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GRED 505 (Topics in mathematics for elementary teachers)
Assignment 3: Numbers and operations in different bases
Vygotsky rightly points out that as long as one operates only with the
decimal system without being aware of the other bases, one has not
mastered the system; rather one is bound by it. When one learns other
bases, one can consciously choose one’s system and thus a new level of
conceptual control is achieved.
Berg, E. E. (1970). L. S. Vygotsky’s theory of the social
and historical origins of consciousness. (Dissertation).
Part 1. Addition
Task 1. Represent base-ten number 13 (one ten and three ones) as the sum of two
other base-ten numbers in all possible ways (without regard to order). How many
different representations are there? Use manipulatives as thinking tools. Draw
pictures of all your representations.
Task 2. Represent base-nine number 13 (one nine and three ones) as the sum of
two other base-nine numbers in all possible ways (without regard to order). How
many different representations are there? Use manipulatives as thinking tools.
Draw pictures of all your representations.
Task 3. Represent base-eight number 13 (one eight and three ones) as the sum of
two other base-eight numbers in all possible ways (without regard to order). How
many different representations are there? Use manipulatives as thinking tools.
Draw pictures of all your representations.
Task 4. Represent base-seven number 13 (one seven and three ones) as the sum
of two other base-seven numbers in all possible ways (without regard to order).
How many different representations are there? Use manipulatives as thinking
tools. Draw pictures of all your representations.
Instructor Sergei Abramovich
