Math 5375 Fall 2012
Constructing Whole Number and Operation
Problems appropriate for writing up in the two-problem paper.
Very strongly recommended to consult with the instructor prior to submission.
- Session 3: Models for multiplication -- use the questions on this
page to develop a cohesive, comparative explanation of the set and array models
for multiplication and the relationship between them.
- Session 5: Numeration Systems -- use the questions on this page to
develop a cohesive, comparative explanation of the Roman and Babylonian systems
in particular, and symbol value and place value systems in general.
- Session 5: Zeroes and Ones -- use the questions on this page as well
as the class discussion and responses to explain options for designing
numeration systems using only two meaningful characters (including true
binary), and compare their properties.
- Session 6: Sticks and Stones -- use the problems on this page to
develop a cohesive explanation of the Mayan system, including a comparative
analysis (relative to the Hindu-Arabic system).
- Session 7: Introduction to Bases -- use the summative questions at
the end of this activity to give clear sets of instructions for conversion to
base $n$ using concrete [proportional] and symbolic representations, and
compare the two. Of course, you may use some of the problems in this activity
as examples, but be sure your instructions are stated in purely general
- Sessions 8-14: Mayan addition and subtraction, Driving in
Septobasiland, Regrouping in Other Bases, Mayan multiplication, Making Groups
in Other Bases, Money in Septobasiland, Mayan division, Division in Other
Bases, Arithmetic in Other Bases -- Use any one of these activities as a basis
for developing a general explanation of the traditional algorithm for
performing any one of the four arithmetic operations (choose one!) in terms of
a general base (i.e., not ten). Be careful to couch your general set of
instructions in terms of a general base, and not any specific one (although of
course all your examples or illustrations will use particular bases).
- Session 15: Russian Peasant algorithm -- Although the two-problem
paper is due before Session 15, some participants may be interested in
analyzing this intriguing alternative algorithm for multiplication. Work
through the questions in the handout, and write a paper which (a) briefly
explains the steps in the algorithm, (b) explains mathematically why the
algorithm is correct, (c) describes the mathematical skills needed and not
needed, and (d) uses these to speculate why a person might prefer this
algorithm over the traditional (partial products) multidigit multiplication
Links to related sites
Links for specific class meetings
- Session 1
- Session 2
- Session 5
- Session 7
- Session 9
- Session 11
- Session 14
This page last modified August 24, 2012.