel it will or won't come out of none, some, or all of the holes. Bobbiy wants to know all of the possible combinations that could be made before deciding.
What are they?
Representative solutions from actual studies of middle level students
Chris
A, D
Fiona
A, B, C, D
Fran
A, B, C, D, AB, AC, BC, BC, CD, AD
Dee
ABCD, BCDA, CDAB, DABC,
AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB, DC
ABC, ABD, ACD, BAC, BCD, BDA, CDA, CAB, CBD, DAB, DBC, DCA
Trav
ABCD, AB, AC, ABD, ABD, BC, BD, CD
Joe
ABCD, ABC, AB, A, BCD, BC, B, CD, C, D
Sara
AB, AC, AD, BC, BD, CD
Daniella
ABCD, ABC, ABD, AB, A
BCD, BC, BD, B
CD, C
D
ACD, AD, AC
None
Barbie
AB, AC, AD, ABC, ABD, ACD, BC, BD, CD, ABCD
Chou
AB, AC, AD, BC, BD, CD,
ABC, ABD, ACD, BCD, ABCD
A, B, C, D
Daniella:
A, B, C, D, ABCD,
AB, AC, AD, BC, BD, CD,
ABC, ABD, ACD, BCD, None
Educator Activity
How would you classify the different solution sets as preoperational, concrete operational, or formal operational? Or any other categorization that would be beneficial for facilitating learning.